id	sid	tid	token	lemma	pos
ajis02-1563	1	1	paper	paper	NOUN
ajis02-1563	1	2	title	title	NOUN
ajis02-1563	1	3	(	(	PUNCT
ajis02-1563	1	4	paper	paper	NOUN
ajis02-1563	1	5	title	title	NOUN
ajis02-1563	1	6	style	style	NOUN
ajis02-1563	1	7	)	)	PUNCT
ajis02-1563	1	8	australasian	australasian	ADJ
ajis02-1563	1	9	journal	journal	NOUN
ajis02-1563	1	10	of	of	ADP
ajis02-1563	1	11	information	information	NOUN
ajis02-1563	1	12	systems	system	NOUN
ajis02-1563	1	13	ahmad	ahmad	PROPN
ajis02-1563	1	14	,	,	PUNCT
ajis02-1563	1	15	traiq	traiq	NOUN
ajis02-1563	1	16	,	,	PUNCT
ajis02-1563	1	17	shabbir	shabbir	PROPN
ajis02-1563	1	18	&	&	CCONJ
ajis02-1563	1	19	khan	khan	PROPN
ajis02-1563	1	20	2017	2017	NUM
ajis02-1563	1	21	,	,	PUNCT
ajis02-1563	1	22	vol	vol	NOUN
ajis02-1563	1	23	21	21	NUM
ajis02-1563	1	24	,	,	PUNCT
ajis02-1563	1	25	selected	select	VERB
ajis02-1563	1	26	papers	paper	NOUN
ajis02-1563	1	27	from	from	ADP
ajis02-1563	1	28	ausdm	ausdm	NOUN
ajis02-1563	1	29	spectral	spectral	ADJ
ajis02-1563	1	30	methods	method	NOUN
ajis02-1563	1	31	for	for	ADP
ajis02-1563	1	32	immunization	immunization	NOUN
ajis02-1563	1	33	of	of	ADP
ajis02-1563	1	34	large	large	ADJ
ajis02-1563	1	35	networks	network	NOUN
ajis02-1563	1	36	1	1	NUM
ajis02-1563	1	37	spectral	spectral	ADJ
ajis02-1563	1	38	methods	method	NOUN
ajis02-1563	1	39	for	for	ADP
ajis02-1563	1	40	immunization	immunization	NOUN
ajis02-1563	1	41	of	of	ADP
ajis02-1563	1	42	large	large	ADJ
ajis02-1563	1	43	networks	network	NOUN
ajis02-1563	1	44	muhammad	muhammad	PROPN
ajis02-1563	1	45	ahmad	ahmad	PROPN
ajis02-1563	1	46	department	department	PROPN
ajis02-1563	1	47	of	of	ADP
ajis02-1563	1	48	computer	computer	NOUN
ajis02-1563	1	49	science	science	NOUN
ajis02-1563	1	50	school	school	NOUN
ajis02-1563	1	51	of	of	ADP
ajis02-1563	1	52	science	science	NOUN
ajis02-1563	1	53	and	and	CCONJ
ajis02-1563	1	54	engineering	engineering	NOUN
ajis02-1563	1	55	lahore	lahore	PROPN
ajis02-1563	1	56	university	university	PROPN
ajis02-1563	1	57	of	of	ADP
ajis02-1563	1	58	management	management	PROPN
ajis02-1563	1	59	sciences	sciences	PROPN
ajis02-1563	1	60	pakistan	pakistan	PROPN
ajis02-1563	1	61	juvaria	juvaria	PROPN
ajis02-1563	1	62	tariq	tariq	PROPN
ajis02-1563	1	63	department	department	PROPN
ajis02-1563	1	64	of	of	ADP
ajis02-1563	1	65	computer	computer	NOUN
ajis02-1563	1	66	science	science	NOUN
ajis02-1563	1	67	school	school	NOUN
ajis02-1563	1	68	of	of	ADP
ajis02-1563	1	69	science	science	NOUN
ajis02-1563	1	70	and	and	CCONJ
ajis02-1563	1	71	engineering	engineering	NOUN
ajis02-1563	1	72	lahore	lahore	PROPN
ajis02-1563	1	73	university	university	PROPN
ajis02-1563	1	74	of	of	ADP
ajis02-1563	1	75	management	management	PROPN
ajis02-1563	1	76	sciences	sciences	PROPN
ajis02-1563	1	77	pakistan	pakistan	PROPN
ajis02-1563	1	78	mudassir	mudassir	PROPN
ajis02-1563	1	79	shabbir	shabbir	PROPN
ajis02-1563	1	80	department	department	PROPN
ajis02-1563	1	81	of	of	ADP
ajis02-1563	1	82	computer	computer	NOUN
ajis02-1563	1	83	science	science	NOUN
ajis02-1563	1	84	information	information	PROPN
ajis02-1563	1	85	technology	technology	PROPN
ajis02-1563	1	86	university	university	PROPN
ajis02-1563	1	87	pakistan	pakistan	PROPN
ajis02-1563	1	88	imdadullah	imdadullah	PROPN
ajis02-1563	1	89	khan	khan	PROPN
ajis02-1563	1	90	department	department	PROPN
ajis02-1563	1	91	of	of	ADP
ajis02-1563	1	92	computer	computer	NOUN
ajis02-1563	1	93	science	science	NOUN
ajis02-1563	1	94	school	school	NOUN
ajis02-1563	1	95	of	of	ADP
ajis02-1563	1	96	science	science	NOUN
ajis02-1563	1	97	and	and	CCONJ
ajis02-1563	1	98	engineering	engineering	NOUN
ajis02-1563	1	99	lahore	lahore	PROPN
ajis02-1563	1	100	university	university	PROPN
ajis02-1563	1	101	of	of	ADP
ajis02-1563	1	102	management	management	PROPN
ajis02-1563	1	103	sciences	sciences	PROPN
ajis02-1563	1	104	pakistan	pakistan	PROPN
ajis02-1563	1	105	imdad.khan@lums.edu.pk	imdad.khan@lums.edu.pk	PROPN
ajis02-1563	1	106	abstract	abstract	ADV
ajis02-1563	1	107	given	give	VERB
ajis02-1563	1	108	a	a	DET
ajis02-1563	1	109	network	network	NOUN
ajis02-1563	1	110	of	of	ADP
ajis02-1563	1	111	nodes	node	NOUN
ajis02-1563	1	112	,	,	PUNCT
ajis02-1563	1	113	minimizing	minimize	VERB
ajis02-1563	1	114	the	the	DET
ajis02-1563	1	115	spread	spread	NOUN
ajis02-1563	1	116	of	of	ADP
ajis02-1563	1	117	a	a	DET
ajis02-1563	1	118	contagion	contagion	NOUN
ajis02-1563	1	119	using	use	VERB
ajis02-1563	1	120	a	a	DET
ajis02-1563	1	121	limited	limited	ADJ
ajis02-1563	1	122	budget	budget	NOUN
ajis02-1563	1	123	is	be	AUX
ajis02-1563	1	124	a	a	DET
ajis02-1563	1	125	well	well	ADV
ajis02-1563	1	126	-	-	PUNCT
ajis02-1563	1	127	studied	study	VERB
ajis02-1563	1	128	problem	problem	NOUN
ajis02-1563	1	129	with	with	ADP
ajis02-1563	1	130	applications	application	NOUN
ajis02-1563	1	131	in	in	ADP
ajis02-1563	1	132	network	network	NOUN
ajis02-1563	1	133	security	security	NOUN
ajis02-1563	1	134	,	,	PUNCT
ajis02-1563	1	135	viral	viral	ADJ
ajis02-1563	1	136	marketing	marketing	NOUN
ajis02-1563	1	137	,	,	PUNCT
ajis02-1563	1	138	social	social	ADJ
ajis02-1563	1	139	networks	network	NOUN
ajis02-1563	1	140	,	,	PUNCT
ajis02-1563	1	141	and	and	CCONJ
ajis02-1563	1	142	public	public	ADJ
ajis02-1563	1	143	health	health	NOUN
ajis02-1563	1	144	.	.	PUNCT
ajis02-1563	2	1	in	in	ADP
ajis02-1563	2	2	real	real	ADJ
ajis02-1563	2	3	graphs	graph	NOUN
ajis02-1563	2	4	,	,	PUNCT
ajis02-1563	2	5	virus	virus	NOUN
ajis02-1563	2	6	may	may	AUX
ajis02-1563	2	7	infect	infect	VERB
ajis02-1563	2	8	a	a	DET
ajis02-1563	2	9	node	node	NOUN
ajis02-1563	2	10	which	which	PRON
ajis02-1563	2	11	in	in	ADP
ajis02-1563	2	12	turn	turn	NOUN
ajis02-1563	2	13	infects	infect	VERB
ajis02-1563	2	14	its	its	PRON
ajis02-1563	2	15	neighbour	neighbour	ADJ
ajis02-1563	2	16	nodes	node	NOUN
ajis02-1563	2	17	and	and	CCONJ
ajis02-1563	2	18	this	this	PRON
ajis02-1563	2	19	may	may	AUX
ajis02-1563	2	20	trigger	trigger	VERB
ajis02-1563	2	21	an	an	DET
ajis02-1563	2	22	epidemic	epidemic	NOUN
ajis02-1563	2	23	in	in	ADP
ajis02-1563	2	24	the	the	DET
ajis02-1563	2	25	whole	whole	ADJ
ajis02-1563	2	26	graph	graph	NOUN
ajis02-1563	2	27	.	.	PUNCT
ajis02-1563	3	1	the	the	DET
ajis02-1563	3	2	goal	goal	NOUN
ajis02-1563	3	3	thus	thus	ADV
ajis02-1563	3	4	is	be	AUX
ajis02-1563	3	5	to	to	PART
ajis02-1563	3	6	select	select	VERB
ajis02-1563	3	7	the	the	DET
ajis02-1563	3	8	best	good	ADJ
ajis02-1563	3	9	k	k	X
ajis02-1563	3	10	nodes	node	NOUN
ajis02-1563	3	11	(	(	PUNCT
ajis02-1563	3	12	budget	budget	NOUN
ajis02-1563	3	13	constraint	constraint	NOUN
ajis02-1563	3	14	)	)	PUNCT
ajis02-1563	3	15	that	that	PRON
ajis02-1563	3	16	are	be	AUX
ajis02-1563	3	17	immunized	immunize	VERB
ajis02-1563	3	18	(	(	PUNCT
ajis02-1563	3	19	vaccinated	vaccinated	ADJ
ajis02-1563	3	20	,	,	PUNCT
ajis02-1563	3	21	screened	screen	VERB
ajis02-1563	3	22	,	,	PUNCT
ajis02-1563	3	23	filtered	filter	VERB
ajis02-1563	3	24	)	)	PUNCT
ajis02-1563	3	25	so	so	ADV
ajis02-1563	3	26	as	as	SCONJ
ajis02-1563	3	27	the	the	DET
ajis02-1563	3	28	remaining	remain	VERB
ajis02-1563	3	29	graph	graph	NOUN
ajis02-1563	3	30	is	be	AUX
ajis02-1563	3	31	less	less	ADV
ajis02-1563	3	32	prone	prone	ADJ
ajis02-1563	3	33	to	to	ADP
ajis02-1563	3	34	the	the	DET
ajis02-1563	3	35	epidemic	epidemic	NOUN
ajis02-1563	3	36	.	.	PUNCT
ajis02-1563	4	1	it	it	PRON
ajis02-1563	4	2	is	be	AUX
ajis02-1563	4	3	known	know	VERB
ajis02-1563	4	4	that	that	SCONJ
ajis02-1563	4	5	the	the	DET
ajis02-1563	4	6	problem	problem	NOUN
ajis02-1563	4	7	is	be	AUX
ajis02-1563	4	8	,	,	PUNCT
ajis02-1563	4	9	in	in	ADP
ajis02-1563	4	10	all	all	DET
ajis02-1563	4	11	practical	practical	ADJ
ajis02-1563	4	12	models	model	NOUN
ajis02-1563	4	13	,	,	PUNCT
ajis02-1563	4	14	computationally	computationally	ADV
ajis02-1563	4	15	intractable	intractable	ADJ
ajis02-1563	4	16	even	even	ADV
ajis02-1563	4	17	for	for	ADP
ajis02-1563	4	18	moderate	moderate	ADJ
ajis02-1563	4	19	sized	sized	ADJ
ajis02-1563	4	20	graphs	graph	NOUN
ajis02-1563	4	21	.	.	PUNCT
ajis02-1563	5	1	in	in	ADP
ajis02-1563	5	2	this	this	DET
ajis02-1563	5	3	paper	paper	NOUN
ajis02-1563	5	4	we	we	PRON
ajis02-1563	5	5	employ	employ	VERB
ajis02-1563	5	6	ideas	idea	NOUN
ajis02-1563	5	7	from	from	ADP
ajis02-1563	5	8	spectral	spectral	ADJ
ajis02-1563	5	9	graph	graph	NOUN
ajis02-1563	5	10	theory	theory	NOUN
ajis02-1563	5	11	to	to	PART
ajis02-1563	5	12	define	define	VERB
ajis02-1563	5	13	relevance	relevance	NOUN
ajis02-1563	5	14	and	and	CCONJ
ajis02-1563	5	15	importance	importance	NOUN
ajis02-1563	5	16	of	of	ADP
ajis02-1563	5	17	nodes	node	NOUN
ajis02-1563	5	18	.	.	PUNCT
ajis02-1563	6	1	using	use	VERB
ajis02-1563	6	2	novel	novel	ADJ
ajis02-1563	6	3	graph	graph	NOUN
ajis02-1563	6	4	theoretic	theoretic	ADJ
ajis02-1563	6	5	techniques	technique	NOUN
ajis02-1563	6	6	,	,	PUNCT
ajis02-1563	6	7	we	we	PRON
ajis02-1563	6	8	then	then	ADV
ajis02-1563	6	9	design	design	VERB
ajis02-1563	6	10	an	an	DET
ajis02-1563	6	11	efficient	efficient	ADJ
ajis02-1563	6	12	approximation	approximation	NOUN
ajis02-1563	6	13	algorithm	algorithm	NOUN
ajis02-1563	6	14	to	to	PART
ajis02-1563	6	15	immunize	immunize	VERB
ajis02-1563	6	16	the	the	DET
ajis02-1563	6	17	graph	graph	NOUN
ajis02-1563	6	18	.	.	PUNCT
ajis02-1563	7	1	theoretical	theoretical	ADJ
ajis02-1563	7	2	guarantees	guarantee	NOUN
ajis02-1563	7	3	on	on	ADP
ajis02-1563	7	4	the	the	DET
ajis02-1563	7	5	running	running	ADJ
ajis02-1563	7	6	time	time	NOUN
ajis02-1563	7	7	of	of	ADP
ajis02-1563	7	8	our	our	PRON
ajis02-1563	7	9	algorithm	algorithm	NOUN
ajis02-1563	7	10	show	show	VERB
ajis02-1563	7	11	that	that	SCONJ
ajis02-1563	7	12	it	it	PRON
ajis02-1563	7	13	is	be	AUX
ajis02-1563	7	14	more	more	ADV
ajis02-1563	7	15	efficient	efficient	ADJ
ajis02-1563	7	16	than	than	ADP
ajis02-1563	7	17	any	any	DET
ajis02-1563	7	18	other	other	ADJ
ajis02-1563	7	19	known	know	VERB
ajis02-1563	7	20	solution	solution	NOUN
ajis02-1563	7	21	in	in	ADP
ajis02-1563	7	22	the	the	DET
ajis02-1563	7	23	literature	literature	NOUN
ajis02-1563	7	24	.	.	PUNCT
ajis02-1563	8	1	we	we	PRON
ajis02-1563	8	2	test	test	VERB
ajis02-1563	8	3	the	the	DET
ajis02-1563	8	4	performance	performance	NOUN
ajis02-1563	8	5	of	of	ADP
ajis02-1563	8	6	our	our	PRON
ajis02-1563	8	7	algorithm	algorithm	NOUN
ajis02-1563	8	8	on	on	ADP
ajis02-1563	8	9	several	several	ADJ
ajis02-1563	8	10	real	real	ADJ
ajis02-1563	8	11	world	world	NOUN
ajis02-1563	8	12	graphs	graph	NOUN
ajis02-1563	8	13	.	.	PUNCT
ajis02-1563	9	1	experiments	experiment	NOUN
ajis02-1563	9	2	show	show	VERB
ajis02-1563	9	3	that	that	SCONJ
ajis02-1563	9	4	our	our	PRON
ajis02-1563	9	5	algorithm	algorithm	NOUN
ajis02-1563	9	6	scales	scale	VERB
ajis02-1563	9	7	well	well	ADV
ajis02-1563	9	8	for	for	ADP
ajis02-1563	9	9	large	large	ADJ
ajis02-1563	9	10	graphs	graph	NOUN
ajis02-1563	9	11	and	and	CCONJ
ajis02-1563	9	12	outperforms	outperform	VERB
ajis02-1563	9	13	state	state	NOUN
ajis02-1563	9	14	of	of	ADP
ajis02-1563	9	15	the	the	DET
ajis02-1563	9	16	art	art	NOUN
ajis02-1563	9	17	algorithms	algorithm	NOUN
ajis02-1563	9	18	both	both	PRON
ajis02-1563	9	19	in	in	ADP
ajis02-1563	9	20	quality	quality	NOUN
ajis02-1563	9	21	(	(	PUNCT
ajis02-1563	9	22	containment	containment	NOUN
ajis02-1563	9	23	of	of	ADP
ajis02-1563	9	24	epidemic	epidemic	NOUN
ajis02-1563	9	25	)	)	PUNCT
ajis02-1563	9	26	and	and	CCONJ
ajis02-1563	9	27	efficiency	efficiency	NOUN
ajis02-1563	9	28	(	(	PUNCT
ajis02-1563	9	29	runtime	runtime	NOUN
ajis02-1563	9	30	and	and	CCONJ
ajis02-1563	9	31	space	space	NOUN
ajis02-1563	9	32	complexity	complexity	NOUN
ajis02-1563	9	33	)	)	PUNCT
ajis02-1563	9	34	.	.	PUNCT
ajis02-1563	10	1	keywords	keyword	NOUN
ajis02-1563	10	2	:	:	PUNCT
ajis02-1563	10	3	graph	graph	NOUN
ajis02-1563	10	4	immunization	immunization	NOUN
ajis02-1563	10	5	;	;	PUNCT
ajis02-1563	10	6	eigendrop	eigendrop	PROPN
ajis02-1563	10	7	;	;	PUNCT
ajis02-1563	10	8	closed	close	VERB
ajis02-1563	10	9	walks	walk	VERB
ajis02-1563	10	10	1	1	NUM
ajis02-1563	10	11	introduction	introduction	NOUN
ajis02-1563	10	12	consider	consider	VERB
ajis02-1563	10	13	a	a	DET
ajis02-1563	10	14	large	large	ADJ
ajis02-1563	10	15	network	network	NOUN
ajis02-1563	10	16	of	of	ADP
ajis02-1563	10	17	hospitals	hospital	NOUN
ajis02-1563	10	18	distributed	distribute	VERB
ajis02-1563	10	19	,	,	PUNCT
ajis02-1563	10	20	geographically	geographically	ADV
ajis02-1563	10	21	,	,	PUNCT
ajis02-1563	10	22	over	over	ADP
ajis02-1563	10	23	a	a	DET
ajis02-1563	10	24	region	region	NOUN
ajis02-1563	10	25	.	.	PUNCT
ajis02-1563	11	1	due	due	ADP
ajis02-1563	11	2	to	to	ADP
ajis02-1563	11	3	presence	presence	NOUN
ajis02-1563	11	4	of	of	ADP
ajis02-1563	11	5	an	an	DET
ajis02-1563	11	6	active	active	ADJ
ajis02-1563	11	7	pathogen	pathogen	NOUN
ajis02-1563	11	8	,	,	PUNCT
ajis02-1563	11	9	there	there	PRON
ajis02-1563	11	10	is	be	VERB
ajis02-1563	11	11	a	a	DET
ajis02-1563	11	12	danger	danger	NOUN
ajis02-1563	11	13	of	of	ADP
ajis02-1563	11	14	pandemic	pandemic	ADJ
ajis02-1563	11	15	in	in	ADP
ajis02-1563	11	16	the	the	DET
ajis02-1563	11	17	region	region	NOUN
ajis02-1563	11	18	.	.	PUNCT
ajis02-1563	12	1	we	we	PRON
ajis02-1563	12	2	assume	assume	VERB
ajis02-1563	12	3	that	that	SCONJ
ajis02-1563	12	4	pathogen	pathogen	NOUN
ajis02-1563	12	5	can	can	AUX
ajis02-1563	12	6	easily	easily	ADV
ajis02-1563	12	7	travel	travel	VERB
ajis02-1563	12	8	between	between	ADP
ajis02-1563	12	9	linked	link	VERB
ajis02-1563	12	10	hospitals	hospital	NOUN
ajis02-1563	12	11	.	.	PUNCT
ajis02-1563	13	1	we	we	PRON
ajis02-1563	13	2	are	be	AUX
ajis02-1563	13	3	concerned	concerned	ADJ
ajis02-1563	13	4	with	with	ADP
ajis02-1563	13	5	keeping	keep	VERB
ajis02-1563	13	6	the	the	DET
ajis02-1563	13	7	maximum	maximum	NOUN
ajis02-1563	13	8	of	of	ADP
ajis02-1563	13	9	the	the	DET
ajis02-1563	13	10	hospital	hospital	NOUN
ajis02-1563	13	11	network	network	NOUN
ajis02-1563	13	12	clean	clean	ADJ
ajis02-1563	13	13	of	of	ADP
ajis02-1563	13	14	pandemic	pandemic	NOUN
ajis02-1563	13	15	.	.	PUNCT
ajis02-1563	14	1	based	base	VERB
ajis02-1563	14	2	on	on	ADP
ajis02-1563	14	3	their	their	PRON
ajis02-1563	14	4	geographic	geographic	ADJ
ajis02-1563	14	5	vicinity	vicinity	NOUN
ajis02-1563	14	6	(	(	PUNCT
ajis02-1563	14	7	or	or	CCONJ
ajis02-1563	14	8	some	some	DET
ajis02-1563	14	9	other	other	ADJ
ajis02-1563	14	10	criteria	criterion	NOUN
ajis02-1563	14	11	)	)	PUNCT
ajis02-1563	14	12	,	,	PUNCT
ajis02-1563	14	13	it	it	PRON
ajis02-1563	14	14	is	be	AUX
ajis02-1563	14	15	known	know	VERB
ajis02-1563	14	16	for	for	ADP
ajis02-1563	14	17	every	every	DET
ajis02-1563	14	18	pair	pair	NOUN
ajis02-1563	14	19	of	of	ADP
ajis02-1563	14	20	hospitals	hospital	NOUN
ajis02-1563	14	21	x	x	X
ajis02-1563	14	22	,	,	PUNCT
ajis02-1563	14	23	y	y	PROPN
ajis02-1563	14	24	whether	whether	SCONJ
ajis02-1563	14	25	contamination	contamination	NOUN
ajis02-1563	14	26	at	at	ADP
ajis02-1563	14	27	x	x	PROPN
ajis02-1563	14	28	forebodes	forebode	NOUN
ajis02-1563	14	29	certain	certain	ADJ
ajis02-1563	14	30	contamination	contamination	NOUN
ajis02-1563	14	31	at	at	ADP
ajis02-1563	14	32	y.	y.	PROPN
ajis02-1563	14	33	if	if	SCONJ
ajis02-1563	14	34	this	this	PRON
ajis02-1563	14	35	is	be	AUX
ajis02-1563	14	36	true	true	ADJ
ajis02-1563	14	37	about	about	ADP
ajis02-1563	14	38	some	some	DET
ajis02-1563	14	39	pair	pair	NOUN
ajis02-1563	14	40	of	of	ADP
ajis02-1563	14	41	hospitals	hospital	NOUN
ajis02-1563	14	42	x	x	X
ajis02-1563	14	43	,	,	PUNCT
ajis02-1563	14	44	y	y	PROPN
ajis02-1563	14	45	,	,	PUNCT
ajis02-1563	14	46	we	we	PRON
ajis02-1563	14	47	call	call	VERB
ajis02-1563	14	48	x	x	PUNCT
ajis02-1563	14	49	and	and	CCONJ
ajis02-1563	14	50	y	y	PROPN
ajis02-1563	14	51	as	as	ADV
ajis02-1563	14	52	linked	link	VERB
ajis02-1563	14	53	(	(	PUNCT
ajis02-1563	14	54	i.e.	i.e.	X
ajis02-1563	14	55	x	x	SYM
ajis02-1563	14	56	and	and	CCONJ
ajis02-1563	14	57	y	y	PROPN
ajis02-1563	14	58	is	be	AUX
ajis02-1563	14	59	an	an	DET
ajis02-1563	14	60	edge	edge	NOUN
ajis02-1563	14	61	in	in	ADP
ajis02-1563	14	62	the	the	DET
ajis02-1563	14	63	network	network	NOUN
ajis02-1563	14	64	graph	graph	NOUN
ajis02-1563	14	65	)	)	PUNCT
ajis02-1563	14	66	.	.	PUNCT
ajis02-1563	15	1	now	now	ADV
ajis02-1563	15	2	a	a	DET
ajis02-1563	15	3	team	team	NOUN
ajis02-1563	15	4	of	of	ADP
ajis02-1563	15	5	scientists	scientist	NOUN
ajis02-1563	15	6	have	have	AUX
ajis02-1563	15	7	developed	develop	VERB
ajis02-1563	15	8	a	a	DET
ajis02-1563	15	9	vaccine	vaccine	NOUN
ajis02-1563	15	10	for	for	ADP
ajis02-1563	15	11	the	the	DET
ajis02-1563	15	12	pathogen	pathogen	NOUN
ajis02-1563	15	13	.	.	PUNCT
ajis02-1563	16	1	unfortunately	unfortunately	ADV
ajis02-1563	16	2	,	,	PUNCT
ajis02-1563	16	3	due	due	ADP
ajis02-1563	16	4	to	to	PART
ajis02-1563	16	5	cost	cost	NOUN
ajis02-1563	16	6	or	or	CCONJ
ajis02-1563	16	7	production	production	NOUN
ajis02-1563	16	8	constraints	constraint	NOUN
ajis02-1563	16	9	the	the	DET
ajis02-1563	16	10	vaccine	vaccine	NOUN
ajis02-1563	16	11	is	be	AUX
ajis02-1563	16	12	only	only	ADV
ajis02-1563	16	13	available	available	ADJ
ajis02-1563	16	14	in	in	ADP
ajis02-1563	16	15	limited	limited	ADJ
ajis02-1563	16	16	quantity	quantity	NOUN
ajis02-1563	16	17	and	and	CCONJ
ajis02-1563	16	18	only	only	ADV
ajis02-1563	16	19	a	a	DET
ajis02-1563	16	20	small	small	ADJ
ajis02-1563	16	21	fraction	fraction	NOUN
ajis02-1563	16	22	of	of	ADP
ajis02-1563	16	23	hospitals	hospital	NOUN
ajis02-1563	16	24	can	can	AUX
ajis02-1563	16	25	receive	receive	VERB
ajis02-1563	16	26	it	it	PRON
ajis02-1563	16	27	.	.	PUNCT
ajis02-1563	17	1	it	it	PRON
ajis02-1563	17	2	is	be	AUX
ajis02-1563	17	3	assumed	assume	VERB
ajis02-1563	17	4	that	that	SCONJ
ajis02-1563	17	5	once	once	SCONJ
ajis02-1563	17	6	a	a	DET
ajis02-1563	17	7	hospital	hospital	NOUN
ajis02-1563	17	8	receives	receive	VERB
ajis02-1563	17	9	the	the	DET
ajis02-1563	17	10	vaccine	vaccine	NOUN
ajis02-1563	17	11	it	it	PRON
ajis02-1563	17	12	australasian	australasian	ADJ
ajis02-1563	17	13	journal	journal	NOUN
ajis02-1563	17	14	of	of	ADP
ajis02-1563	17	15	information	information	NOUN
ajis02-1563	17	16	systems	system	NOUN
ajis02-1563	17	17	ahmad	ahmad	PROPN
ajis02-1563	17	18	,	,	PUNCT
ajis02-1563	17	19	traiq	traiq	NOUN
ajis02-1563	17	20	,	,	PUNCT
ajis02-1563	17	21	shabbir	shabbir	PROPN
ajis02-1563	17	22	&	&	CCONJ
ajis02-1563	17	23	khan	khan	PROPN
ajis02-1563	17	24	2017	2017	NUM
ajis02-1563	17	25	,	,	PUNCT
ajis02-1563	17	26	vol	vol	NOUN
ajis02-1563	17	27	21	21	NUM
ajis02-1563	17	28	,	,	PUNCT
ajis02-1563	17	29	selected	select	VERB
ajis02-1563	17	30	papers	paper	NOUN
ajis02-1563	17	31	from	from	ADP
ajis02-1563	17	32	ausdm	ausdm	NOUN
ajis02-1563	17	33	spectral	spectral	ADJ
ajis02-1563	17	34	methods	method	NOUN
ajis02-1563	17	35	for	for	ADP
ajis02-1563	17	36	immunization	immunization	NOUN
ajis02-1563	17	37	of	of	ADP
ajis02-1563	17	38	large	large	ADJ
ajis02-1563	17	39	networks	network	NOUN
ajis02-1563	17	40	2	2	NUM
ajis02-1563	17	41	can	can	AUX
ajis02-1563	17	42	not	not	PART
ajis02-1563	17	43	be	be	AUX
ajis02-1563	17	44	contaminated	contaminate	VERB
ajis02-1563	17	45	nor	nor	CCONJ
ajis02-1563	17	46	can	can	AUX
ajis02-1563	17	47	it	it	PRON
ajis02-1563	17	48	contaminate	contaminate	VERB
ajis02-1563	17	49	any	any	DET
ajis02-1563	17	50	other	other	ADJ
ajis02-1563	17	51	hospital	hospital	NOUN
ajis02-1563	17	52	.	.	PUNCT
ajis02-1563	18	1	given	give	VERB
ajis02-1563	18	2	the	the	DET
ajis02-1563	18	3	scarcity	scarcity	NOUN
ajis02-1563	18	4	of	of	ADP
ajis02-1563	18	5	the	the	DET
ajis02-1563	18	6	vaccine	vaccine	NOUN
ajis02-1563	18	7	resource	resource	NOUN
ajis02-1563	18	8	it	it	PRON
ajis02-1563	18	9	is	be	AUX
ajis02-1563	18	10	a	a	DET
ajis02-1563	18	11	very	very	ADV
ajis02-1563	18	12	serious	serious	ADJ
ajis02-1563	18	13	question	question	NOUN
ajis02-1563	18	14	to	to	PART
ajis02-1563	18	15	ask	ask	VERB
ajis02-1563	18	16	whether	whether	SCONJ
ajis02-1563	18	17	a	a	DET
ajis02-1563	18	18	given	give	VERB
ajis02-1563	18	19	hospital	hospital	NOUN
ajis02-1563	18	20	should	should	AUX
ajis02-1563	18	21	or	or	CCONJ
ajis02-1563	18	22	should	should	AUX
ajis02-1563	18	23	not	not	PART
ajis02-1563	18	24	receive	receive	VERB
ajis02-1563	18	25	the	the	DET
ajis02-1563	18	26	vaccine	vaccine	NOUN
ajis02-1563	18	27	so	so	SCONJ
ajis02-1563	18	28	as	as	SCONJ
ajis02-1563	18	29	to	to	PART
ajis02-1563	18	30	minimize	minimize	VERB
ajis02-1563	18	31	the	the	DET
ajis02-1563	18	32	overall	overall	ADJ
ajis02-1563	18	33	spread	spread	NOUN
ajis02-1563	18	34	of	of	ADP
ajis02-1563	18	35	the	the	DET
ajis02-1563	18	36	pathogen	pathogen	NOUN
ajis02-1563	18	37	in	in	ADP
ajis02-1563	18	38	the	the	DET
ajis02-1563	18	39	region	region	NOUN
ajis02-1563	18	40	.	.	PUNCT
ajis02-1563	19	1	this	this	DET
ajis02-1563	19	2	question	question	NOUN
ajis02-1563	19	3	,	,	PUNCT
ajis02-1563	19	4	in	in	ADP
ajis02-1563	19	5	essence	essence	NOUN
ajis02-1563	19	6	,	,	PUNCT
ajis02-1563	19	7	is	be	AUX
ajis02-1563	19	8	the	the	DET
ajis02-1563	19	9	topic	topic	NOUN
ajis02-1563	19	10	of	of	ADP
ajis02-1563	19	11	this	this	DET
ajis02-1563	19	12	work	work	NOUN
ajis02-1563	19	13	,	,	PUNCT
ajis02-1563	19	14	which	which	PRON
ajis02-1563	19	15	appears	appear	VERB
ajis02-1563	19	16	in	in	ADP
ajis02-1563	19	17	various	various	ADJ
ajis02-1563	19	18	other	other	ADJ
ajis02-1563	19	19	scenarios	scenario	NOUN
ajis02-1563	19	20	.	.	PUNCT
ajis02-1563	20	1	an	an	DET
ajis02-1563	20	2	efficient	efficient	ADJ
ajis02-1563	20	3	solution	solution	NOUN
ajis02-1563	20	4	to	to	ADP
ajis02-1563	20	5	this	this	DET
ajis02-1563	20	6	problem	problem	NOUN
ajis02-1563	20	7	can	can	AUX
ajis02-1563	20	8	be	be	AUX
ajis02-1563	20	9	applied	apply	VERB
ajis02-1563	20	10	to	to	PART
ajis02-1563	20	11	diverse	diverse	ADJ
ajis02-1563	20	12	array	array	NOUN
ajis02-1563	20	13	of	of	ADP
ajis02-1563	20	14	high	high	ADJ
ajis02-1563	20	15	-	-	PUNCT
ajis02-1563	20	16	impact	impact	NOUN
ajis02-1563	20	17	applications	application	NOUN
ajis02-1563	20	18	in	in	ADP
ajis02-1563	20	19	public	public	ADJ
ajis02-1563	20	20	health	health	NOUN
ajis02-1563	20	21	.	.	PUNCT
ajis02-1563	21	1	it	it	PRON
ajis02-1563	21	2	will	will	AUX
ajis02-1563	21	3	also	also	ADV
ajis02-1563	21	4	be	be	AUX
ajis02-1563	21	5	an	an	DET
ajis02-1563	21	6	important	important	ADJ
ajis02-1563	21	7	tool	tool	NOUN
ajis02-1563	21	8	in	in	ADP
ajis02-1563	21	9	cyber	cyber	NOUN
ajis02-1563	21	10	-	-	PUNCT
ajis02-1563	21	11	security	security	NOUN
ajis02-1563	21	12	solutions	solution	NOUN
ajis02-1563	21	13	.	.	PUNCT
ajis02-1563	22	1	finding	find	VERB
ajis02-1563	22	2	important	important	ADJ
ajis02-1563	22	3	players	player	NOUN
ajis02-1563	22	4	in	in	ADP
ajis02-1563	22	5	social	social	ADJ
ajis02-1563	22	6	networks	network	NOUN
ajis02-1563	22	7	is	be	AUX
ajis02-1563	22	8	a	a	DET
ajis02-1563	22	9	fundamental	fundamental	ADJ
ajis02-1563	22	10	problem	problem	NOUN
ajis02-1563	22	11	in	in	ADP
ajis02-1563	22	12	viral	viral	ADJ
ajis02-1563	22	13	marketing	marketing	NOUN
ajis02-1563	22	14	,	,	PUNCT
ajis02-1563	22	15	online	online	ADJ
ajis02-1563	22	16	advertisement	advertisement	NOUN
ajis02-1563	22	17	and	and	CCONJ
ajis02-1563	22	18	social	social	ADJ
ajis02-1563	22	19	networks	network	NOUN
ajis02-1563	22	20	monitoring	monitoring	NOUN
ajis02-1563	22	21	.	.	PUNCT
ajis02-1563	23	1	in	in	ADP
ajis02-1563	23	2	its	its	PRON
ajis02-1563	23	3	essence	essence	NOUN
ajis02-1563	23	4	,	,	PUNCT
ajis02-1563	23	5	the	the	DET
ajis02-1563	23	6	problem	problem	NOUN
ajis02-1563	23	7	of	of	ADP
ajis02-1563	23	8	finding	find	VERB
ajis02-1563	23	9	important	important	ADJ
ajis02-1563	23	10	nodes	node	NOUN
ajis02-1563	23	11	in	in	ADP
ajis02-1563	23	12	a	a	DET
ajis02-1563	23	13	network	network	NOUN
ajis02-1563	23	14	can	can	AUX
ajis02-1563	23	15	be	be	AUX
ajis02-1563	23	16	reduced	reduce	VERB
ajis02-1563	23	17	to	to	ADP
ajis02-1563	23	18	the	the	DET
ajis02-1563	23	19	main	main	ADJ
ajis02-1563	23	20	problem	problem	NOUN
ajis02-1563	23	21	of	of	ADP
ajis02-1563	23	22	this	this	DET
ajis02-1563	23	23	paper	paper	NOUN
ajis02-1563	23	24	.	.	PUNCT
ajis02-1563	24	1	this	this	PRON
ajis02-1563	24	2	is	be	AUX
ajis02-1563	24	3	known	know	VERB
ajis02-1563	24	4	,	,	PUNCT
ajis02-1563	24	5	in	in	ADP
ajis02-1563	24	6	the	the	DET
ajis02-1563	24	7	literature	literature	NOUN
ajis02-1563	24	8	,	,	PUNCT
ajis02-1563	24	9	as	as	ADP
ajis02-1563	24	10	the	the	DET
ajis02-1563	24	11	network	network	NOUN
ajis02-1563	24	12	immunization	immunization	NOUN
ajis02-1563	24	13	problem	problem	NOUN
ajis02-1563	24	14	.	.	PUNCT
ajis02-1563	25	1	the	the	DET
ajis02-1563	25	2	problem	problem	NOUN
ajis02-1563	25	3	is	be	AUX
ajis02-1563	25	4	studied	study	VERB
ajis02-1563	25	5	in	in	ADP
ajis02-1563	25	6	terms	term	NOUN
ajis02-1563	25	7	of	of	ADP
ajis02-1563	25	8	graphs	graph	NOUN
ajis02-1563	25	9	where	where	SCONJ
ajis02-1563	25	10	each	each	DET
ajis02-1563	25	11	node	node	NOUN
ajis02-1563	25	12	represents	represent	VERB
ajis02-1563	25	13	a	a	DET
ajis02-1563	25	14	hospital	hospital	NOUN
ajis02-1563	25	15	(	(	PUNCT
ajis02-1563	25	16	or	or	CCONJ
ajis02-1563	25	17	any	any	DET
ajis02-1563	25	18	other	other	ADJ
ajis02-1563	25	19	resourcehungry	resourcehungry	ADJ
ajis02-1563	25	20	entity	entity	NOUN
ajis02-1563	25	21	)	)	PUNCT
ajis02-1563	25	22	and	and	CCONJ
ajis02-1563	25	23	an	an	DET
ajis02-1563	25	24	edge	edge	NOUN
ajis02-1563	25	25	between	between	ADP
ajis02-1563	25	26	a	a	DET
ajis02-1563	25	27	pair	pair	NOUN
ajis02-1563	25	28	of	of	ADP
ajis02-1563	25	29	nodes	node	NOUN
ajis02-1563	25	30	represents	represent	VERB
ajis02-1563	25	31	the	the	DET
ajis02-1563	25	32	link	link	NOUN
ajis02-1563	25	33	between	between	ADP
ajis02-1563	25	34	the	the	DET
ajis02-1563	25	35	pair	pair	NOUN
ajis02-1563	25	36	of	of	ADP
ajis02-1563	25	37	hospitals	hospital	NOUN
ajis02-1563	25	38	.	.	PUNCT
ajis02-1563	26	1	we	we	PRON
ajis02-1563	26	2	use	use	VERB
ajis02-1563	26	3	the	the	DET
ajis02-1563	26	4	susceptible−infected−susceptible	susceptible−infected−susceptible	ADJ
ajis02-1563	26	5	(	(	PUNCT
ajis02-1563	26	6	sis	sis	NOUN
ajis02-1563	26	7	)	)	PUNCT
ajis02-1563	26	8	model	model	NOUN
ajis02-1563	26	9	of	of	ADP
ajis02-1563	26	10	infection	infection	NOUN
ajis02-1563	26	11	spread	spread	VERB
ajis02-1563	26	12	in	in	ADP
ajis02-1563	26	13	the	the	DET
ajis02-1563	26	14	network	network	NOUN
ajis02-1563	26	15	that	that	PRON
ajis02-1563	26	16	is	be	AUX
ajis02-1563	26	17	detailed	detail	VERB
ajis02-1563	26	18	in	in	ADP
ajis02-1563	26	19	section	section	NOUN
ajis02-1563	26	20	3	3	NUM
ajis02-1563	26	21	.	.	PUNCT
ajis02-1563	27	1	as	as	ADP
ajis02-1563	27	2	in	in	ADP
ajis02-1563	27	3	(	(	PUNCT
ajis02-1563	27	4	chen	chen	PROPN
ajis02-1563	27	5	2016	2016	NUM
ajis02-1563	27	6	)	)	PUNCT
ajis02-1563	27	7	,	,	PUNCT
ajis02-1563	27	8	we	we	PRON
ajis02-1563	27	9	formulate	formulate	VERB
ajis02-1563	27	10	the	the	DET
ajis02-1563	27	11	problem	problem	NOUN
ajis02-1563	27	12	as	as	SCONJ
ajis02-1563	27	13	follows	follow	VERB
ajis02-1563	27	14	.	.	PUNCT
ajis02-1563	28	1	problem	problem	NOUN
ajis02-1563	28	2	1	1	NUM
ajis02-1563	28	3	:	:	PUNCT
ajis02-1563	28	4	given	give	VERB
ajis02-1563	28	5	a	a	DET
ajis02-1563	28	6	simple	simple	ADJ
ajis02-1563	28	7	undirected	undirected	ADJ
ajis02-1563	28	8	graph	graph	NOUN
ajis02-1563	28	9	g	g	PROPN
ajis02-1563	28	10	=	=	PUNCT
ajis02-1563	28	11	(	(	PUNCT
ajis02-1563	28	12	v	v	NOUN
ajis02-1563	28	13	,	,	PUNCT
ajis02-1563	28	14	e	e	NOUN
ajis02-1563	28	15	)	)	PUNCT
ajis02-1563	28	16	and	and	CCONJ
ajis02-1563	28	17	an	an	DET
ajis02-1563	28	18	integer	integer	NOUN
ajis02-1563	28	19	k	k	AUX
ajis02-1563	28	20	find	find	VERB
ajis02-1563	28	21	a	a	DET
ajis02-1563	28	22	set	set	NOUN
ajis02-1563	28	23	s	s	X
ajis02-1563	28	24	of	of	ADP
ajis02-1563	28	25	k	k	PROPN
ajis02-1563	28	26	nodes	node	NOUN
ajis02-1563	28	27	such	such	ADJ
ajis02-1563	28	28	that	that	SCONJ
ajis02-1563	28	29	if	if	SCONJ
ajis02-1563	28	30	we	we	PRON
ajis02-1563	28	31	“	"	PUNCT
ajis02-1563	28	32	immunize	immunize	VERB
ajis02-1563	28	33	”	"	PUNCT
ajis02-1563	28	34	s	s	PROPN
ajis02-1563	28	35	,	,	PUNCT
ajis02-1563	28	36	renders	render	VERB
ajis02-1563	28	37	g	g	NOUN
ajis02-1563	28	38	least	least	ADJ
ajis02-1563	28	39	“	"	PUNCT
ajis02-1563	28	40	vulnerable	vulnerable	ADJ
ajis02-1563	28	41	”	"	PUNCT
ajis02-1563	28	42	to	to	ADP
ajis02-1563	28	43	an	an	DET
ajis02-1563	28	44	attack	attack	NOUN
ajis02-1563	28	45	over	over	ADP
ajis02-1563	28	46	all	all	DET
ajis02-1563	28	47	choices	choice	NOUN
ajis02-1563	28	48	of	of	ADP
ajis02-1563	28	49	s.	s.	PROPN
ajis02-1563	28	50	clearly	clearly	ADV
ajis02-1563	28	51	,	,	PUNCT
ajis02-1563	28	52	the	the	DET
ajis02-1563	28	53	problem	problem	NOUN
ajis02-1563	28	54	is	be	AUX
ajis02-1563	28	55	ill	ill	ADV
ajis02-1563	28	56	-	-	PUNCT
ajis02-1563	28	57	defined	define	VERB
ajis02-1563	28	58	,	,	PUNCT
ajis02-1563	28	59	unless	unless	SCONJ
ajis02-1563	28	60	a	a	DET
ajis02-1563	28	61	precise	precise	ADJ
ajis02-1563	28	62	and	and	CCONJ
ajis02-1563	28	63	quantifiable	quantifiable	ADJ
ajis02-1563	28	64	definition	definition	NOUN
ajis02-1563	28	65	of	of	ADP
ajis02-1563	28	66	the	the	DET
ajis02-1563	28	67	vulnerability	vulnerability	NOUN
ajis02-1563	28	68	of	of	ADP
ajis02-1563	28	69	a	a	DET
ajis02-1563	28	70	network	network	NOUN
ajis02-1563	28	71	is	be	AUX
ajis02-1563	28	72	provided	provide	VERB
ajis02-1563	28	73	.	.	PUNCT
ajis02-1563	29	1	to	to	ADP
ajis02-1563	29	2	this	this	DET
ajis02-1563	29	3	end	end	NOUN
ajis02-1563	29	4	,	,	PUNCT
ajis02-1563	29	5	it	it	PRON
ajis02-1563	29	6	turns	turn	VERB
ajis02-1563	29	7	out	out	ADP
ajis02-1563	29	8	that	that	SCONJ
ajis02-1563	29	9	the	the	DET
ajis02-1563	29	10	largest	large	ADJ
ajis02-1563	29	11	eigenvalue	eigenvalue	NOUN
ajis02-1563	29	12	of	of	ADP
ajis02-1563	29	13	the	the	DET
ajis02-1563	29	14	adjacency	adjacency	NOUN
ajis02-1563	29	15	matrix	matrix	NOUN
ajis02-1563	29	16	of	of	ADP
ajis02-1563	29	17	the	the	DET
ajis02-1563	29	18	graph	graph	NOUN
ajis02-1563	29	19	is	be	AUX
ajis02-1563	29	20	a	a	DET
ajis02-1563	29	21	good	good	ADJ
ajis02-1563	29	22	measure	measure	NOUN
ajis02-1563	29	23	of	of	ADP
ajis02-1563	29	24	vulnerability	vulnerability	NOUN
ajis02-1563	29	25	of	of	ADP
ajis02-1563	29	26	the	the	DET
ajis02-1563	29	27	graph	graph	NOUN
ajis02-1563	29	28	(	(	PUNCT
ajis02-1563	29	29	chakrabarti	chakrabarti	PROPN
ajis02-1563	29	30	2008	2008	NUM
ajis02-1563	29	31	)	)	PUNCT
ajis02-1563	29	32	.	.	PUNCT
ajis02-1563	30	1	1.1	1.1	NUM
ajis02-1563	30	2	problem	problem	NOUN
ajis02-1563	30	3	formulation	formulation	NOUN
ajis02-1563	30	4	and	and	CCONJ
ajis02-1563	30	5	solution	solution	NOUN
ajis02-1563	30	6	approach	approach	NOUN
ajis02-1563	30	7	for	for	ADP
ajis02-1563	30	8	a	a	DET
ajis02-1563	30	9	simple	simple	ADJ
ajis02-1563	30	10	undirected	undirected	ADJ
ajis02-1563	30	11	graph	graph	NOUN
ajis02-1563	30	12	g=(v	g=(v	NOUN
ajis02-1563	30	13	,	,	PUNCT
ajis02-1563	30	14	e	e	NOUN
ajis02-1563	30	15	)	)	PUNCT
ajis02-1563	30	16	with	with	ADP
ajis02-1563	30	17	|v|=n	|v|=n	PROPN
ajis02-1563	30	18	and	and	CCONJ
ajis02-1563	30	19	|e|=m	|e|=m	NOUN
ajis02-1563	30	20	,	,	PUNCT
ajis02-1563	30	21	the	the	DET
ajis02-1563	30	22	adjacency	adjacency	NOUN
ajis02-1563	30	23	matrix	matrix	NOUN
ajis02-1563	30	24	ag	ag	PROPN
ajis02-1563	30	25	(	(	PUNCT
ajis02-1563	30	26	or	or	CCONJ
ajis02-1563	30	27	just	just	ADV
ajis02-1563	30	28	a	a	PRON
ajis02-1563	30	29	whenever	whenever	SCONJ
ajis02-1563	30	30	the	the	DET
ajis02-1563	30	31	graph	graph	NOUN
ajis02-1563	30	32	g	g	NOUN
ajis02-1563	30	33	is	be	AUX
ajis02-1563	30	34	clear	clear	ADJ
ajis02-1563	30	35	from	from	ADP
ajis02-1563	30	36	the	the	DET
ajis02-1563	30	37	context	context	NOUN
ajis02-1563	30	38	)	)	PUNCT
ajis02-1563	30	39	is	be	AUX
ajis02-1563	30	40	an	an	DET
ajis02-1563	30	41	n×n	n×n	PROPN
ajis02-1563	30	42	binary	binary	ADJ
ajis02-1563	30	43	matrix	matrix	NOUN
ajis02-1563	30	44	with	with	ADP
ajis02-1563	30	45	columns	column	NOUN
ajis02-1563	30	46	and	and	CCONJ
ajis02-1563	30	47	rows	row	NOUN
ajis02-1563	30	48	representing	represent	VERB
ajis02-1563	30	49	the	the	DET
ajis02-1563	30	50	vertices	vertex	NOUN
ajis02-1563	30	51	of	of	ADP
ajis02-1563	30	52	g	g	NOUN
ajis02-1563	30	53	and	and	CCONJ
ajis02-1563	30	54	cell	cell	NOUN
ajis02-1563	30	55	entries	entry	NOUN
ajis02-1563	30	56	representing	represent	VERB
ajis02-1563	30	57	the	the	DET
ajis02-1563	30	58	edges	edge	NOUN
ajis02-1563	30	59	i.e.	i.e.	X
ajis02-1563	30	60	ag(i	ag(i	X
ajis02-1563	30	61	,	,	PUNCT
ajis02-1563	31	1	j)=1	j)=1	PROPN
ajis02-1563	31	2	if	if	SCONJ
ajis02-1563	31	3	and	and	CCONJ
ajis02-1563	31	4	only	only	ADV
ajis02-1563	31	5	if	if	SCONJ
ajis02-1563	31	6	there	there	PRON
ajis02-1563	31	7	is	be	VERB
ajis02-1563	31	8	an	an	DET
ajis02-1563	31	9	edge	edge	NOUN
ajis02-1563	31	10	from	from	ADP
ajis02-1563	31	11	vertex	vertex	NOUN
ajis02-1563	31	12	i	i	PRON
ajis02-1563	31	13	to	to	PART
ajis02-1563	31	14	vertex	vertex	PROPN
ajis02-1563	31	15	j.	j.	PROPN
ajis02-1563	31	16	eigen	eigen	PROPN
ajis02-1563	31	17	spectrum	spectrum	PROPN
ajis02-1563	31	18	,	,	PUNCT
ajis02-1563	31	19	{	{	PUNCT
ajis02-1563	31	20	𝜆𝑖}𝑖=1	𝜆𝑖}𝑖=1	NOUN
ajis02-1563	31	21	𝑛	𝑛	VERB
ajis02-1563	31	22	,	,	PUNCT
ajis02-1563	31	23	of	of	ADP
ajis02-1563	31	24	adjacency	adjacency	NOUN
ajis02-1563	31	25	and	and	CCONJ
ajis02-1563	31	26	laplacian	laplacian	ADJ
ajis02-1563	31	27	matrices	matrix	NOUN
ajis02-1563	31	28	has	have	AUX
ajis02-1563	31	29	been	be	AUX
ajis02-1563	31	30	studied	study	VERB
ajis02-1563	31	31	a	a	DET
ajis02-1563	31	32	lot	lot	NOUN
ajis02-1563	31	33	for	for	ADP
ajis02-1563	31	34	certain	certain	ADJ
ajis02-1563	31	35	graph	graph	NOUN
ajis02-1563	31	36	properties	property	NOUN
ajis02-1563	31	37	(	(	PUNCT
ajis02-1563	31	38	chung	chung	PROPN
ajis02-1563	31	39	1997	1997	NUM
ajis02-1563	31	40	)	)	PUNCT
ajis02-1563	31	41	.	.	PUNCT
ajis02-1563	32	1	of	of	ADP
ajis02-1563	32	2	particular	particular	ADJ
ajis02-1563	32	3	interest	interest	NOUN
ajis02-1563	32	4	to	to	ADP
ajis02-1563	32	5	us	we	PRON
ajis02-1563	32	6	is	be	AUX
ajis02-1563	32	7	the	the	DET
ajis02-1563	32	8	largest	large	ADJ
ajis02-1563	32	9	eigenvalue	eigenvalue	NOUN
ajis02-1563	32	10	(	(	PUNCT
ajis02-1563	32	11	denoted	denote	VERB
ajis02-1563	32	12	by	by	ADP
ajis02-1563	32	13	λ1(a	λ1(a	NOUN
ajis02-1563	32	14	)	)	PUNCT
ajis02-1563	32	15	or	or	CCONJ
ajis02-1563	32	16	λ1(g	λ1(g	NUM
ajis02-1563	32	17	)	)	PUNCT
ajis02-1563	32	18	or	or	CCONJ
ajis02-1563	32	19	λ1	λ1	VERB
ajis02-1563	32	20	when	when	SCONJ
ajis02-1563	32	21	g	g	PROPN
ajis02-1563	32	22	is	be	AUX
ajis02-1563	32	23	obvious	obvious	ADJ
ajis02-1563	32	24	from	from	ADP
ajis02-1563	32	25	the	the	DET
ajis02-1563	32	26	context	context	NOUN
ajis02-1563	32	27	)	)	PUNCT
ajis02-1563	32	28	of	of	ADP
ajis02-1563	32	29	the	the	DET
ajis02-1563	32	30	adjacency	adjacency	NOUN
ajis02-1563	32	31	matrix	matrix	NOUN
ajis02-1563	32	32	also	also	ADV
ajis02-1563	32	33	referred	refer	VERB
ajis02-1563	32	34	to	to	ADP
ajis02-1563	32	35	as	as	ADP
ajis02-1563	32	36	the	the	DET
ajis02-1563	32	37	first	first	ADJ
ajis02-1563	32	38	eigenvalue	eigenvalue	NOUN
ajis02-1563	32	39	in	in	ADP
ajis02-1563	32	40	literature	literature	NOUN
ajis02-1563	32	41	.	.	PUNCT
ajis02-1563	33	1	epidemic	epidemic	NOUN
ajis02-1563	33	2	threshold	threshold	NOUN
ajis02-1563	33	3	is	be	AUX
ajis02-1563	33	4	an	an	DET
ajis02-1563	33	5	intrinsic	intrinsic	ADJ
ajis02-1563	33	6	property	property	NOUN
ajis02-1563	33	7	of	of	ADP
ajis02-1563	33	8	a	a	DET
ajis02-1563	33	9	network	network	NOUN
ajis02-1563	33	10	.	.	PUNCT
ajis02-1563	34	1	it	it	PRON
ajis02-1563	34	2	is	be	AUX
ajis02-1563	34	3	well	well	ADV
ajis02-1563	34	4	known	know	VERB
ajis02-1563	34	5	in	in	ADP
ajis02-1563	34	6	the	the	DET
ajis02-1563	34	7	epidemiology	epidemiology	NOUN
ajis02-1563	34	8	literature	literature	NOUN
ajis02-1563	34	9	that	that	SCONJ
ajis02-1563	34	10	if	if	SCONJ
ajis02-1563	34	11	the	the	DET
ajis02-1563	34	12	“	"	PUNCT
ajis02-1563	34	13	virus	virus	NOUN
ajis02-1563	34	14	strength	strength	NOUN
ajis02-1563	34	15	”	"	PUNCT
ajis02-1563	34	16	is	be	AUX
ajis02-1563	34	17	more	more	ADJ
ajis02-1563	34	18	than	than	ADP
ajis02-1563	34	19	the	the	DET
ajis02-1563	34	20	network	network	NOUN
ajis02-1563	34	21	's	's	PART
ajis02-1563	34	22	epidemic	epidemic	NOUN
ajis02-1563	34	23	threshold	threshold	NOUN
ajis02-1563	34	24	,	,	PUNCT
ajis02-1563	34	25	then	then	ADV
ajis02-1563	34	26	an	an	DET
ajis02-1563	34	27	outbreak	outbreak	NOUN
ajis02-1563	34	28	will	will	AUX
ajis02-1563	34	29	occur	occur	VERB
ajis02-1563	34	30	.	.	PUNCT
ajis02-1563	35	1	the	the	DET
ajis02-1563	35	2	epidemic	epidemic	NOUN
ajis02-1563	35	3	threshold	threshold	NOUN
ajis02-1563	35	4	of	of	ADP
ajis02-1563	35	5	an	an	DET
ajis02-1563	35	6	undirected	undirected	ADJ
ajis02-1563	35	7	graph	graph	NOUN
ajis02-1563	35	8	g	g	PROPN
ajis02-1563	35	9	is	be	AUX
ajis02-1563	35	10	directly	directly	ADV
ajis02-1563	35	11	proportional	proportional	ADJ
ajis02-1563	35	12	to	to	ADP
ajis02-1563	35	13	λ1(g	λ1(g	PROPN
ajis02-1563	35	14	)	)	PUNCT
ajis02-1563	35	15	(	(	PUNCT
ajis02-1563	35	16	chakrabarti	chakrabarti	PROPN
ajis02-1563	35	17	2008	2008	NUM
ajis02-1563	35	18	)	)	PUNCT
ajis02-1563	35	19	.	.	PUNCT
ajis02-1563	36	1	for	for	ADP
ajis02-1563	36	2	this	this	DET
ajis02-1563	36	3	reason	reason	NOUN
ajis02-1563	36	4	in	in	ADP
ajis02-1563	36	5	the	the	DET
ajis02-1563	36	6	epidemiology	epidemiology	NOUN
ajis02-1563	36	7	community	community	NOUN
ajis02-1563	36	8	,	,	PUNCT
ajis02-1563	36	9	the	the	DET
ajis02-1563	36	10	largest	large	ADJ
ajis02-1563	36	11	eigenvalue	eigenvalue	NOUN
ajis02-1563	36	12	of	of	ADP
ajis02-1563	36	13	graphs	graph	NOUN
ajis02-1563	36	14	is	be	AUX
ajis02-1563	36	15	used	use	VERB
ajis02-1563	36	16	to	to	PART
ajis02-1563	36	17	study	study	VERB
ajis02-1563	36	18	mathematical	mathematical	ADJ
ajis02-1563	36	19	models	model	NOUN
ajis02-1563	36	20	of	of	ADP
ajis02-1563	36	21	diseases	disease	NOUN
ajis02-1563	36	22	spreads	spread	NOUN
ajis02-1563	36	23	and	and	CCONJ
ajis02-1563	36	24	outbreaks	outbreak	NOUN
ajis02-1563	36	25	(	(	PUNCT
ajis02-1563	36	26	ganesh	ganesh	NOUN
ajis02-1563	36	27	2005	2005	NUM
ajis02-1563	36	28	)	)	PUNCT
ajis02-1563	36	29	.	.	PUNCT
ajis02-1563	37	1	in	in	ADP
ajis02-1563	37	2	general	general	ADJ
ajis02-1563	37	3	λ1	λ1	PROPN
ajis02-1563	37	4	is	be	AUX
ajis02-1563	37	5	related	relate	VERB
ajis02-1563	37	6	to	to	ADP
ajis02-1563	37	7	the	the	DET
ajis02-1563	37	8	global	global	ADJ
ajis02-1563	37	9	connectivity	connectivity	NOUN
ajis02-1563	37	10	of	of	ADP
ajis02-1563	37	11	a	a	DET
ajis02-1563	37	12	graph	graph	NOUN
ajis02-1563	37	13	.	.	PUNCT
ajis02-1563	38	1	for	for	ADP
ajis02-1563	38	2	example	example	NOUN
ajis02-1563	38	3	we	we	PRON
ajis02-1563	38	4	know	know	VERB
ajis02-1563	38	5	that	that	SCONJ
ajis02-1563	38	6	δ	δ	PROPN
ajis02-1563	38	7	≥	≥	PRON
ajis02-1563	38	8	𝜆1	𝜆1	VERB
ajis02-1563	38	9	≥	≥	NUM
ajis02-1563	38	10	𝑑𝑎𝑣𝑔	𝑑𝑎𝑣𝑔	NOUN
ajis02-1563	38	11	where	where	SCONJ
ajis02-1563	38	12	δ	δ	PROPN
ajis02-1563	38	13	and	and	CCONJ
ajis02-1563	38	14	davg	davg	NOUN
ajis02-1563	38	15	are	be	AUX
ajis02-1563	38	16	the	the	DET
ajis02-1563	38	17	maximum	maximum	ADJ
ajis02-1563	38	18	and	and	CCONJ
ajis02-1563	38	19	average	average	ADJ
ajis02-1563	38	20	degrees	degree	NOUN
ajis02-1563	38	21	in	in	ADP
ajis02-1563	38	22	the	the	DET
ajis02-1563	38	23	graph	graph	NOUN
ajis02-1563	38	24	,	,	PUNCT
ajis02-1563	38	25	respectively	respectively	ADV
ajis02-1563	38	26	(	(	PUNCT
ajis02-1563	38	27	west	west	NOUN
ajis02-1563	38	28	2001	2001	NUM
ajis02-1563	38	29	)	)	PUNCT
ajis02-1563	38	30	.	.	PUNCT
ajis02-1563	39	1	in	in	ADP
ajis02-1563	39	2	the	the	DET
ajis02-1563	39	3	context	context	NOUN
ajis02-1563	39	4	of	of	ADP
ajis02-1563	39	5	the	the	DET
ajis02-1563	39	6	discussion	discussion	NOUN
ajis02-1563	39	7	above	above	ADP
ajis02-1563	39	8	it	it	PRON
ajis02-1563	39	9	seems	seem	VERB
ajis02-1563	39	10	only	only	ADV
ajis02-1563	39	11	logical	logical	ADJ
ajis02-1563	39	12	to	to	PART
ajis02-1563	39	13	delete	delete	VERB
ajis02-1563	39	14	/	/	SYM
ajis02-1563	39	15	immunize	immunize	NOUN
ajis02-1563	39	16	the	the	DET
ajis02-1563	39	17	vertices	vertex	NOUN
ajis02-1563	39	18	in	in	ADP
ajis02-1563	39	19	g	g	PROPN
ajis02-1563	39	20	such	such	ADJ
ajis02-1563	39	21	that	that	SCONJ
ajis02-1563	39	22	the	the	DET
ajis02-1563	39	23	remaining	remain	VERB
ajis02-1563	39	24	graph	graph	NOUN
ajis02-1563	39	25	has	have	VERB
ajis02-1563	39	26	minimum	minimum	ADJ
ajis02-1563	39	27	possible	possible	ADJ
ajis02-1563	39	28	largest	large	ADJ
ajis02-1563	39	29	eigenvalue	eigenvalue	NOUN
ajis02-1563	39	30	.	.	PUNCT
ajis02-1563	40	1	let	let	AUX
ajis02-1563	40	2	g=(v	g=(v	PROPN
ajis02-1563	40	3	,	,	PUNCT
ajis02-1563	40	4	e	e	NOUN
ajis02-1563	40	5	)	)	PUNCT
ajis02-1563	40	6	be	be	AUX
ajis02-1563	40	7	a	a	DET
ajis02-1563	40	8	graph	graph	NOUN
ajis02-1563	40	9	and	and	CCONJ
ajis02-1563	40	10	let	let	VERB
ajis02-1563	40	11	a	a	PRON
ajis02-1563	40	12	be	be	AUX
ajis02-1563	40	13	its	its	PRON
ajis02-1563	40	14	adjacency	adjacency	NOUN
ajis02-1563	40	15	matrix	matrix	NOUN
ajis02-1563	40	16	.	.	PUNCT
ajis02-1563	41	1	for	for	ADP
ajis02-1563	41	2	a	a	DET
ajis02-1563	41	3	subset	subset	NOUN
ajis02-1563	41	4	of	of	ADP
ajis02-1563	41	5	vertices	vertex	NOUN
ajis02-1563	41	6	s	s	PART
ajis02-1563	41	7	⊆	⊆	NUM
ajis02-1563	41	8	v	v	NOUN
ajis02-1563	41	9	,	,	PUNCT
ajis02-1563	41	10	we	we	PRON
ajis02-1563	41	11	denote	denote	VERB
ajis02-1563	41	12	by	by	ADP
ajis02-1563	41	13	g	g	PROPN
ajis02-1563	41	14	-	-	PUNCT
ajis02-1563	41	15	s	s	VERB
ajis02-1563	41	16	the	the	DET
ajis02-1563	41	17	subgraph	subgraph	NOUN
ajis02-1563	41	18	induced	induce	VERB
ajis02-1563	41	19	on	on	ADP
ajis02-1563	41	20	vertices	vertex	NOUN
ajis02-1563	41	21	in	in	ADP
ajis02-1563	41	22	v∖s	v∖s	PROPN
ajis02-1563	41	23	.	.	PUNCT
ajis02-1563	42	1	similarly	similarly	ADV
ajis02-1563	42	2	,	,	PUNCT
ajis02-1563	42	3	for	for	ADP
ajis02-1563	42	4	s	s	PROPN
ajis02-1563	42	5	⊆	⊆	NUM
ajis02-1563	42	6	v	v	NOUN
ajis02-1563	42	7	,	,	PUNCT
ajis02-1563	42	8	we	we	PRON
ajis02-1563	42	9	define	define	VERB
ajis02-1563	42	10	a	a	DET
ajis02-1563	42	11	-	-	PUNCT
ajis02-1563	42	12	s	s	NOUN
ajis02-1563	42	13	to	to	PART
ajis02-1563	42	14	be	be	AUX
ajis02-1563	42	15	the	the	DET
ajis02-1563	42	16	submatrix	submatrix	NOUN
ajis02-1563	42	17	of	of	ADP
ajis02-1563	42	18	a	a	PRON
ajis02-1563	42	19	obtained	obtain	VERB
ajis02-1563	42	20	by	by	ADP
ajis02-1563	42	21	deleting	delete	VERB
ajis02-1563	42	22	rows	row	NOUN
ajis02-1563	42	23	and	and	CCONJ
ajis02-1563	42	24	columns	column	NOUN
ajis02-1563	42	25	in	in	ADP
ajis02-1563	42	26	a	a	PRON
ajis02-1563	42	27	at	at	ADP
ajis02-1563	42	28	corresponding	correspond	VERB
ajis02-1563	42	29	indices	index	NOUN
ajis02-1563	42	30	in	in	ADP
ajis02-1563	42	31	s.	s.	PROPN
ajis02-1563	42	32	by	by	ADP
ajis02-1563	42	33	definition	definition	NOUN
ajis02-1563	42	34	of	of	ADP
ajis02-1563	42	35	induced	induced	ADJ
ajis02-1563	42	36	subgraph	subgraph	NOUN
ajis02-1563	42	37	,	,	PUNCT
ajis02-1563	42	38	it	it	PRON
ajis02-1563	42	39	is	be	AUX
ajis02-1563	42	40	clear	clear	ADJ
ajis02-1563	42	41	that	that	SCONJ
ajis02-1563	42	42	a	a	X
ajis02-1563	42	43	-	-	PUNCT
ajis02-1563	42	44	s	s	NOUN
ajis02-1563	42	45	is	be	AUX
ajis02-1563	42	46	the	the	DET
ajis02-1563	42	47	adjacency	adjacency	NOUN
ajis02-1563	42	48	matrix	matrix	NOUN
ajis02-1563	42	49	of	of	ADP
ajis02-1563	42	50	g	g	PROPN
ajis02-1563	42	51	-	-	PUNCT
ajis02-1563	42	52	s.	s.	PROPN
ajis02-1563	42	53	we	we	PRON
ajis02-1563	42	54	will	will	AUX
ajis02-1563	42	55	denote	denote	VERB
ajis02-1563	42	56	by	by	ADP
ajis02-1563	42	57	gs	gs	INTJ
ajis02-1563	42	58	the	the	DET
ajis02-1563	42	59	subgraph	subgraph	NOUN
ajis02-1563	42	60	of	of	ADP
ajis02-1563	42	61	g	g	PROPN
ajis02-1563	42	62	induced	induce	VERB
ajis02-1563	42	63	by	by	ADP
ajis02-1563	42	64	vertices	vertex	NOUN
ajis02-1563	42	65	in	in	ADP
ajis02-1563	42	66	s	s	PRON
ajis02-1563	42	67	and	and	CCONJ
ajis02-1563	42	68	as	as	ADP
ajis02-1563	42	69	denotes	denote	NOUN
ajis02-1563	42	70	the	the	DET
ajis02-1563	42	71	adjacency	adjacency	NOUN
ajis02-1563	42	72	matrix	matrix	NOUN
ajis02-1563	42	73	of	of	ADP
ajis02-1563	42	74	gs	gs	PROPN
ajis02-1563	42	75	.	.	PUNCT
ajis02-1563	43	1	the	the	DET
ajis02-1563	43	2	precise	precise	ADJ
ajis02-1563	43	3	formulation	formulation	NOUN
ajis02-1563	43	4	of	of	ADP
ajis02-1563	43	5	the	the	DET
ajis02-1563	43	6	above	above	ADJ
ajis02-1563	43	7	problem	problem	NOUN
ajis02-1563	43	8	is	be	AUX
ajis02-1563	43	9	given	give	VERB
ajis02-1563	43	10	as	as	SCONJ
ajis02-1563	43	11	follows	follow	VERB
ajis02-1563	43	12	:	:	PUNCT
ajis02-1563	43	13	problem	problem	NOUN
ajis02-1563	43	14	2	2	NUM
ajis02-1563	43	15	:	:	PUNCT
ajis02-1563	43	16	given	give	VERB
ajis02-1563	43	17	a	a	DET
ajis02-1563	43	18	simple	simple	ADJ
ajis02-1563	43	19	undirected	undirected	ADJ
ajis02-1563	43	20	graph	graph	NOUN
ajis02-1563	43	21	g	g	PROPN
ajis02-1563	43	22	=	=	PUNCT
ajis02-1563	43	23	(	(	PUNCT
ajis02-1563	43	24	v	v	NOUN
ajis02-1563	43	25	,	,	PUNCT
ajis02-1563	43	26	e	e	NOUN
ajis02-1563	43	27	)	)	PUNCT
ajis02-1563	43	28	find	find	VERB
ajis02-1563	43	29	a	a	DET
ajis02-1563	43	30	set	set	NOUN
ajis02-1563	43	31	s	s	NOUN
ajis02-1563	43	32	of	of	ADP
ajis02-1563	43	33	k	k	PROPN
ajis02-1563	43	34	vertices	vertex	NOUN
ajis02-1563	43	35	so	so	SCONJ
ajis02-1563	43	36	that	that	SCONJ
ajis02-1563	43	37	λ1(a	λ1(a	PROPN
ajis02-1563	43	38	-	-	PUNCT
ajis02-1563	43	39	s	s	PART
ajis02-1563	43	40	)	)	PUNCT
ajis02-1563	43	41	is	be	AUX
ajis02-1563	43	42	the	the	DET
ajis02-1563	43	43	minimum	minimum	NOUN
ajis02-1563	43	44	possible	possible	ADJ
ajis02-1563	43	45	over	over	ADP
ajis02-1563	43	46	all	all	DET
ajis02-1563	43	47	choices	choice	NOUN
ajis02-1563	43	48	of	of	ADP
ajis02-1563	43	49	s	s	NOUN
ajis02-1563	43	50	⊆	⊆	NUM
ajis02-1563	43	51	v.	v.	ADP
ajis02-1563	43	52	australasian	australasian	ADJ
ajis02-1563	43	53	journal	journal	NOUN
ajis02-1563	43	54	of	of	ADP
ajis02-1563	43	55	information	information	NOUN
ajis02-1563	43	56	systems	system	NOUN
ajis02-1563	43	57	ahmad	ahmad	PROPN
ajis02-1563	43	58	,	,	PUNCT
ajis02-1563	43	59	traiq	traiq	NOUN
ajis02-1563	43	60	,	,	PUNCT
ajis02-1563	43	61	shabbir	shabbir	PROPN
ajis02-1563	43	62	&	&	CCONJ
ajis02-1563	43	63	khan	khan	PROPN
ajis02-1563	43	64	2017	2017	NUM
ajis02-1563	43	65	,	,	PUNCT
ajis02-1563	43	66	vol	vol	NOUN
ajis02-1563	43	67	21	21	NUM
ajis02-1563	43	68	,	,	PUNCT
ajis02-1563	43	69	selected	select	VERB
ajis02-1563	43	70	papers	paper	NOUN
ajis02-1563	43	71	from	from	ADP
ajis02-1563	43	72	ausdm	ausdm	NOUN
ajis02-1563	43	73	spectral	spectral	ADJ
ajis02-1563	43	74	methods	method	NOUN
ajis02-1563	43	75	for	for	ADP
ajis02-1563	43	76	immunization	immunization	NOUN
ajis02-1563	43	77	of	of	ADP
ajis02-1563	43	78	large	large	ADJ
ajis02-1563	43	79	networks	network	NOUN
ajis02-1563	43	80	3	3	NUM
ajis02-1563	43	81	since	since	SCONJ
ajis02-1563	43	82	λ1(g	λ1(g	PROPN
ajis02-1563	43	83	)	)	PUNCT
ajis02-1563	43	84	can	can	AUX
ajis02-1563	43	85	be	be	AUX
ajis02-1563	43	86	computed	compute	VERB
ajis02-1563	43	87	in	in	ADP
ajis02-1563	43	88	o(m	o(m	PROPN
ajis02-1563	43	89	)	)	PUNCT
ajis02-1563	43	90	time	time	NOUN
ajis02-1563	43	91	(	(	PUNCT
ajis02-1563	43	92	chen	chen	PROPN
ajis02-1563	43	93	2016	2016	NUM
ajis02-1563	43	94	)	)	PUNCT
ajis02-1563	43	95	,	,	PUNCT
ajis02-1563	43	96	the	the	DET
ajis02-1563	43	97	natural	natural	ADJ
ajis02-1563	43	98	algorithm	algorithm	NOUN
ajis02-1563	43	99	to	to	PART
ajis02-1563	43	100	find	find	VERB
ajis02-1563	43	101	the	the	DET
ajis02-1563	43	102	optimal	optimal	ADJ
ajis02-1563	43	103	set	set	NOUN
ajis02-1563	43	104	s	s	NOUN
ajis02-1563	43	105	takes	take	VERB
ajis02-1563	43	106	time	time	NOUN
ajis02-1563	43	107	𝑂	𝑂	PROPN
ajis02-1563	43	108	(	(	PUNCT
ajis02-1563	43	109	(	(	PUNCT
ajis02-1563	43	110	𝑛	𝑛	PROPN
ajis02-1563	43	111	𝑘	𝑘	NOUN
ajis02-1563	43	112	)	)	PUNCT
ajis02-1563	43	113	𝑚	𝑚	NOUN
ajis02-1563	43	114	)	)	PUNCT
ajis02-1563	43	115	,	,	PUNCT
ajis02-1563	43	116	which	which	PRON
ajis02-1563	43	117	is	be	AUX
ajis02-1563	43	118	exponential	exponential	ADJ
ajis02-1563	43	119	in	in	ADP
ajis02-1563	43	120	k.	k.	PROPN
ajis02-1563	43	121	indeed	indeed	ADV
ajis02-1563	43	122	lemma	lemma	PROPN
ajis02-1563	43	123	1	1	NUM
ajis02-1563	43	124	asserts	assert	VERB
ajis02-1563	43	125	that	that	SCONJ
ajis02-1563	43	126	the	the	DET
ajis02-1563	43	127	general	general	NOUN
ajis02-1563	43	128	the	the	DET
ajis02-1563	43	129	problem	problem	NOUN
ajis02-1563	43	130	is	be	AUX
ajis02-1563	43	131	intractable	intractable	ADJ
ajis02-1563	43	132	(	(	PUNCT
ajis02-1563	43	133	see	see	VERB
ajis02-1563	43	134	section	section	NOUN
ajis02-1563	43	135	2	2	NUM
ajis02-1563	43	136	for	for	ADP
ajis02-1563	43	137	a	a	DET
ajis02-1563	43	138	proof	proof	NOUN
ajis02-1563	43	139	)	)	PUNCT
ajis02-1563	43	140	.	.	PUNCT
ajis02-1563	44	1	lemma	lemma	PROPN
ajis02-1563	44	2	1	1	NUM
ajis02-1563	44	3	:	:	PUNCT
ajis02-1563	44	4	problem	problem	NOUN
ajis02-1563	44	5	2	2	NUM
ajis02-1563	44	6	is	be	AUX
ajis02-1563	44	7	np	np	NOUN
ajis02-1563	44	8	-	-	PUNCT
ajis02-1563	44	9	hard	hard	ADJ
ajis02-1563	44	10	.	.	PUNCT
ajis02-1563	45	1	in	in	ADP
ajis02-1563	45	2	this	this	DET
ajis02-1563	45	3	work	work	NOUN
ajis02-1563	45	4	we	we	PRON
ajis02-1563	45	5	propose	propose	VERB
ajis02-1563	45	6	a	a	DET
ajis02-1563	45	7	novel	novel	ADJ
ajis02-1563	45	8	algorithm	algorithm	NOUN
ajis02-1563	45	9	to	to	PART
ajis02-1563	45	10	approximately	approximately	ADV
ajis02-1563	45	11	solve	solve	VERB
ajis02-1563	45	12	problem	problem	NOUN
ajis02-1563	45	13	2	2	X
ajis02-1563	45	14	.	.	PUNCT
ajis02-1563	46	1	our	our	PRON
ajis02-1563	46	2	algorithm	algorithm	NOUN
ajis02-1563	46	3	is	be	AUX
ajis02-1563	46	4	quite	quite	ADV
ajis02-1563	46	5	intuitive	intuitive	ADJ
ajis02-1563	46	6	,	,	PUNCT
ajis02-1563	46	7	promises	promise	VERB
ajis02-1563	46	8	a	a	DET
ajis02-1563	46	9	better	well	ADJ
ajis02-1563	46	10	approximation	approximation	NOUN
ajis02-1563	46	11	compared	compare	VERB
ajis02-1563	46	12	to	to	ADP
ajis02-1563	46	13	known	know	VERB
ajis02-1563	46	14	approaches	approach	NOUN
ajis02-1563	46	15	,	,	PUNCT
ajis02-1563	46	16	and	and	CCONJ
ajis02-1563	46	17	is	be	AUX
ajis02-1563	46	18	easy	easy	ADJ
ajis02-1563	46	19	to	to	PART
ajis02-1563	46	20	implement	implement	VERB
ajis02-1563	46	21	.	.	PUNCT
ajis02-1563	47	1	we	we	PRON
ajis02-1563	47	2	propose	propose	VERB
ajis02-1563	47	3	a	a	DET
ajis02-1563	47	4	combinatorial	combinatorial	ADJ
ajis02-1563	47	5	formulation	formulation	NOUN
ajis02-1563	47	6	of	of	ADP
ajis02-1563	47	7	the	the	DET
ajis02-1563	47	8	problem	problem	NOUN
ajis02-1563	47	9	in	in	ADP
ajis02-1563	47	10	which	which	PRON
ajis02-1563	47	11	we	we	PRON
ajis02-1563	47	12	construct	construct	VERB
ajis02-1563	47	13	a	a	DET
ajis02-1563	47	14	subset	subset	NOUN
ajis02-1563	47	15	of	of	ADP
ajis02-1563	47	16	vertices	vertex	NOUN
ajis02-1563	47	17	based	base	VERB
ajis02-1563	47	18	on	on	ADP
ajis02-1563	47	19	a	a	DET
ajis02-1563	47	20	defined	define	VERB
ajis02-1563	47	21	shield	shield	NOUN
ajis02-1563	47	22	value	value	NOUN
ajis02-1563	47	23	.	.	PUNCT
ajis02-1563	48	1	our	our	PRON
ajis02-1563	48	2	shield	shield	NOUN
ajis02-1563	48	3	value	value	NOUN
ajis02-1563	48	4	measures	measure	VERB
ajis02-1563	48	5	the	the	DET
ajis02-1563	48	6	contribution	contribution	NOUN
ajis02-1563	48	7	of	of	ADP
ajis02-1563	48	8	the	the	DET
ajis02-1563	48	9	vertices	vertex	NOUN
ajis02-1563	48	10	towards	towards	ADP
ajis02-1563	48	11	the	the	DET
ajis02-1563	48	12	largest	large	ADJ
ajis02-1563	48	13	eigenvalue	eigenvalue	NOUN
ajis02-1563	48	14	of	of	ADP
ajis02-1563	48	15	the	the	DET
ajis02-1563	48	16	graph	graph	NOUN
ajis02-1563	48	17	.	.	PUNCT
ajis02-1563	49	1	definition	definition	NOUN
ajis02-1563	49	2	of	of	ADP
ajis02-1563	49	3	our	our	PRON
ajis02-1563	49	4	shield	shield	NOUN
ajis02-1563	49	5	value	value	NOUN
ajis02-1563	49	6	uses	use	VERB
ajis02-1563	49	7	basic	basic	ADJ
ajis02-1563	49	8	theoretical	theoretical	ADJ
ajis02-1563	49	9	tools	tool	NOUN
ajis02-1563	49	10	from	from	ADP
ajis02-1563	49	11	spectral	spectral	ADJ
ajis02-1563	49	12	graph	graph	NOUN
ajis02-1563	49	13	theory	theory	NOUN
ajis02-1563	49	14	and	and	CCONJ
ajis02-1563	49	15	relies	rely	VERB
ajis02-1563	49	16	on	on	ADP
ajis02-1563	49	17	simple	simple	ADJ
ajis02-1563	49	18	combinatorial	combinatorial	ADJ
ajis02-1563	49	19	interpretation	interpretation	NOUN
ajis02-1563	49	20	of	of	ADP
ajis02-1563	49	21	largest	large	ADJ
ajis02-1563	49	22	eigenvalue	eigenvalue	NOUN
ajis02-1563	49	23	.	.	PUNCT
ajis02-1563	50	1	removing	remove	VERB
ajis02-1563	50	2	vertices	vertex	NOUN
ajis02-1563	50	3	with	with	ADP
ajis02-1563	50	4	high	high	ADJ
ajis02-1563	50	5	shield	shield	NOUN
ajis02-1563	50	6	values	value	NOUN
ajis02-1563	50	7	would	would	AUX
ajis02-1563	50	8	yield	yield	VERB
ajis02-1563	50	9	optimal	optimal	ADJ
ajis02-1563	50	10	immunization	immunization	NOUN
ajis02-1563	50	11	results	result	NOUN
ajis02-1563	50	12	.	.	PUNCT
ajis02-1563	51	1	we	we	PRON
ajis02-1563	51	2	provide	provide	VERB
ajis02-1563	51	3	an	an	DET
ajis02-1563	51	4	efficient	efficient	ADJ
ajis02-1563	51	5	approximation	approximation	NOUN
ajis02-1563	51	6	algorithm	algorithm	NOUN
ajis02-1563	51	7	to	to	PART
ajis02-1563	51	8	estimate	estimate	VERB
ajis02-1563	51	9	the	the	DET
ajis02-1563	51	10	shield	shield	NOUN
ajis02-1563	51	11	values	value	NOUN
ajis02-1563	51	12	of	of	ADP
ajis02-1563	51	13	vertices	vertex	NOUN
ajis02-1563	51	14	.	.	PUNCT
ajis02-1563	52	1	we	we	PRON
ajis02-1563	52	2	provide	provide	VERB
ajis02-1563	52	3	detailed	detailed	ADJ
ajis02-1563	52	4	analysis	analysis	NOUN
ajis02-1563	52	5	of	of	ADP
ajis02-1563	52	6	running	run	VERB
ajis02-1563	52	7	time	time	NOUN
ajis02-1563	52	8	and	and	CCONJ
ajis02-1563	52	9	space	space	NOUN
ajis02-1563	52	10	complexity	complexity	NOUN
ajis02-1563	52	11	of	of	ADP
ajis02-1563	52	12	our	our	PRON
ajis02-1563	52	13	algorithm	algorithm	NOUN
ajis02-1563	52	14	.	.	PUNCT
ajis02-1563	53	1	we	we	PRON
ajis02-1563	53	2	also	also	ADV
ajis02-1563	53	3	empirically	empirically	ADV
ajis02-1563	53	4	evaluate	evaluate	VERB
ajis02-1563	53	5	our	our	PRON
ajis02-1563	53	6	algorithm	algorithm	NOUN
ajis02-1563	53	7	on	on	ADP
ajis02-1563	53	8	several	several	ADJ
ajis02-1563	53	9	real	real	ADJ
ajis02-1563	53	10	world	world	NOUN
ajis02-1563	53	11	data	datum	NOUN
ajis02-1563	53	12	sets	set	NOUN
ajis02-1563	53	13	.	.	PUNCT
ajis02-1563	54	1	the	the	DET
ajis02-1563	54	2	results	result	NOUN
ajis02-1563	54	3	show	show	VERB
ajis02-1563	54	4	that	that	SCONJ
ajis02-1563	54	5	our	our	PRON
ajis02-1563	54	6	algorithm	algorithm	NOUN
ajis02-1563	54	7	achieves	achieve	VERB
ajis02-1563	54	8	much	much	ADV
ajis02-1563	54	9	better	well	ADJ
ajis02-1563	54	10	immunization	immunization	NOUN
ajis02-1563	54	11	performance	performance	NOUN
ajis02-1563	54	12	compared	compare	VERB
ajis02-1563	54	13	to	to	ADP
ajis02-1563	54	14	previously	previously	ADV
ajis02-1563	54	15	known	know	VERB
ajis02-1563	54	16	solutions	solution	NOUN
ajis02-1563	54	17	.	.	PUNCT
ajis02-1563	55	1	moreover	moreover	ADV
ajis02-1563	55	2	,	,	PUNCT
ajis02-1563	55	3	ideas	idea	NOUN
ajis02-1563	55	4	developed	develop	VERB
ajis02-1563	55	5	in	in	ADP
ajis02-1563	55	6	this	this	DET
ajis02-1563	55	7	work	work	NOUN
ajis02-1563	55	8	are	be	AUX
ajis02-1563	55	9	general	general	ADJ
ajis02-1563	55	10	and	and	CCONJ
ajis02-1563	55	11	can	can	AUX
ajis02-1563	55	12	have	have	VERB
ajis02-1563	55	13	many	many	ADJ
ajis02-1563	55	14	other	other	ADJ
ajis02-1563	55	15	potential	potential	ADJ
ajis02-1563	55	16	applications	application	NOUN
ajis02-1563	55	17	.	.	PUNCT
ajis02-1563	56	1	indeed	indeed	ADV
ajis02-1563	56	2	this	this	DET
ajis02-1563	56	3	method	method	NOUN
ajis02-1563	56	4	has	have	AUX
ajis02-1563	56	5	been	be	AUX
ajis02-1563	56	6	successfully	successfully	ADV
ajis02-1563	56	7	used	use	VERB
ajis02-1563	56	8	for	for	ADP
ajis02-1563	56	9	estimating	estimate	VERB
ajis02-1563	56	10	the	the	DET
ajis02-1563	56	11	spectral	spectral	ADJ
ajis02-1563	56	12	radius	radius	NOUN
ajis02-1563	56	13	of	of	ADP
ajis02-1563	56	14	large	large	ADJ
ajis02-1563	56	15	graphs	graph	NOUN
ajis02-1563	56	16	(	(	PUNCT
ajis02-1563	56	17	abbas	abbas	PROPN
ajis02-1563	56	18	2017	2017	NUM
ajis02-1563	56	19	)	)	PUNCT
ajis02-1563	56	20	.	.	PUNCT
ajis02-1563	57	1	rest	rest	NOUN
ajis02-1563	57	2	of	of	ADP
ajis02-1563	57	3	the	the	DET
ajis02-1563	57	4	paper	paper	NOUN
ajis02-1563	57	5	is	be	AUX
ajis02-1563	57	6	organized	organize	VERB
ajis02-1563	57	7	as	as	SCONJ
ajis02-1563	57	8	follows	follow	VERB
ajis02-1563	57	9	.	.	PUNCT
ajis02-1563	58	1	in	in	ADP
ajis02-1563	58	2	section	section	NOUN
ajis02-1563	58	3	2	2	NUM
ajis02-1563	58	4	we	we	PRON
ajis02-1563	58	5	provide	provide	VERB
ajis02-1563	58	6	a	a	DET
ajis02-1563	58	7	detailed	detailed	ADJ
ajis02-1563	58	8	background	background	NOUN
ajis02-1563	58	9	to	to	PART
ajis02-1563	58	10	problem	problem	VERB
ajis02-1563	58	11	2	2	NUM
ajis02-1563	58	12	and	and	CCONJ
ajis02-1563	58	13	discuss	discuss	VERB
ajis02-1563	58	14	its	its	PRON
ajis02-1563	58	15	computational	computational	ADJ
ajis02-1563	58	16	intractability	intractability	NOUN
ajis02-1563	58	17	and	and	CCONJ
ajis02-1563	58	18	approaches	approach	NOUN
ajis02-1563	58	19	to	to	PART
ajis02-1563	58	20	approximate	approximate	VERB
ajis02-1563	58	21	it	it	PRON
ajis02-1563	58	22	.	.	PUNCT
ajis02-1563	59	1	an	an	DET
ajis02-1563	59	2	extensive	extensive	ADJ
ajis02-1563	59	3	literature	literature	NOUN
ajis02-1563	59	4	review	review	NOUN
ajis02-1563	59	5	of	of	ADP
ajis02-1563	59	6	the	the	DET
ajis02-1563	59	7	immunization	immunization	NOUN
ajis02-1563	59	8	problem	problem	NOUN
ajis02-1563	59	9	is	be	AUX
ajis02-1563	59	10	provided	provide	VERB
ajis02-1563	59	11	in	in	ADP
ajis02-1563	59	12	section	section	NOUN
ajis02-1563	59	13	3	3	NUM
ajis02-1563	59	14	.	.	PUNCT
ajis02-1563	60	1	we	we	PRON
ajis02-1563	60	2	propose	propose	VERB
ajis02-1563	60	3	our	our	PRON
ajis02-1563	60	4	algorithm	algorithm	NOUN
ajis02-1563	60	5	in	in	ADP
ajis02-1563	60	6	section	section	NOUN
ajis02-1563	60	7	4	4	NUM
ajis02-1563	60	8	along	along	ADP
ajis02-1563	60	9	with	with	ADP
ajis02-1563	60	10	its	its	PRON
ajis02-1563	60	11	approximation	approximation	NOUN
ajis02-1563	60	12	guarantees	guarantee	NOUN
ajis02-1563	60	13	and	and	CCONJ
ajis02-1563	60	14	complexity	complexity	NOUN
ajis02-1563	60	15	analysis	analysis	NOUN
ajis02-1563	60	16	.	.	PUNCT
ajis02-1563	61	1	section	section	NOUN
ajis02-1563	61	2	5	5	NUM
ajis02-1563	61	3	contains	contain	VERB
ajis02-1563	61	4	results	result	NOUN
ajis02-1563	61	5	of	of	ADP
ajis02-1563	61	6	experimentation	experimentation	NOUN
ajis02-1563	61	7	on	on	ADP
ajis02-1563	61	8	real	real	ADJ
ajis02-1563	61	9	world	world	NOUN
ajis02-1563	61	10	graphs	graph	NOUN
ajis02-1563	61	11	.	.	PUNCT
ajis02-1563	62	1	this	this	DET
ajis02-1563	62	2	section	section	NOUN
ajis02-1563	62	3	also	also	ADV
ajis02-1563	62	4	provides	provide	VERB
ajis02-1563	62	5	comparison	comparison	NOUN
ajis02-1563	62	6	of	of	ADP
ajis02-1563	62	7	performance	performance	NOUN
ajis02-1563	62	8	of	of	ADP
ajis02-1563	62	9	our	our	PRON
ajis02-1563	62	10	algorithm	algorithm	NOUN
ajis02-1563	62	11	with	with	ADP
ajis02-1563	62	12	other	other	ADJ
ajis02-1563	62	13	known	know	VERB
ajis02-1563	62	14	algorithms	algorithm	NOUN
ajis02-1563	62	15	.	.	PUNCT
ajis02-1563	63	1	afterwards	afterwards	ADV
ajis02-1563	63	2	we	we	PRON
ajis02-1563	63	3	conclude	conclude	VERB
ajis02-1563	63	4	with	with	ADP
ajis02-1563	63	5	a	a	DET
ajis02-1563	63	6	discussion	discussion	NOUN
ajis02-1563	63	7	on	on	ADP
ajis02-1563	63	8	future	future	ADJ
ajis02-1563	63	9	directions	direction	NOUN
ajis02-1563	63	10	.	.	PUNCT
ajis02-1563	64	1	a	a	DET
ajis02-1563	64	2	preliminary	preliminary	ADJ
ajis02-1563	64	3	version	version	NOUN
ajis02-1563	64	4	of	of	ADP
ajis02-1563	64	5	this	this	DET
ajis02-1563	64	6	paper	paper	NOUN
ajis02-1563	64	7	has	have	AUX
ajis02-1563	64	8	already	already	ADV
ajis02-1563	64	9	been	be	AUX
ajis02-1563	64	10	appeared	appear	VERB
ajis02-1563	64	11	in	in	ADP
ajis02-1563	64	12	(	(	PUNCT
ajis02-1563	64	13	ahmad	ahmad	PROPN
ajis02-1563	64	14	2016	2016	NUM
ajis02-1563	64	15	)	)	PUNCT
ajis02-1563	64	16	.	.	PUNCT
ajis02-1563	65	1	2	2	NUM
ajis02-1563	65	2	background	background	NOUN
ajis02-1563	65	3	as	as	SCONJ
ajis02-1563	65	4	argued	argue	VERB
ajis02-1563	65	5	earlier	early	ADV
ajis02-1563	65	6	,	,	PUNCT
ajis02-1563	65	7	the	the	DET
ajis02-1563	65	8	brute	brute	ADJ
ajis02-1563	65	9	-	-	PUNCT
ajis02-1563	65	10	force	force	NOUN
ajis02-1563	65	11	solution	solution	NOUN
ajis02-1563	65	12	,	,	PUNCT
ajis02-1563	65	13	that	that	PRON
ajis02-1563	65	14	checks	check	VERB
ajis02-1563	65	15	the	the	DET
ajis02-1563	65	16	eigendrop	eigendrop	NOUN
ajis02-1563	65	17	achieved	achieve	VERB
ajis02-1563	65	18	by	by	ADP
ajis02-1563	65	19	each	each	DET
ajis02-1563	65	20	possible	possible	ADJ
ajis02-1563	65	21	subset	subset	NOUN
ajis02-1563	65	22	of	of	ADP
ajis02-1563	65	23	size	size	NOUN
ajis02-1563	65	24	k	k	PROPN
ajis02-1563	65	25	and	and	CCONJ
ajis02-1563	65	26	selects	select	VERB
ajis02-1563	65	27	the	the	DET
ajis02-1563	65	28	subset	subset	NOUN
ajis02-1563	65	29	achieving	achieve	VERB
ajis02-1563	65	30	the	the	DET
ajis02-1563	65	31	largest	large	ADJ
ajis02-1563	65	32	eigendrop	eigendrop	NOUN
ajis02-1563	65	33	,	,	PUNCT
ajis02-1563	65	34	has	have	VERB
ajis02-1563	65	35	runtime	runtime	NOUN
ajis02-1563	65	36	𝑂	𝑂	PROPN
ajis02-1563	65	37	(	(	PUNCT
ajis02-1563	65	38	(	(	PUNCT
ajis02-1563	65	39	𝑛	𝑛	PROPN
ajis02-1563	65	40	𝑘	𝑘	NOUN
ajis02-1563	65	41	)	)	PUNCT
ajis02-1563	65	42	𝑚	𝑚	NOUN
ajis02-1563	65	43	)	)	PUNCT
ajis02-1563	65	44	,	,	PUNCT
ajis02-1563	65	45	where	where	SCONJ
ajis02-1563	65	46	m	m	NOUN
ajis02-1563	65	47	is	be	AUX
ajis02-1563	65	48	the	the	DET
ajis02-1563	65	49	number	number	NOUN
ajis02-1563	65	50	of	of	ADP
ajis02-1563	65	51	edges	edge	NOUN
ajis02-1563	65	52	in	in	ADP
ajis02-1563	65	53	the	the	DET
ajis02-1563	65	54	graph	graph	NOUN
ajis02-1563	65	55	.	.	PUNCT
ajis02-1563	66	1	this	this	DET
ajis02-1563	66	2	running	running	NOUN
ajis02-1563	66	3	time	time	NOUN
ajis02-1563	66	4	is	be	AUX
ajis02-1563	66	5	exponential	exponential	ADJ
ajis02-1563	66	6	in	in	ADP
ajis02-1563	66	7	size	size	NOUN
ajis02-1563	66	8	of	of	ADP
ajis02-1563	66	9	input	input	NOUN
ajis02-1563	66	10	(	(	PUNCT
ajis02-1563	66	11	k	k	NOUN
ajis02-1563	66	12	)	)	PUNCT
ajis02-1563	66	13	.	.	PUNCT
ajis02-1563	67	1	we	we	PRON
ajis02-1563	67	2	prove	prove	VERB
ajis02-1563	67	3	that	that	SCONJ
ajis02-1563	67	4	the	the	DET
ajis02-1563	67	5	problem	problem	NOUN
ajis02-1563	67	6	under	under	ADP
ajis02-1563	67	7	consideration	consideration	NOUN
ajis02-1563	67	8	is	be	AUX
ajis02-1563	67	9	np	np	NOUN
ajis02-1563	67	10	-	-	PUNCT
ajis02-1563	67	11	hard	hard	ADJ
ajis02-1563	67	12	.	.	PUNCT
ajis02-1563	68	1	proof	proof	NOUN
ajis02-1563	68	2	:	:	PUNCT
ajis02-1563	68	3	a	a	DET
ajis02-1563	68	4	simple	simple	ADJ
ajis02-1563	68	5	reduction	reduction	NOUN
ajis02-1563	68	6	from	from	ADP
ajis02-1563	68	7	minimum	minimum	ADJ
ajis02-1563	68	8	vertex	vertex	NOUN
ajis02-1563	68	9	cover	cover	NOUN
ajis02-1563	68	10	problem	problem	NOUN
ajis02-1563	68	11	goes	go	VERB
ajis02-1563	68	12	as	as	SCONJ
ajis02-1563	68	13	follows	follow	VERB
ajis02-1563	68	14	:	:	PUNCT
ajis02-1563	68	15	if	if	SCONJ
ajis02-1563	68	16	there	there	PRON
ajis02-1563	68	17	exist	exist	VERB
ajis02-1563	68	18	k	k	PROPN
ajis02-1563	68	19	vertices	vertex	NOUN
ajis02-1563	68	20	that	that	PRON
ajis02-1563	68	21	cover	cover	VERB
ajis02-1563	68	22	all	all	DET
ajis02-1563	68	23	the	the	DET
ajis02-1563	68	24	edges	edge	NOUN
ajis02-1563	68	25	in	in	ADP
ajis02-1563	68	26	the	the	DET
ajis02-1563	68	27	graph	graph	NOUN
ajis02-1563	68	28	,	,	PUNCT
ajis02-1563	68	29	then	then	ADV
ajis02-1563	68	30	from	from	ADP
ajis02-1563	68	31	the	the	DET
ajis02-1563	68	32	following	following	ADJ
ajis02-1563	68	33	fact	fact	NOUN
ajis02-1563	68	34	,	,	PUNCT
ajis02-1563	68	35	deleting	delete	VERB
ajis02-1563	68	36	those	those	DET
ajis02-1563	68	37	vertices	vertex	NOUN
ajis02-1563	68	38	will	will	AUX
ajis02-1563	68	39	imply	imply	VERB
ajis02-1563	68	40	that	that	SCONJ
ajis02-1563	68	41	λ1(a	λ1(a	PROPN
ajis02-1563	68	42	-	-	PUNCT
ajis02-1563	68	43	s	s	X
ajis02-1563	68	44	)	)	PUNCT
ajis02-1563	68	45	=	=	SYM
ajis02-1563	68	46	0	0	X
ajis02-1563	68	47	.	.	PUNCT
ajis02-1563	69	1	fact	fact	NOUN
ajis02-1563	69	2	1	1	NUM
ajis02-1563	69	3	:	:	PUNCT
ajis02-1563	69	4	empty	empty	ADJ
ajis02-1563	69	5	graph	graph	NOUN
ajis02-1563	69	6	(	(	PUNCT
ajis02-1563	69	7	graph	graph	NOUN
ajis02-1563	69	8	with	with	ADP
ajis02-1563	69	9	no	no	DET
ajis02-1563	69	10	edges	edge	NOUN
ajis02-1563	69	11	)	)	PUNCT
ajis02-1563	69	12	on	on	ADP
ajis02-1563	69	13	n	n	DET
ajis02-1563	69	14	vertices	vertex	NOUN
ajis02-1563	69	15	has	have	AUX
ajis02-1563	69	16	eigenvalue	eigenvalue	PROPN
ajis02-1563	69	17	zero	zero	NUM
ajis02-1563	69	18	with	with	ADP
ajis02-1563	69	19	multiplicity	multiplicity	NOUN
ajis02-1563	69	20	n.	n.	NOUN
ajis02-1563	69	21	conversely	conversely	ADV
ajis02-1563	69	22	if	if	SCONJ
ajis02-1563	69	23	there	there	PRON
ajis02-1563	69	24	exists	exist	VERB
ajis02-1563	69	25	a	a	DET
ajis02-1563	69	26	k	k	NOUN
ajis02-1563	69	27	-	-	PUNCT
ajis02-1563	69	28	set	set	VERB
ajis02-1563	69	29	s	s	NOUN
ajis02-1563	69	30	of	of	ADP
ajis02-1563	69	31	vertices	vertex	NOUN
ajis02-1563	69	32	such	such	ADJ
ajis02-1563	69	33	that	that	SCONJ
ajis02-1563	69	34	λ1(a	λ1(a	PROPN
ajis02-1563	69	35	-	-	PUNCT
ajis02-1563	69	36	s	s	X
ajis02-1563	69	37	)	)	PUNCT
ajis02-1563	69	38	=	=	SYM
ajis02-1563	69	39	0	0	NUM
ajis02-1563	69	40	,	,	PUNCT
ajis02-1563	69	41	then	then	ADV
ajis02-1563	69	42	s	s	VERB
ajis02-1563	69	43	must	must	AUX
ajis02-1563	69	44	be	be	AUX
ajis02-1563	69	45	a	a	DET
ajis02-1563	69	46	vertex	vertex	NOUN
ajis02-1563	69	47	cover	cover	NOUN
ajis02-1563	69	48	;	;	PUNCT
ajis02-1563	69	49	since	since	SCONJ
ajis02-1563	69	50	otherwise	otherwise	ADV
ajis02-1563	69	51	it	it	PRON
ajis02-1563	69	52	contradicts	contradict	VERB
ajis02-1563	69	53	the	the	DET
ajis02-1563	69	54	following	following	ADJ
ajis02-1563	69	55	implication	implication	NOUN
ajis02-1563	69	56	of	of	ADP
ajis02-1563	69	57	the	the	DET
ajis02-1563	69	58	perron	perron	PROPN
ajis02-1563	69	59	-	-	PUNCT
ajis02-1563	69	60	frobenius	frobenius	NOUN
ajis02-1563	69	61	theorem	theorem	NOUN
ajis02-1563	69	62	.	.	PUNCT
ajis02-1563	70	1	fact	fact	NOUN
ajis02-1563	70	2	2	2	NUM
ajis02-1563	70	3	:	:	PUNCT
ajis02-1563	70	4	(	(	PUNCT
ajis02-1563	70	5	serre	serre	X
ajis02-1563	70	6	2002	2002	NUM
ajis02-1563	70	7	)	)	PUNCT
ajis02-1563	70	8	deleting	delete	VERB
ajis02-1563	70	9	any	any	DET
ajis02-1563	70	10	edge	edge	NOUN
ajis02-1563	70	11	from	from	ADP
ajis02-1563	70	12	a	a	DET
ajis02-1563	70	13	simple	simple	ADJ
ajis02-1563	70	14	connected	connected	ADJ
ajis02-1563	70	15	graph	graph	NOUN
ajis02-1563	70	16	g	g	PRON
ajis02-1563	70	17	strictly	strictly	ADV
ajis02-1563	70	18	decreases	decrease	VERB
ajis02-1563	70	19	the	the	DET
ajis02-1563	70	20	largest	large	ADJ
ajis02-1563	70	21	eigenvalue	eigenvalue	NOUN
ajis02-1563	70	22	of	of	ADP
ajis02-1563	70	23	the	the	DET
ajis02-1563	70	24	corresponding	corresponding	ADJ
ajis02-1563	70	25	adjacency	adjacency	NOUN
ajis02-1563	70	26	matrix	matrix	NOUN
ajis02-1563	70	27	.	.	PUNCT
ajis02-1563	71	1	for	for	ADP
ajis02-1563	71	2	a	a	DET
ajis02-1563	71	3	reduction	reduction	NOUN
ajis02-1563	71	4	from	from	ADP
ajis02-1563	71	5	max	max	PROPN
ajis02-1563	71	6	independent	independent	ADJ
ajis02-1563	71	7	set	set	NOUN
ajis02-1563	71	8	problem	problem	NOUN
ajis02-1563	71	9	that	that	PRON
ajis02-1563	71	10	does	do	AUX
ajis02-1563	71	11	n't	not	PART
ajis02-1563	71	12	use	use	VERB
ajis02-1563	71	13	perron	perron	PROPN
ajis02-1563	71	14	-	-	PUNCT
ajis02-1563	71	15	frobenius	frobenius	NOUN
ajis02-1563	71	16	theorem	theorem	NOUN
ajis02-1563	71	17	see	see	VERB
ajis02-1563	71	18	appendix	appendix	NOUN
ajis02-1563	71	19	of	of	ADP
ajis02-1563	71	20	(	(	PUNCT
ajis02-1563	71	21	chen	chen	PROPN
ajis02-1563	71	22	2016	2016	NUM
ajis02-1563	71	23	)	)	PUNCT
ajis02-1563	71	24	.	.	PUNCT
ajis02-1563	72	1	although	although	SCONJ
ajis02-1563	72	2	problem	problem	NOUN
ajis02-1563	72	3	2	2	NUM
ajis02-1563	72	4	is	be	AUX
ajis02-1563	72	5	np	np	NOUN
ajis02-1563	72	6	-	-	PUNCT
ajis02-1563	72	7	hard	hard	ADJ
ajis02-1563	72	8	,	,	PUNCT
ajis02-1563	72	9	the	the	DET
ajis02-1563	72	10	following	follow	VERB
ajis02-1563	72	11	greedy	greedy	ADJ
ajis02-1563	72	12	algorithm	algorithm	NOUN
ajis02-1563	72	13	guarantees	guarantee	VERB
ajis02-1563	72	14	a	a	DET
ajis02-1563	72	15	(	(	PUNCT
ajis02-1563	72	16	1	1	NUM
ajis02-1563	72	17	−	−	PROPN
ajis02-1563	72	18	1	1	NUM
ajis02-1563	72	19	𝑒	𝑒	NOUN
ajis02-1563	72	20	)	)	PUNCT
ajis02-1563	72	21	-approximation	-approximation	NOUN
ajis02-1563	72	22	to	to	ADP
ajis02-1563	72	23	the	the	DET
ajis02-1563	72	24	optimal	optimal	ADJ
ajis02-1563	72	25	solution	solution	NOUN
ajis02-1563	72	26	to	to	ADP
ajis02-1563	72	27	problem	problem	NOUN
ajis02-1563	72	28	2	2	NUM
ajis02-1563	72	29	.	.	PUNCT
ajis02-1563	72	30	approximation	approximation	NOUN
ajis02-1563	72	31	guarantee	guarantee	NOUN
ajis02-1563	72	32	of	of	ADP
ajis02-1563	72	33	greedy-1	greedy-1	PROPN
ajis02-1563	72	34	follows	follow	VERB
ajis02-1563	72	35	from	from	ADP
ajis02-1563	72	36	theorem	theorem	ADJ
ajis02-1563	72	37	1	1	NUM
ajis02-1563	72	38	.	.	PUNCT
ajis02-1563	72	39	australasian	australasian	ADJ
ajis02-1563	72	40	journal	journal	NOUN
ajis02-1563	72	41	of	of	ADP
ajis02-1563	72	42	information	information	NOUN
ajis02-1563	72	43	systems	system	NOUN
ajis02-1563	72	44	ahmad	ahmad	PROPN
ajis02-1563	72	45	,	,	PUNCT
ajis02-1563	72	46	traiq	traiq	NOUN
ajis02-1563	72	47	,	,	PUNCT
ajis02-1563	72	48	shabbir	shabbir	PROPN
ajis02-1563	72	49	&	&	CCONJ
ajis02-1563	72	50	khan	khan	PROPN
ajis02-1563	72	51	2017	2017	NUM
ajis02-1563	72	52	,	,	PUNCT
ajis02-1563	72	53	vol	vol	NOUN
ajis02-1563	72	54	21	21	NUM
ajis02-1563	72	55	,	,	PUNCT
ajis02-1563	72	56	selected	select	VERB
ajis02-1563	72	57	papers	paper	NOUN
ajis02-1563	72	58	from	from	ADP
ajis02-1563	72	59	ausdm	ausdm	NOUN
ajis02-1563	72	60	spectral	spectral	ADJ
ajis02-1563	72	61	methods	method	NOUN
ajis02-1563	72	62	for	for	ADP
ajis02-1563	72	63	immunization	immunization	NOUN
ajis02-1563	72	64	of	of	ADP
ajis02-1563	72	65	large	large	ADJ
ajis02-1563	72	66	networks	network	NOUN
ajis02-1563	72	67	4	4	NUM
ajis02-1563	72	68	algorithm	algorithm	NOUN
ajis02-1563	72	69	1	1	NUM
ajis02-1563	72	70	:	:	PUNCT
ajis02-1563	72	71	greedy-1	greedy-1	PROPN
ajis02-1563	72	72	(	(	PUNCT
ajis02-1563	72	73	𝑮	𝑮	PROPN
ajis02-1563	72	74	,	,	PUNCT
ajis02-1563	72	75	𝒌	𝒌	ADJ
ajis02-1563	72	76	)	)	PUNCT
ajis02-1563	72	77	𝑆	𝑆	PROPN
ajis02-1563	72	78	←	←	PROPN
ajis02-1563	72	79	∅	∅	NOUN
ajis02-1563	72	80	𝑤ℎ𝑖𝑙𝑒	𝑤ℎ𝑖𝑙𝑒	NOUN
ajis02-1563	72	81	|𝑆|	|𝑆|	VERB
ajis02-1563	72	82	<	<	X
ajis02-1563	72	83	𝑘	𝑘	ADP
ajis02-1563	72	84	𝑣	𝑣	DET
ajis02-1563	72	85	←	←	PROPN
ajis02-1563	72	86	𝑎𝑟𝑔𝑚𝑎𝑥	𝑎𝑟𝑔𝑚𝑎𝑥	NOUN
ajis02-1563	72	87	v∈v∖s	v∈v∖s	PROPN
ajis02-1563	72	88	(	(	PUNCT
ajis02-1563	72	89	𝜆1(𝐴−𝑆∪{𝑣	𝜆1(𝐴−𝑆∪{𝑣	PROPN
ajis02-1563	72	90	}	}	PUNCT
ajis02-1563	72	91	)	)	PUNCT
ajis02-1563	72	92	)	)	PUNCT
ajis02-1563	73	1	𝑆	𝑆	PROPN
ajis02-1563	73	2	←	←	PROPN
ajis02-1563	73	3	𝑆	𝑆	PROPN
ajis02-1563	73	4	∪	∪	NOUN
ajis02-1563	73	5	{	{	PUNCT
ajis02-1563	73	6	𝑣	𝑣	NOUN
ajis02-1563	73	7	}	}	PUNCT
ajis02-1563	73	8	𝑟𝑒𝑡𝑢𝑟𝑛	𝑟𝑒𝑡𝑢𝑟𝑛	VERB
ajis02-1563	73	9	𝑆	𝑆	PROPN
ajis02-1563	73	10	theorem	theorem	VERB
ajis02-1563	73	11	1	1	NUM
ajis02-1563	73	12	:	:	PUNCT
ajis02-1563	73	13	(	(	PUNCT
ajis02-1563	73	14	nemhauser	nemhauser	NOUN
ajis02-1563	73	15	1978	1978	NUM
ajis02-1563	73	16	)	)	PUNCT
ajis02-1563	73	17	let	let	VERB
ajis02-1563	73	18	f	f	PRON
ajis02-1563	73	19	be	be	AUX
ajis02-1563	73	20	a	a	DET
ajis02-1563	73	21	non	non	ADJ
ajis02-1563	73	22	-	-	ADJ
ajis02-1563	73	23	negative	negative	ADJ
ajis02-1563	73	24	,	,	PUNCT
ajis02-1563	73	25	monotone	monotone	ADJ
ajis02-1563	73	26	and	and	CCONJ
ajis02-1563	73	27	sub	sub	ADJ
ajis02-1563	73	28	-	-	ADJ
ajis02-1563	73	29	modular	modular	ADJ
ajis02-1563	73	30	function	function	NOUN
ajis02-1563	73	31	,	,	PUNCT
ajis02-1563	73	32	𝑓	𝑓	X
ajis02-1563	73	33	:	:	PUNCT
ajis02-1563	73	34	2𝛺	2𝛺	PROPN
ajis02-1563	73	35	→	→	SYM
ajis02-1563	73	36	ℝ.	ℝ.	PROPN
ajis02-1563	73	37	suppose	suppose	VERB
ajis02-1563	73	38	𝔸	𝔸	PROPN
ajis02-1563	73	39	is	be	AUX
ajis02-1563	73	40	an	an	DET
ajis02-1563	73	41	algorithm	algorithm	NOUN
ajis02-1563	73	42	,	,	PUNCT
ajis02-1563	73	43	that	that	PRON
ajis02-1563	73	44	choose	choose	VERB
ajis02-1563	73	45	a	a	DET
ajis02-1563	73	46	k	k	PROPN
ajis02-1563	73	47	elements	element	NOUN
ajis02-1563	73	48	set	set	VERB
ajis02-1563	73	49	s	s	PRON
ajis02-1563	73	50	by	by	ADP
ajis02-1563	73	51	adding	add	VERB
ajis02-1563	73	52	an	an	DET
ajis02-1563	73	53	element	element	NOUN
ajis02-1563	73	54	u	u	NOUN
ajis02-1563	73	55	at	at	ADP
ajis02-1563	73	56	each	each	DET
ajis02-1563	73	57	step	step	NOUN
ajis02-1563	73	58	such	such	ADJ
ajis02-1563	73	59	that	that	SCONJ
ajis02-1563	73	60	𝑢	𝑢	ADJ
ajis02-1563	73	61	=	=	NOUN
ajis02-1563	73	62	𝑎𝑟𝑔	𝑎𝑟𝑔	VERB
ajis02-1563	73	63	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
ajis02-1563	73	64	𝑥∈𝛺∖	𝑥∈𝛺∖	ADJ
ajis02-1563	73	65	𝑆	𝑆	PROPN
ajis02-1563	73	66	𝑓(𝑆	𝑓(𝑆	PROPN
ajis02-1563	73	67	∪	∪	VERB
ajis02-1563	73	68	{	{	PUNCT
ajis02-1563	73	69	𝑥	𝑥	NOUN
ajis02-1563	73	70	}	}	PUNCT
ajis02-1563	73	71	)	)	PUNCT
ajis02-1563	73	72	.	.	PUNCT
ajis02-1563	74	1	then	then	ADV
ajis02-1563	74	2	𝔸	𝔸	PROPN
ajis02-1563	74	3	is	be	AUX
ajis02-1563	74	4	a	a	DET
ajis02-1563	74	5	(	(	PUNCT
ajis02-1563	74	6	1	1	NUM
ajis02-1563	74	7	−	−	PROPN
ajis02-1563	74	8	1	1	NUM
ajis02-1563	74	9	𝑒	𝑒	NOUN
ajis02-1563	74	10	)	)	PUNCT
ajis02-1563	74	11	-approximate	-approximate	NOUN
ajis02-1563	74	12	algorithm	algorithm	NOUN
ajis02-1563	74	13	.	.	PUNCT
ajis02-1563	75	1	in	in	ADP
ajis02-1563	75	2	(	(	PUNCT
ajis02-1563	75	3	chen	chen	PROPN
ajis02-1563	75	4	2016	2016	NUM
ajis02-1563	75	5	)	)	PUNCT
ajis02-1563	75	6	each	each	DET
ajis02-1563	75	7	subset	subset	VERB
ajis02-1563	75	8	was	be	AUX
ajis02-1563	75	9	assigned	assign	VERB
ajis02-1563	75	10	a	a	DET
ajis02-1563	75	11	score	score	NOUN
ajis02-1563	75	12	,	,	PUNCT
ajis02-1563	75	13	called	call	VERB
ajis02-1563	75	14	shield	shield	NOUN
ajis02-1563	75	15	-	-	PUNCT
ajis02-1563	75	16	value	value	NOUN
ajis02-1563	75	17	that	that	PRON
ajis02-1563	75	18	was	be	AUX
ajis02-1563	75	19	meant	mean	VERB
ajis02-1563	75	20	to	to	PART
ajis02-1563	75	21	approximate	approximate	VERB
ajis02-1563	75	22	eigendrop	eigendrop	NOUN
ajis02-1563	75	23	achieved	achieve	VERB
ajis02-1563	75	24	by	by	ADP
ajis02-1563	75	25	that	that	DET
ajis02-1563	75	26	set	set	NOUN
ajis02-1563	75	27	.	.	PUNCT
ajis02-1563	76	1	for	for	ADP
ajis02-1563	76	2	a	a	DET
ajis02-1563	76	3	set	set	NOUN
ajis02-1563	76	4	s	s	NOUN
ajis02-1563	76	5	of	of	ADP
ajis02-1563	76	6	size	size	NOUN
ajis02-1563	76	7	k	k	PROPN
ajis02-1563	76	8	,	,	PUNCT
ajis02-1563	76	9	shield	shield	NOUN
ajis02-1563	76	10	value	value	NOUN
ajis02-1563	76	11	,	,	PUNCT
ajis02-1563	76	12	sv(s	sv(s	NUM
ajis02-1563	76	13	)	)	PUNCT
ajis02-1563	76	14	can	can	AUX
ajis02-1563	76	15	be	be	AUX
ajis02-1563	76	16	computed	compute	VERB
ajis02-1563	76	17	in	in	ADP
ajis02-1563	76	18	o(k2	o(k2	NOUN
ajis02-1563	76	19	)	)	PUNCT
ajis02-1563	76	20	when	when	SCONJ
ajis02-1563	76	21	the	the	DET
ajis02-1563	76	22	eigenvector	eigenvector	NOUN
ajis02-1563	76	23	corresponding	correspond	VERB
ajis02-1563	76	24	to	to	ADP
ajis02-1563	76	25	largest	large	ADJ
ajis02-1563	76	26	eigenvalue	eigenvalue	NOUN
ajis02-1563	76	27	is	be	AUX
ajis02-1563	76	28	known	know	VERB
ajis02-1563	76	29	.	.	PUNCT
ajis02-1563	77	1	hence	hence	ADV
ajis02-1563	77	2	,	,	PUNCT
ajis02-1563	77	3	the	the	DET
ajis02-1563	77	4	straightforward	straightforward	ADJ
ajis02-1563	77	5	method	method	NOUN
ajis02-1563	77	6	of	of	ADP
ajis02-1563	77	7	finding	find	VERB
ajis02-1563	77	8	the	the	DET
ajis02-1563	77	9	set	set	NOUN
ajis02-1563	77	10	with	with	ADP
ajis02-1563	77	11	largest	large	ADJ
ajis02-1563	77	12	shield	shield	NOUN
ajis02-1563	77	13	value	value	NOUN
ajis02-1563	77	14	takes	take	VERB
ajis02-1563	77	15	𝑂	𝑂	PROPN
ajis02-1563	77	16	(	(	PUNCT
ajis02-1563	77	17	(	(	PUNCT
ajis02-1563	77	18	𝑛	𝑛	PROPN
ajis02-1563	77	19	𝑘	𝑘	PROPN
ajis02-1563	77	20	)	)	PUNCT
ajis02-1563	77	21	𝑘2	𝑘2	PROPN
ajis02-1563	77	22	)	)	PUNCT
ajis02-1563	77	23	time	time	NOUN
ajis02-1563	77	24	.	.	PUNCT
ajis02-1563	78	1	using	use	VERB
ajis02-1563	78	2	the	the	DET
ajis02-1563	78	3	fact	fact	NOUN
ajis02-1563	78	4	that	that	SCONJ
ajis02-1563	78	5	the	the	DET
ajis02-1563	78	6	objective	objective	ADJ
ajis02-1563	78	7	function	function	NOUN
ajis02-1563	78	8	based	base	VERB
ajis02-1563	78	9	on	on	ADP
ajis02-1563	78	10	shield	shield	NOUN
ajis02-1563	78	11	value	value	NOUN
ajis02-1563	78	12	is	be	AUX
ajis02-1563	78	13	sub	sub	ADJ
ajis02-1563	78	14	-	-	ADJ
ajis02-1563	78	15	modular	modular	ADJ
ajis02-1563	78	16	,	,	PUNCT
ajis02-1563	78	17	(	(	PUNCT
ajis02-1563	78	18	chen	chen	PROPN
ajis02-1563	78	19	2016	2016	NUM
ajis02-1563	78	20	)	)	PUNCT
ajis02-1563	78	21	gave	give	VERB
ajis02-1563	78	22	a	a	DET
ajis02-1563	78	23	greedy	greedy	ADJ
ajis02-1563	78	24	algorithm	algorithm	NOUN
ajis02-1563	78	25	with	with	ADP
ajis02-1563	78	26	runtime	runtime	NOUN
ajis02-1563	78	27	o(nk2+m	o(nk2+m	PROPN
ajis02-1563	78	28	)	)	PUNCT
ajis02-1563	78	29	.	.	PUNCT
ajis02-1563	79	1	by	by	ADP
ajis02-1563	79	2	theorem	theorem	NOUN
ajis02-1563	79	3	1	1	NUM
ajis02-1563	79	4	their	their	PRON
ajis02-1563	79	5	algorithm	algorithm	NOUN
ajis02-1563	79	6	guarantees	guarantee	VERB
ajis02-1563	79	7	a	a	DET
ajis02-1563	79	8	(	(	PUNCT
ajis02-1563	79	9	1	1	NUM
ajis02-1563	79	10	−	−	PROPN
ajis02-1563	79	11	1	1	NUM
ajis02-1563	79	12	𝑒	𝑒	NOUN
ajis02-1563	79	13	)	)	PUNCT
ajis02-1563	79	14	-approximation	-approximation	NOUN
ajis02-1563	79	15	to	to	ADP
ajis02-1563	79	16	the	the	DET
ajis02-1563	79	17	optimal	optimal	ADJ
ajis02-1563	79	18	shield	shield	NOUN
ajis02-1563	79	19	value	value	NOUN
ajis02-1563	79	20	.	.	PUNCT
ajis02-1563	80	1	3	3	NUM
ajis02-1563	80	2	related	relate	VERB
ajis02-1563	80	3	work	work	NOUN
ajis02-1563	80	4	while	while	SCONJ
ajis02-1563	80	5	the	the	DET
ajis02-1563	80	6	focus	focus	NOUN
ajis02-1563	80	7	of	of	ADP
ajis02-1563	80	8	this	this	DET
ajis02-1563	80	9	paper	paper	NOUN
ajis02-1563	80	10	is	be	AUX
ajis02-1563	80	11	to	to	PART
ajis02-1563	80	12	target	target	VERB
ajis02-1563	80	13	node	node	ADJ
ajis02-1563	80	14	immunization	immunization	NOUN
ajis02-1563	80	15	problem	problem	NOUN
ajis02-1563	80	16	using	use	VERB
ajis02-1563	80	17	spectral	spectral	ADJ
ajis02-1563	80	18	graph	graph	NOUN
ajis02-1563	80	19	theoretic	theoretic	ADJ
ajis02-1563	80	20	techniques	technique	NOUN
ajis02-1563	80	21	,	,	PUNCT
ajis02-1563	80	22	there	there	PRON
ajis02-1563	80	23	is	be	VERB
ajis02-1563	80	24	vast	vast	ADJ
ajis02-1563	80	25	amount	amount	NOUN
ajis02-1563	80	26	of	of	ADP
ajis02-1563	80	27	literature	literature	NOUN
ajis02-1563	80	28	on	on	ADP
ajis02-1563	80	29	this	this	DET
ajis02-1563	80	30	problem	problem	NOUN
ajis02-1563	80	31	with	with	ADP
ajis02-1563	80	32	approaches	approach	NOUN
ajis02-1563	80	33	from	from	ADP
ajis02-1563	80	34	diverse	diverse	ADJ
ajis02-1563	80	35	areas	area	NOUN
ajis02-1563	80	36	of	of	ADP
ajis02-1563	80	37	the	the	DET
ajis02-1563	80	38	subject	subject	NOUN
ajis02-1563	80	39	.	.	PUNCT
ajis02-1563	81	1	initially	initially	ADV
ajis02-1563	81	2	in	in	ADP
ajis02-1563	81	3	2003	2003	NUM
ajis02-1563	81	4	brieseneister	brieseneister	NOUN
ajis02-1563	81	5	,	,	PUNCT
ajis02-1563	81	6	lincoln	lincoln	PROPN
ajis02-1563	81	7	and	and	CCONJ
ajis02-1563	81	8	porras	porras	PROPN
ajis02-1563	81	9	(	(	PUNCT
ajis02-1563	81	10	briesemeister	briesemeister	NOUN
ajis02-1563	81	11	2003	2003	NUM
ajis02-1563	81	12	)	)	PUNCT
ajis02-1563	81	13	studied	study	VERB
ajis02-1563	81	14	the	the	DET
ajis02-1563	81	15	propagation	propagation	NOUN
ajis02-1563	81	16	styles	style	NOUN
ajis02-1563	81	17	of	of	ADP
ajis02-1563	81	18	viruses	virus	NOUN
ajis02-1563	81	19	in	in	ADP
ajis02-1563	81	20	communication	communication	NOUN
ajis02-1563	81	21	networks	network	NOUN
ajis02-1563	81	22	.	.	PUNCT
ajis02-1563	82	1	along	along	ADP
ajis02-1563	82	2	with	with	ADP
ajis02-1563	82	3	this	this	PRON
ajis02-1563	82	4	,	,	PUNCT
ajis02-1563	82	5	the	the	DET
ajis02-1563	82	6	effects	effect	NOUN
ajis02-1563	82	7	of	of	ADP
ajis02-1563	82	8	graph	graph	NOUN
ajis02-1563	82	9	topology	topology	NOUN
ajis02-1563	82	10	in	in	ADP
ajis02-1563	82	11	the	the	DET
ajis02-1563	82	12	spread	spread	NOUN
ajis02-1563	82	13	of	of	ADP
ajis02-1563	82	14	an	an	DET
ajis02-1563	82	15	epidemic	epidemic	NOUN
ajis02-1563	82	16	are	be	AUX
ajis02-1563	82	17	described	describe	VERB
ajis02-1563	82	18	in	in	ADP
ajis02-1563	82	19	(	(	PUNCT
ajis02-1563	82	20	ganesh	ganesh	NOUN
ajis02-1563	82	21	2005	2005	NUM
ajis02-1563	82	22	)	)	PUNCT
ajis02-1563	82	23	and	and	CCONJ
ajis02-1563	82	24	the	the	DET
ajis02-1563	82	25	conditions	condition	NOUN
ajis02-1563	82	26	under	under	ADP
ajis02-1563	82	27	which	which	PRON
ajis02-1563	82	28	an	an	DET
ajis02-1563	82	29	epidemic	epidemic	NOUN
ajis02-1563	82	30	will	will	AUX
ajis02-1563	82	31	eventually	eventually	ADV
ajis02-1563	82	32	die	die	VERB
ajis02-1563	82	33	out	out	ADP
ajis02-1563	82	34	are	be	AUX
ajis02-1563	82	35	discussed	discuss	VERB
ajis02-1563	82	36	.	.	PUNCT
ajis02-1563	83	1	similarly	similarly	ADV
ajis02-1563	83	2	chakrabarti	chakrabarti	VERB
ajis02-1563	83	3	et	et	PROPN
ajis02-1563	83	4	.	.	PUNCT
ajis02-1563	84	1	al	al	PROPN
ajis02-1563	84	2	in	in	ADP
ajis02-1563	84	3	(	(	PUNCT
ajis02-1563	84	4	chakrabarti	chakrabarti	PROPN
ajis02-1563	84	5	2008	2008	NUM
ajis02-1563	84	6	)	)	PUNCT
ajis02-1563	84	7	devise	devise	VERB
ajis02-1563	84	8	a	a	DET
ajis02-1563	84	9	nonlinear	nonlinear	ADJ
ajis02-1563	84	10	dynamical	dynamical	ADJ
ajis02-1563	84	11	system	system	NOUN
ajis02-1563	84	12	(	(	PUNCT
ajis02-1563	84	13	nlds	nld	NOUN
ajis02-1563	84	14	)	)	PUNCT
ajis02-1563	84	15	to	to	PART
ajis02-1563	84	16	model	model	VERB
ajis02-1563	84	17	virus	virus	NOUN
ajis02-1563	84	18	propagation	propagation	NOUN
ajis02-1563	84	19	in	in	ADP
ajis02-1563	84	20	communication	communication	NOUN
ajis02-1563	84	21	networks	network	NOUN
ajis02-1563	84	22	.	.	PUNCT
ajis02-1563	85	1	they	they	PRON
ajis02-1563	85	2	use	use	VERB
ajis02-1563	85	3	the	the	DET
ajis02-1563	85	4	idea	idea	NOUN
ajis02-1563	85	5	of	of	ADP
ajis02-1563	85	6	birth	birth	NOUN
ajis02-1563	85	7	rate	rate	NOUN
ajis02-1563	85	8	β	β	NOUN
ajis02-1563	85	9	,	,	PUNCT
ajis02-1563	85	10	death	death	NOUN
ajis02-1563	85	11	rate	rate	NOUN
ajis02-1563	85	12	δ	δ	PROPN
ajis02-1563	85	13	,	,	PUNCT
ajis02-1563	85	14	and	and	CCONJ
ajis02-1563	85	15	epidemic	epidemic	NOUN
ajis02-1563	85	16	threshold	threshold	NOUN
ajis02-1563	85	17	τ	τ	PROPN
ajis02-1563	85	18	,	,	PUNCT
ajis02-1563	85	19	for	for	ADP
ajis02-1563	85	20	a	a	DET
ajis02-1563	85	21	virus	virus	NOUN
ajis02-1563	85	22	attack	attack	NOUN
ajis02-1563	85	23	where	where	SCONJ
ajis02-1563	85	24	birth	birth	NOUN
ajis02-1563	85	25	rate	rate	NOUN
ajis02-1563	85	26	is	be	AUX
ajis02-1563	85	27	the	the	DET
ajis02-1563	85	28	rate	rate	NOUN
ajis02-1563	85	29	with	with	ADP
ajis02-1563	85	30	which	which	PRON
ajis02-1563	85	31	infection	infection	NOUN
ajis02-1563	85	32	propagates	propagate	VERB
ajis02-1563	85	33	,	,	PUNCT
ajis02-1563	85	34	death	death	NOUN
ajis02-1563	85	35	rate	rate	NOUN
ajis02-1563	85	36	is	be	AUX
ajis02-1563	85	37	the	the	DET
ajis02-1563	85	38	node	node	ADJ
ajis02-1563	85	39	curing	curing	NOUN
ajis02-1563	85	40	rate	rate	NOUN
ajis02-1563	85	41	and	and	CCONJ
ajis02-1563	85	42	epidemic	epidemic	NOUN
ajis02-1563	85	43	threshold	threshold	NOUN
ajis02-1563	85	44	is	be	AUX
ajis02-1563	85	45	a	a	DET
ajis02-1563	85	46	value	value	NOUN
ajis02-1563	85	47	such	such	ADJ
ajis02-1563	85	48	that	that	SCONJ
ajis02-1563	85	49	if	if	SCONJ
ajis02-1563	85	50	𝛽	𝛽	NOUN
ajis02-1563	85	51	𝛿	𝛿	X
ajis02-1563	85	52	<	<	X
ajis02-1563	85	53	𝜏	𝜏	NOUN
ajis02-1563	85	54	,	,	PUNCT
ajis02-1563	85	55	infection	infection	NOUN
ajis02-1563	85	56	will	will	AUX
ajis02-1563	85	57	die	die	VERB
ajis02-1563	85	58	out	out	ADP
ajis02-1563	85	59	quickly	quickly	ADV
ajis02-1563	85	60	else	else	ADV
ajis02-1563	85	61	if	if	SCONJ
ajis02-1563	85	62	𝛽	𝛽	NOUN
ajis02-1563	85	63	𝛿	𝛿	X
ajis02-1563	85	64	>	>	X
ajis02-1563	85	65	𝜏	𝜏	DET
ajis02-1563	85	66	infection	infection	NOUN
ajis02-1563	85	67	will	will	AUX
ajis02-1563	85	68	survive	survive	VERB
ajis02-1563	85	69	and	and	CCONJ
ajis02-1563	85	70	will	will	AUX
ajis02-1563	85	71	result	result	VERB
ajis02-1563	85	72	in	in	ADP
ajis02-1563	85	73	an	an	DET
ajis02-1563	85	74	epidemic	epidemic	NOUN
ajis02-1563	85	75	.	.	PUNCT
ajis02-1563	86	1	virus	virus	NOUN
ajis02-1563	86	2	propagation	propagation	NOUN
ajis02-1563	86	3	is	be	AUX
ajis02-1563	86	4	studied	study	VERB
ajis02-1563	86	5	in	in	ADP
ajis02-1563	86	6	both	both	CCONJ
ajis02-1563	86	7	directed	direct	VERB
ajis02-1563	86	8	and	and	CCONJ
ajis02-1563	86	9	undirected	undirected	ADJ
ajis02-1563	86	10	graphs	graph	NOUN
ajis02-1563	86	11	.	.	PUNCT
ajis02-1563	87	1	for	for	ADP
ajis02-1563	87	2	undirected	undirected	ADJ
ajis02-1563	87	3	graphs	graph	NOUN
ajis02-1563	87	4	,	,	PUNCT
ajis02-1563	87	5	they	they	PRON
ajis02-1563	87	6	prove	prove	VERB
ajis02-1563	87	7	that	that	SCONJ
ajis02-1563	87	8	epidemic	epidemic	NOUN
ajis02-1563	87	9	threshold	threshold	NOUN
ajis02-1563	87	10	τ	τ	PROPN
ajis02-1563	87	11	equals	equal	VERB
ajis02-1563	87	12	1	1	NUM
ajis02-1563	87	13	/	/	SYM
ajis02-1563	87	14	λ	λ	NOUN
ajis02-1563	87	15	,	,	PUNCT
ajis02-1563	87	16	where	where	SCONJ
ajis02-1563	87	17	λ	λ	PROPN
ajis02-1563	87	18	is	be	AUX
ajis02-1563	87	19	the	the	DET
ajis02-1563	87	20	largest	large	ADJ
ajis02-1563	87	21	eigenvalue	eigenvalue	NOUN
ajis02-1563	87	22	of	of	ADP
ajis02-1563	87	23	the	the	DET
ajis02-1563	87	24	graph	graph	NOUN
ajis02-1563	87	25	.	.	PUNCT
ajis02-1563	88	1	thus	thus	ADV
ajis02-1563	88	2	for	for	ADP
ajis02-1563	88	3	a	a	DET
ajis02-1563	88	4	given	give	VERB
ajis02-1563	88	5	undirected	undirected	ADJ
ajis02-1563	88	6	graph	graph	NOUN
ajis02-1563	88	7	,	,	PUNCT
ajis02-1563	88	8	if	if	SCONJ
ajis02-1563	88	9	β	β	X
ajis02-1563	88	10	/	/	SYM
ajis02-1563	88	11	δ>1	δ>1	NOUN
ajis02-1563	88	12	/	/	SYM
ajis02-1563	88	13	λ	λ	PROPN
ajis02-1563	88	14	,	,	PUNCT
ajis02-1563	88	15	then	then	ADV
ajis02-1563	88	16	the	the	DET
ajis02-1563	88	17	epidemic	epidemic	NOUN
ajis02-1563	88	18	will	will	AUX
ajis02-1563	88	19	die	die	VERB
ajis02-1563	88	20	out	out	ADP
ajis02-1563	88	21	eventually	eventually	ADV
ajis02-1563	88	22	.	.	PUNCT
ajis02-1563	89	1	but	but	CCONJ
ajis02-1563	89	2	none	none	NOUN
ajis02-1563	89	3	of	of	ADP
ajis02-1563	89	4	these	these	PRON
ajis02-1563	89	5	specifically	specifically	ADV
ajis02-1563	89	6	discuss	discuss	VERB
ajis02-1563	89	7	the	the	DET
ajis02-1563	89	8	graph	graph	NOUN
ajis02-1563	89	9	immunization	immunization	NOUN
ajis02-1563	89	10	problem	problem	NOUN
ajis02-1563	89	11	.	.	PUNCT
ajis02-1563	90	1	afterwards	afterwards	ADV
ajis02-1563	90	2	the	the	DET
ajis02-1563	90	3	problem	problem	NOUN
ajis02-1563	90	4	is	be	AUX
ajis02-1563	90	5	studied	study	VERB
ajis02-1563	90	6	using	use	VERB
ajis02-1563	90	7	the	the	DET
ajis02-1563	90	8	edge	edge	NOUN
ajis02-1563	90	9	manipulation	manipulation	NOUN
ajis02-1563	90	10	scheme	scheme	NOUN
ajis02-1563	90	11	.	.	PUNCT
ajis02-1563	91	1	in	in	ADP
ajis02-1563	91	2	(	(	PUNCT
ajis02-1563	91	3	kuhlman	kuhlman	PROPN
ajis02-1563	91	4	2013	2013	NUM
ajis02-1563	91	5	)	)	PUNCT
ajis02-1563	91	6	dynamical	dynamical	ADJ
ajis02-1563	91	7	systems	system	NOUN
ajis02-1563	91	8	are	be	AUX
ajis02-1563	91	9	used	use	VERB
ajis02-1563	91	10	to	to	PART
ajis02-1563	91	11	delete	delete	VERB
ajis02-1563	91	12	appropriate	appropriate	ADJ
ajis02-1563	91	13	edges	edge	NOUN
ajis02-1563	91	14	to	to	PART
ajis02-1563	91	15	minimize	minimize	VERB
ajis02-1563	91	16	contagion	contagion	NOUN
ajis02-1563	91	17	spread	spread	NOUN
ajis02-1563	91	18	.	.	PUNCT
ajis02-1563	92	1	while	while	SCONJ
ajis02-1563	92	2	tong	tong	PROPN
ajis02-1563	92	3	et	et	PROPN
ajis02-1563	92	4	al	al	PROPN
ajis02-1563	92	5	.	.	PUNCT
ajis02-1563	93	1	in	in	ADP
ajis02-1563	93	2	(	(	PUNCT
ajis02-1563	93	3	tong	tong	PROPN
ajis02-1563	93	4	2012	2012	NUM
ajis02-1563	93	5	)	)	PUNCT
ajis02-1563	93	6	remove	remove	VERB
ajis02-1563	93	7	k	k	PROPN
ajis02-1563	93	8	edges	edge	NOUN
ajis02-1563	93	9	from	from	ADP
ajis02-1563	93	10	the	the	DET
ajis02-1563	93	11	graph	graph	NOUN
ajis02-1563	93	12	in	in	ADP
ajis02-1563	93	13	a	a	DET
ajis02-1563	93	14	manner	manner	NOUN
ajis02-1563	93	15	that	that	PRON
ajis02-1563	93	16	eigendrop	eigendrop	NOUN
ajis02-1563	93	17	(	(	PUNCT
ajis02-1563	93	18	difference	difference	NOUN
ajis02-1563	93	19	in	in	ADP
ajis02-1563	93	20	largest	large	ADJ
ajis02-1563	93	21	eigenvalues	eigenvalue	NOUN
ajis02-1563	93	22	of	of	ADP
ajis02-1563	93	23	original	original	ADJ
ajis02-1563	93	24	and	and	CCONJ
ajis02-1563	93	25	resultant	resultant	NOUN
ajis02-1563	93	26	graphs	graph	NOUN
ajis02-1563	93	27	)	)	PUNCT
ajis02-1563	93	28	is	be	AUX
ajis02-1563	93	29	maximized	maximize	VERB
ajis02-1563	93	30	.	.	PUNCT
ajis02-1563	94	1	for	for	ADP
ajis02-1563	94	2	this	this	DET
ajis02-1563	94	3	edges	edge	NOUN
ajis02-1563	94	4	are	be	AUX
ajis02-1563	94	5	selected	select	VERB
ajis02-1563	94	6	on	on	ADP
ajis02-1563	94	7	the	the	DET
ajis02-1563	94	8	basis	basis	NOUN
ajis02-1563	94	9	of	of	ADP
ajis02-1563	94	10	left	left	ADJ
ajis02-1563	94	11	and	and	CCONJ
ajis02-1563	94	12	right	right	ADJ
ajis02-1563	94	13	eigenvectors	eigenvector	NOUN
ajis02-1563	94	14	of	of	ADP
ajis02-1563	94	15	leading	lead	VERB
ajis02-1563	94	16	eigenvalue	eigenvalue	NOUN
ajis02-1563	94	17	of	of	ADP
ajis02-1563	94	18	the	the	DET
ajis02-1563	94	19	graph	graph	NOUN
ajis02-1563	94	20	such	such	ADJ
ajis02-1563	94	21	that	that	PRON
ajis02-1563	94	22	for	for	SCONJ
ajis02-1563	94	23	each	each	DET
ajis02-1563	94	24	edge	edge	NOUN
ajis02-1563	94	25	ex	ex	NOUN
ajis02-1563	94	26	,	,	PUNCT
ajis02-1563	94	27	score(ex	score(ex	NOUN
ajis02-1563	94	28	)	)	PUNCT
ajis02-1563	94	29	is	be	AUX
ajis02-1563	94	30	the	the	DET
ajis02-1563	94	31	dot	dot	NOUN
ajis02-1563	94	32	product	product	NOUN
ajis02-1563	94	33	of	of	ADP
ajis02-1563	94	34	the	the	DET
ajis02-1563	94	35	left	left	ADJ
ajis02-1563	94	36	and	and	CCONJ
ajis02-1563	94	37	right	right	ADJ
ajis02-1563	94	38	eigenvectors	eigenvector	NOUN
ajis02-1563	94	39	of	of	ADP
ajis02-1563	94	40	leading	lead	VERB
ajis02-1563	94	41	eigenvalue	eigenvalue	NOUN
ajis02-1563	94	42	of	of	ADP
ajis02-1563	94	43	the	the	DET
ajis02-1563	94	44	adjacency	adjacency	NOUN
ajis02-1563	94	45	matrix	matrix	NOUN
ajis02-1563	94	46	of	of	ADP
ajis02-1563	94	47	a.	a.	NOUN
ajis02-1563	94	48	graph	graph	NOUN
ajis02-1563	94	49	vulnerability	vulnerability	NOUN
ajis02-1563	94	50	is	be	AUX
ajis02-1563	94	51	defined	define	VERB
ajis02-1563	94	52	as	as	ADP
ajis02-1563	94	53	measure	measure	NOUN
ajis02-1563	94	54	of	of	ADP
ajis02-1563	94	55	how	how	SCONJ
ajis02-1563	94	56	much	much	ADJ
ajis02-1563	94	57	a	a	DET
ajis02-1563	94	58	graph	graph	NOUN
ajis02-1563	94	59	is	be	AUX
ajis02-1563	94	60	likely	likely	ADJ
ajis02-1563	94	61	to	to	PART
ajis02-1563	94	62	be	be	AUX
ajis02-1563	94	63	affected	affect	VERB
ajis02-1563	94	64	by	by	ADP
ajis02-1563	94	65	a	a	DET
ajis02-1563	94	66	virus	virus	NOUN
ajis02-1563	94	67	attack	attack	NOUN
ajis02-1563	94	68	.	.	PUNCT
ajis02-1563	95	1	as	as	ADP
ajis02-1563	95	2	in	in	ADP
ajis02-1563	95	3	(	(	PUNCT
ajis02-1563	95	4	tong	tong	PROPN
ajis02-1563	95	5	2012	2012	NUM
ajis02-1563	95	6	)	)	PUNCT
ajis02-1563	95	7	,	,	PUNCT
ajis02-1563	95	8	the	the	DET
ajis02-1563	95	9	largest	large	ADJ
ajis02-1563	95	10	eigenvalue	eigenvalue	NOUN
ajis02-1563	95	11	is	be	AUX
ajis02-1563	95	12	selected	select	VERB
ajis02-1563	95	13	as	as	ADP
ajis02-1563	95	14	a	a	DET
ajis02-1563	95	15	measure	measure	NOUN
ajis02-1563	95	16	of	of	ADP
ajis02-1563	95	17	graph	graph	NOUN
ajis02-1563	95	18	vulnerability	vulnerability	NOUN
ajis02-1563	95	19	,	,	PUNCT
ajis02-1563	95	20	in	in	ADP
ajis02-1563	95	21	(	(	PUNCT
ajis02-1563	95	22	chen	chen	PROPN
ajis02-1563	95	23	2016	2016	NUM
ajis02-1563	95	24	)	)	PUNCT
ajis02-1563	95	25	they	they	PRON
ajis02-1563	95	26	also	also	ADV
ajis02-1563	95	27	use	use	VERB
ajis02-1563	95	28	largest	large	ADJ
ajis02-1563	95	29	eigenvalue	eigenvalue	NOUN
ajis02-1563	95	30	for	for	ADP
ajis02-1563	95	31	the	the	DET
ajis02-1563	95	32	purpose	purpose	NOUN
ajis02-1563	95	33	but	but	CCONJ
ajis02-1563	95	34	instead	instead	ADV
ajis02-1563	95	35	of	of	ADP
ajis02-1563	95	36	removing	remove	VERB
ajis02-1563	95	37	edges	edge	NOUN
ajis02-1563	95	38	,	,	PUNCT
ajis02-1563	95	39	nodes	node	NOUN
ajis02-1563	95	40	are	be	AUX
ajis02-1563	95	41	deleted	delete	VERB
ajis02-1563	95	42	to	to	PART
ajis02-1563	95	43	maximize	maximize	VERB
ajis02-1563	95	44	the	the	DET
ajis02-1563	95	45	eigendrop	eigendrop	NOUN
ajis02-1563	95	46	.	.	PUNCT
ajis02-1563	96	1	undirected	undirected	ADJ
ajis02-1563	96	2	,	,	PUNCT
ajis02-1563	96	3	unweighted	unweighted	ADJ
ajis02-1563	96	4	graphs	graph	NOUN
ajis02-1563	96	5	are	be	AUX
ajis02-1563	96	6	considered	consider	VERB
ajis02-1563	96	7	and	and	CCONJ
ajis02-1563	96	8	nodes	node	NOUN
ajis02-1563	96	9	are	be	AUX
ajis02-1563	96	10	selected	select	VERB
ajis02-1563	96	11	by	by	ADP
ajis02-1563	96	12	an	an	DET
ajis02-1563	96	13	approximation	approximation	NOUN
ajis02-1563	96	14	scheme	scheme	NOUN
ajis02-1563	96	15	using	use	VERB
ajis02-1563	96	16	the	the	DET
ajis02-1563	96	17	eigenvector	eigenvector	NOUN
ajis02-1563	96	18	corresponding	correspond	VERB
ajis02-1563	96	19	to	to	ADP
ajis02-1563	96	20	largest	large	ADJ
ajis02-1563	96	21	eigenvalue	eigenvalue	NOUN
ajis02-1563	96	22	which	which	PRON
ajis02-1563	96	23	cause	cause	VERB
ajis02-1563	96	24	the	the	DET
ajis02-1563	96	25	maximum	maximum	ADJ
ajis02-1563	96	26	drop	drop	NOUN
ajis02-1563	96	27	.	.	PUNCT
ajis02-1563	97	1	australasian	australasian	ADJ
ajis02-1563	97	2	journal	journal	NOUN
ajis02-1563	97	3	of	of	ADP
ajis02-1563	97	4	information	information	NOUN
ajis02-1563	97	5	systems	system	NOUN
ajis02-1563	97	6	ahmad	ahmad	PROPN
ajis02-1563	97	7	,	,	PUNCT
ajis02-1563	97	8	traiq	traiq	NOUN
ajis02-1563	97	9	,	,	PUNCT
ajis02-1563	97	10	shabbir	shabbir	PROPN
ajis02-1563	97	11	&	&	CCONJ
ajis02-1563	97	12	khan	khan	PROPN
ajis02-1563	97	13	2017	2017	NUM
ajis02-1563	97	14	,	,	PUNCT
ajis02-1563	97	15	vol	vol	NOUN
ajis02-1563	97	16	21	21	NUM
ajis02-1563	97	17	,	,	PUNCT
ajis02-1563	97	18	selected	select	VERB
ajis02-1563	97	19	papers	paper	NOUN
ajis02-1563	97	20	from	from	ADP
ajis02-1563	97	21	ausdm	ausdm	NOUN
ajis02-1563	97	22	spectral	spectral	ADJ
ajis02-1563	97	23	methods	method	NOUN
ajis02-1563	97	24	for	for	ADP
ajis02-1563	97	25	immunization	immunization	NOUN
ajis02-1563	97	26	of	of	ADP
ajis02-1563	97	27	large	large	ADJ
ajis02-1563	97	28	networks	network	NOUN
ajis02-1563	97	29	5	5	NUM
ajis02-1563	97	30	zhang	zhang	PROPN
ajis02-1563	97	31	et	et	PROPN
ajis02-1563	97	32	al	al	PROPN
ajis02-1563	97	33	.	.	PROPN
ajis02-1563	98	1	and	and	CCONJ
ajis02-1563	98	2	song	song	NOUN
ajis02-1563	98	3	et	et	PROPN
ajis02-1563	98	4	al	al	PROPN
ajis02-1563	98	5	.	.	PROPN
ajis02-1563	99	1	adapt	adapt	VERB
ajis02-1563	99	2	the	the	DET
ajis02-1563	99	3	non	non	ADJ
ajis02-1563	99	4	-	-	ADJ
ajis02-1563	99	5	preemptive	preemptive	ADJ
ajis02-1563	99	6	strategy	strategy	NOUN
ajis02-1563	99	7	i.e.	i.e.	X
ajis02-1563	99	8	selection	selection	NOUN
ajis02-1563	99	9	of	of	ADP
ajis02-1563	99	10	nodes	node	NOUN
ajis02-1563	99	11	for	for	ADP
ajis02-1563	99	12	immunization	immunization	NOUN
ajis02-1563	99	13	is	be	AUX
ajis02-1563	99	14	done	do	VERB
ajis02-1563	99	15	after	after	SCONJ
ajis02-1563	99	16	the	the	DET
ajis02-1563	99	17	virus	virus	NOUN
ajis02-1563	99	18	starts	start	VERB
ajis02-1563	99	19	propagating	propagate	VERB
ajis02-1563	99	20	across	across	ADP
ajis02-1563	99	21	the	the	DET
ajis02-1563	99	22	graph	graph	NOUN
ajis02-1563	99	23	.	.	PUNCT
ajis02-1563	100	1	for	for	ADP
ajis02-1563	100	2	this	this	PRON
ajis02-1563	100	3	they	they	PRON
ajis02-1563	100	4	use	use	VERB
ajis02-1563	100	5	discrete	discrete	ADJ
ajis02-1563	100	6	time	time	NOUN
ajis02-1563	100	7	model	model	NOUN
ajis02-1563	100	8	to	to	PART
ajis02-1563	100	9	obtain	obtain	VERB
ajis02-1563	100	10	additional	additional	ADJ
ajis02-1563	100	11	information	information	NOUN
ajis02-1563	100	12	of	of	ADP
ajis02-1563	100	13	infected	infected	ADJ
ajis02-1563	100	14	and	and	CCONJ
ajis02-1563	100	15	healthy	healthy	ADJ
ajis02-1563	100	16	nodes	node	NOUN
ajis02-1563	100	17	at	at	ADP
ajis02-1563	100	18	each	each	DET
ajis02-1563	100	19	time	time	NOUN
ajis02-1563	100	20	stamp	stamp	NOUN
ajis02-1563	100	21	.	.	PUNCT
ajis02-1563	101	1	in	in	ADP
ajis02-1563	101	2	(	(	PUNCT
ajis02-1563	101	3	song	song	NOUN
ajis02-1563	101	4	2015	2015	NUM
ajis02-1563	101	5	)	)	PUNCT
ajis02-1563	101	6	directed	direct	VERB
ajis02-1563	101	7	and	and	CCONJ
ajis02-1563	101	8	weighted	weight	VERB
ajis02-1563	101	9	graphs	graph	NOUN
ajis02-1563	101	10	are	be	AUX
ajis02-1563	101	11	used	use	VERB
ajis02-1563	101	12	in	in	ADP
ajis02-1563	101	13	which	which	PRON
ajis02-1563	101	14	weights	weight	NOUN
ajis02-1563	101	15	represent	represent	VERB
ajis02-1563	101	16	the	the	DET
ajis02-1563	101	17	probability	probability	NOUN
ajis02-1563	101	18	of	of	ADP
ajis02-1563	101	19	a	a	DET
ajis02-1563	101	20	healthy	healthy	ADJ
ajis02-1563	101	21	node	node	NOUN
ajis02-1563	101	22	being	be	AUX
ajis02-1563	101	23	infected	infect	VERB
ajis02-1563	101	24	by	by	ADP
ajis02-1563	101	25	its	its	PRON
ajis02-1563	101	26	neighbours	neighbour	NOUN
ajis02-1563	101	27	and	and	CCONJ
ajis02-1563	101	28	node	node	ADJ
ajis02-1563	101	29	selection	selection	NOUN
ajis02-1563	101	30	is	be	AUX
ajis02-1563	101	31	done	do	VERB
ajis02-1563	101	32	on	on	ADP
ajis02-1563	101	33	the	the	DET
ajis02-1563	101	34	basis	basis	NOUN
ajis02-1563	101	35	of	of	ADP
ajis02-1563	101	36	these	these	DET
ajis02-1563	101	37	probabilities	probability	NOUN
ajis02-1563	101	38	.	.	PUNCT
ajis02-1563	102	1	then	then	ADV
ajis02-1563	102	2	results	result	NOUN
ajis02-1563	102	3	are	be	AUX
ajis02-1563	102	4	evaluated	evaluate	VERB
ajis02-1563	102	5	on	on	ADP
ajis02-1563	102	6	the	the	DET
ajis02-1563	102	7	basis	basis	NOUN
ajis02-1563	102	8	of	of	ADP
ajis02-1563	102	9	save	save	NOUN
ajis02-1563	102	10	ratio	ratio	NOUN
ajis02-1563	102	11	(	(	PUNCT
ajis02-1563	102	12	sr	sr	PROPN
ajis02-1563	102	13	)	)	PUNCT
ajis02-1563	102	14	which	which	PRON
ajis02-1563	102	15	is	be	AUX
ajis02-1563	102	16	the	the	DET
ajis02-1563	102	17	ratio	ratio	NOUN
ajis02-1563	102	18	between	between	ADP
ajis02-1563	102	19	the	the	DET
ajis02-1563	102	20	number	number	NOUN
ajis02-1563	102	21	of	of	ADP
ajis02-1563	102	22	infected	infected	ADJ
ajis02-1563	102	23	nodes	node	NOUN
ajis02-1563	102	24	when	when	SCONJ
ajis02-1563	102	25	k	k	PROPN
ajis02-1563	102	26	nodes	node	NOUN
ajis02-1563	102	27	are	be	AUX
ajis02-1563	102	28	immunized	immunize	VERB
ajis02-1563	102	29	over	over	ADP
ajis02-1563	102	30	the	the	DET
ajis02-1563	102	31	number	number	NOUN
ajis02-1563	102	32	of	of	ADP
ajis02-1563	102	33	infected	infected	ADJ
ajis02-1563	102	34	nodes	node	NOUN
ajis02-1563	102	35	when	when	SCONJ
ajis02-1563	102	36	no	no	DET
ajis02-1563	102	37	node	node	NOUN
ajis02-1563	102	38	is	be	AUX
ajis02-1563	102	39	immunized	immunize	VERB
ajis02-1563	102	40	.	.	PUNCT
ajis02-1563	103	1	(	(	PUNCT
ajis02-1563	103	2	zhang	zhang	PROPN
ajis02-1563	103	3	2014a	2014a	NUM
ajis02-1563	103	4	)	)	PUNCT
ajis02-1563	104	1	and	and	CCONJ
ajis02-1563	104	2	(	(	PUNCT
ajis02-1563	104	3	zhang	zhang	PROPN
ajis02-1563	104	4	2014b	2014b	NUM
ajis02-1563	104	5	)	)	PUNCT
ajis02-1563	104	6	consider	consider	VERB
ajis02-1563	104	7	undirected	undirected	ADJ
ajis02-1563	104	8	graphs	graph	NOUN
ajis02-1563	104	9	and	and	CCONJ
ajis02-1563	104	10	incorporates	incorporate	VERB
ajis02-1563	104	11	dominator	dominator	NOUN
ajis02-1563	104	12	trees	tree	NOUN
ajis02-1563	104	13	for	for	ADP
ajis02-1563	104	14	selecting	selecting	NOUN
ajis02-1563	104	15	nodes	node	NOUN
ajis02-1563	104	16	.	.	PUNCT
ajis02-1563	105	1	results	result	NOUN
ajis02-1563	105	2	are	be	AUX
ajis02-1563	105	3	evaluated	evaluate	VERB
ajis02-1563	105	4	in	in	ADP
ajis02-1563	105	5	terms	term	NOUN
ajis02-1563	105	6	of	of	ADP
ajis02-1563	105	7	expected	expect	VERB
ajis02-1563	105	8	number	number	NOUN
ajis02-1563	105	9	of	of	ADP
ajis02-1563	105	10	remaining	remain	VERB
ajis02-1563	105	11	infected	infect	VERB
ajis02-1563	105	12	nodes	node	NOUN
ajis02-1563	105	13	in	in	ADP
ajis02-1563	105	14	the	the	DET
ajis02-1563	105	15	graph	graph	NOUN
ajis02-1563	105	16	after	after	ADP
ajis02-1563	105	17	the	the	DET
ajis02-1563	105	18	process	process	NOUN
ajis02-1563	105	19	of	of	ADP
ajis02-1563	105	20	immunization	immunization	NOUN
ajis02-1563	105	21	.	.	PUNCT
ajis02-1563	106	1	in	in	ADP
ajis02-1563	106	2	filter	filter	NOUN
ajis02-1563	106	3	placement	placement	NOUN
ajis02-1563	106	4	(	(	PUNCT
ajis02-1563	106	5	erdös	erdös	ADJ
ajis02-1563	106	6	2012	2012	NUM
ajis02-1563	106	7	)	)	PUNCT
ajis02-1563	106	8	,	,	PUNCT
ajis02-1563	106	9	those	those	DET
ajis02-1563	106	10	nodes	node	NOUN
ajis02-1563	106	11	are	be	AUX
ajis02-1563	106	12	identified	identify	VERB
ajis02-1563	106	13	which	which	PRON
ajis02-1563	106	14	are	be	AUX
ajis02-1563	106	15	cause	cause	NOUN
ajis02-1563	106	16	of	of	ADP
ajis02-1563	106	17	maximum	maximum	ADJ
ajis02-1563	106	18	information	information	NOUN
ajis02-1563	106	19	multiplicity	multiplicity	NOUN
ajis02-1563	106	20	.	.	PUNCT
ajis02-1563	107	1	moreover	moreover	ADV
ajis02-1563	107	2	some	some	DET
ajis02-1563	107	3	reverse	reverse	ADJ
ajis02-1563	107	4	engineering	engineering	NOUN
ajis02-1563	107	5	techniques	technique	NOUN
ajis02-1563	107	6	are	be	AUX
ajis02-1563	107	7	also	also	ADV
ajis02-1563	107	8	used	use	VERB
ajis02-1563	107	9	for	for	ADP
ajis02-1563	107	10	similar	similar	ADJ
ajis02-1563	107	11	problems	problem	NOUN
ajis02-1563	107	12	.	.	PUNCT
ajis02-1563	108	1	prakash	prakash	PROPN
ajis02-1563	108	2	et	et	PROPN
ajis02-1563	108	3	al	al	PROPN
ajis02-1563	108	4	.	.	PUNCT
ajis02-1563	109	1	(	(	PUNCT
ajis02-1563	109	2	prakash	prakash	PROPN
ajis02-1563	109	3	2012	2012	NUM
ajis02-1563	109	4	)	)	PUNCT
ajis02-1563	109	5	study	study	VERB
ajis02-1563	109	6	the	the	DET
ajis02-1563	109	7	graphs	graph	NOUN
ajis02-1563	109	8	in	in	ADP
ajis02-1563	109	9	which	which	PRON
ajis02-1563	109	10	virus	virus	NOUN
ajis02-1563	109	11	has	have	AUX
ajis02-1563	109	12	already	already	ADV
ajis02-1563	109	13	spread	spread	VERB
ajis02-1563	109	14	for	for	ADP
ajis02-1563	109	15	some	some	DET
ajis02-1563	109	16	time	time	NOUN
ajis02-1563	109	17	and	and	CCONJ
ajis02-1563	109	18	they	they	PRON
ajis02-1563	109	19	point	point	VERB
ajis02-1563	109	20	out	out	ADP
ajis02-1563	109	21	those	those	DET
ajis02-1563	109	22	nodes	node	NOUN
ajis02-1563	109	23	from	from	ADP
ajis02-1563	109	24	where	where	SCONJ
ajis02-1563	109	25	the	the	DET
ajis02-1563	109	26	spread	spread	NOUN
ajis02-1563	109	27	started	start	VERB
ajis02-1563	109	28	.	.	PUNCT
ajis02-1563	110	1	from	from	ADP
ajis02-1563	110	2	this	this	PRON
ajis02-1563	110	3	they	they	PRON
ajis02-1563	110	4	find	find	VERB
ajis02-1563	110	5	out	out	ADP
ajis02-1563	110	6	the	the	DET
ajis02-1563	110	7	likelihood	likelihood	NOUN
ajis02-1563	110	8	of	of	ADP
ajis02-1563	110	9	other	other	ADJ
ajis02-1563	110	10	nodes	node	NOUN
ajis02-1563	110	11	being	be	AUX
ajis02-1563	110	12	affected	affect	VERB
ajis02-1563	110	13	.	.	PUNCT
ajis02-1563	111	1	another	another	DET
ajis02-1563	111	2	direction	direction	NOUN
ajis02-1563	111	3	to	to	PART
ajis02-1563	111	4	look	look	VERB
ajis02-1563	111	5	at	at	ADP
ajis02-1563	111	6	the	the	DET
ajis02-1563	111	7	problem	problem	NOUN
ajis02-1563	111	8	is	be	AUX
ajis02-1563	111	9	to	to	PART
ajis02-1563	111	10	consider	consider	VERB
ajis02-1563	111	11	graphs	graph	NOUN
ajis02-1563	111	12	in	in	ADP
ajis02-1563	111	13	which	which	PRON
ajis02-1563	111	14	some	some	DET
ajis02-1563	111	15	nodes	node	NOUN
ajis02-1563	111	16	are	be	AUX
ajis02-1563	111	17	already	already	ADV
ajis02-1563	111	18	infected	infect	VERB
ajis02-1563	111	19	and	and	CCONJ
ajis02-1563	111	20	these	these	DET
ajis02-1563	111	21	nodes	node	NOUN
ajis02-1563	111	22	can	can	AUX
ajis02-1563	111	23	spread	spread	VERB
ajis02-1563	111	24	virus	virus	NOUN
ajis02-1563	111	25	among	among	ADP
ajis02-1563	111	26	other	other	ADJ
ajis02-1563	111	27	reachable	reachable	ADJ
ajis02-1563	111	28	nodes	node	NOUN
ajis02-1563	111	29	or	or	CCONJ
ajis02-1563	111	30	graphs	graph	NOUN
ajis02-1563	111	31	in	in	ADP
ajis02-1563	111	32	which	which	PRON
ajis02-1563	111	33	all	all	DET
ajis02-1563	111	34	nodes	node	NOUN
ajis02-1563	111	35	are	be	AUX
ajis02-1563	111	36	contaminated	contaminate	VERB
ajis02-1563	111	37	and	and	CCONJ
ajis02-1563	111	38	the	the	DET
ajis02-1563	111	39	goal	goal	NOUN
ajis02-1563	111	40	is	be	AUX
ajis02-1563	111	41	to	to	PART
ajis02-1563	111	42	decontaminate	decontaminate	VERB
ajis02-1563	111	43	the	the	DET
ajis02-1563	111	44	graph	graph	NOUN
ajis02-1563	111	45	by	by	ADP
ajis02-1563	111	46	using	use	VERB
ajis02-1563	111	47	some	some	DET
ajis02-1563	111	48	agent	agent	NOUN
ajis02-1563	111	49	nodes	node	NOUN
ajis02-1563	111	50	which	which	PRON
ajis02-1563	111	51	traverse	traverse	VERB
ajis02-1563	111	52	along	along	ADP
ajis02-1563	111	53	the	the	DET
ajis02-1563	111	54	edges	edge	NOUN
ajis02-1563	111	55	of	of	ADP
ajis02-1563	111	56	the	the	DET
ajis02-1563	111	57	graph	graph	NOUN
ajis02-1563	111	58	and	and	CCONJ
ajis02-1563	111	59	clean	clean	VERB
ajis02-1563	111	60	the	the	DET
ajis02-1563	111	61	nodes	node	NOUN
ajis02-1563	111	62	.	.	PUNCT
ajis02-1563	112	1	the	the	DET
ajis02-1563	112	2	problem	problem	NOUN
ajis02-1563	112	3	is	be	AUX
ajis02-1563	112	4	usually	usually	ADV
ajis02-1563	112	5	referred	refer	VERB
ajis02-1563	112	6	to	to	ADP
ajis02-1563	112	7	as	as	ADP
ajis02-1563	112	8	decontamination	decontamination	NOUN
ajis02-1563	112	9	of	of	ADP
ajis02-1563	112	10	graph	graph	NOUN
ajis02-1563	112	11	or	or	CCONJ
ajis02-1563	112	12	graph	graph	VERB
ajis02-1563	112	13	searching	searching	NOUN
ajis02-1563	112	14	problem	problem	NOUN
ajis02-1563	112	15	.	.	PUNCT
ajis02-1563	113	1	different	different	ADJ
ajis02-1563	113	2	models	model	NOUN
ajis02-1563	113	3	are	be	AUX
ajis02-1563	113	4	studied	study	VERB
ajis02-1563	113	5	to	to	PART
ajis02-1563	113	6	solve	solve	VERB
ajis02-1563	113	7	the	the	DET
ajis02-1563	113	8	problem	problem	NOUN
ajis02-1563	113	9	and	and	CCONJ
ajis02-1563	113	10	most	most	ADJ
ajis02-1563	113	11	of	of	ADP
ajis02-1563	113	12	them	they	PRON
ajis02-1563	113	13	assume	assume	VERB
ajis02-1563	113	14	the	the	DET
ajis02-1563	113	15	monotonicity	monotonicity	NOUN
ajis02-1563	113	16	in	in	ADP
ajis02-1563	113	17	decontamination	decontamination	NOUN
ajis02-1563	113	18	i.e.	i.e.	X
ajis02-1563	113	19	once	once	SCONJ
ajis02-1563	113	20	a	a	DET
ajis02-1563	113	21	node	node	NOUN
ajis02-1563	113	22	is	be	AUX
ajis02-1563	113	23	decontaminated	decontaminate	VERB
ajis02-1563	113	24	then	then	ADV
ajis02-1563	113	25	it	it	PRON
ajis02-1563	113	26	can	can	AUX
ajis02-1563	113	27	not	not	PART
ajis02-1563	113	28	get	get	AUX
ajis02-1563	113	29	contaminated	contaminate	VERB
ajis02-1563	113	30	again	again	ADV
ajis02-1563	113	31	(	(	PUNCT
ajis02-1563	113	32	bienstock	bienstock	NOUN
ajis02-1563	113	33	1991	1991	NUM
ajis02-1563	113	34	)	)	PUNCT
ajis02-1563	113	35	,	,	PUNCT
ajis02-1563	113	36	(	(	PUNCT
ajis02-1563	113	37	flocchini	flocchini	ADJ
ajis02-1563	113	38	2008	2008	NUM
ajis02-1563	113	39	)	)	PUNCT
ajis02-1563	113	40	,	,	PUNCT
ajis02-1563	113	41	(	(	PUNCT
ajis02-1563	113	42	flocchini	flocchini	ADJ
ajis02-1563	113	43	2007	2007	NUM
ajis02-1563	113	44	)	)	PUNCT
ajis02-1563	113	45	,	,	PUNCT
ajis02-1563	113	46	(	(	PUNCT
ajis02-1563	113	47	fraigniaud	fraigniaud	NOUN
ajis02-1563	113	48	2008	2008	NUM
ajis02-1563	113	49	)	)	PUNCT
ajis02-1563	113	50	.	.	PUNCT
ajis02-1563	114	1	but	but	CCONJ
ajis02-1563	114	2	non	non	ADJ
ajis02-1563	114	3	-	-	ADJ
ajis02-1563	114	4	monotonic	monotonic	ADJ
ajis02-1563	114	5	strategies	strategy	NOUN
ajis02-1563	114	6	are	be	AUX
ajis02-1563	114	7	also	also	ADV
ajis02-1563	114	8	studied	study	VERB
ajis02-1563	114	9	(	(	PUNCT
ajis02-1563	114	10	daadaa	daadaa	NOUN
ajis02-1563	114	11	2016	2016	NUM
ajis02-1563	114	12	)	)	PUNCT
ajis02-1563	114	13	.	.	PUNCT
ajis02-1563	115	1	other	other	ADJ
ajis02-1563	115	2	work	work	NOUN
ajis02-1563	115	3	that	that	PRON
ajis02-1563	115	4	is	be	AUX
ajis02-1563	115	5	related	relate	VERB
ajis02-1563	115	6	to	to	PART
ajis02-1563	115	7	node	node	VERB
ajis02-1563	115	8	immunization	immunization	NOUN
ajis02-1563	115	9	is	be	AUX
ajis02-1563	115	10	the	the	DET
ajis02-1563	115	11	selection	selection	NOUN
ajis02-1563	115	12	of	of	ADP
ajis02-1563	115	13	most	most	ADJ
ajis02-1563	115	14	influential	influential	ADJ
ajis02-1563	115	15	nodes	node	NOUN
ajis02-1563	115	16	in	in	ADP
ajis02-1563	115	17	a	a	DET
ajis02-1563	115	18	given	give	VERB
ajis02-1563	115	19	network	network	NOUN
ajis02-1563	115	20	to	to	PART
ajis02-1563	115	21	maximize	maximize	VERB
ajis02-1563	115	22	the	the	DET
ajis02-1563	115	23	diffusion	diffusion	NOUN
ajis02-1563	115	24	of	of	ADP
ajis02-1563	115	25	new	new	ADJ
ajis02-1563	115	26	information	information	NOUN
ajis02-1563	115	27	in	in	ADP
ajis02-1563	115	28	a	a	DET
ajis02-1563	115	29	network	network	NOUN
ajis02-1563	115	30	.	.	PUNCT
ajis02-1563	116	1	kempe	kempe	PROPN
ajis02-1563	116	2	et	et	PROPN
ajis02-1563	116	3	al	al	PROPN
ajis02-1563	116	4	.	.	PROPN
ajis02-1563	116	5	provided	provide	VERB
ajis02-1563	116	6	the	the	DET
ajis02-1563	116	7	provably	provably	ADV
ajis02-1563	116	8	efficient	efficient	ADJ
ajis02-1563	116	9	approximation	approximation	NOUN
ajis02-1563	116	10	algorithm	algorithm	NOUN
ajis02-1563	116	11	for	for	ADP
ajis02-1563	116	12	the	the	DET
ajis02-1563	116	13	problem	problem	NOUN
ajis02-1563	116	14	(	(	PUNCT
ajis02-1563	116	15	kempe	kempe	ADJ
ajis02-1563	116	16	2003	2003	NUM
ajis02-1563	116	17	)	)	PUNCT
ajis02-1563	116	18	.	.	PUNCT
ajis02-1563	117	1	seeman	seeman	NOUN
ajis02-1563	117	2	and	and	CCONJ
ajis02-1563	117	3	singer	singer	NOUN
ajis02-1563	117	4	(	(	PUNCT
ajis02-1563	117	5	seeman	seeman	NOUN
ajis02-1563	117	6	2013	2013	NUM
ajis02-1563	117	7	)	)	PUNCT
ajis02-1563	117	8	use	use	VERB
ajis02-1563	117	9	stochastic	stochastic	ADJ
ajis02-1563	117	10	optimization	optimization	NOUN
ajis02-1563	117	11	models	model	NOUN
ajis02-1563	117	12	to	to	PART
ajis02-1563	117	13	maximize	maximize	VERB
ajis02-1563	117	14	the	the	DET
ajis02-1563	117	15	information	information	NOUN
ajis02-1563	117	16	diffusion	diffusion	NOUN
ajis02-1563	117	17	in	in	ADP
ajis02-1563	117	18	social	social	ADJ
ajis02-1563	117	19	networks	network	NOUN
ajis02-1563	117	20	.	.	PUNCT
ajis02-1563	118	1	influence	influence	NOUN
ajis02-1563	118	2	maximization	maximization	NOUN
ajis02-1563	118	3	problem	problem	NOUN
ajis02-1563	118	4	is	be	AUX
ajis02-1563	118	5	slightly	slightly	ADV
ajis02-1563	118	6	different	different	ADJ
ajis02-1563	118	7	from	from	ADP
ajis02-1563	118	8	immunization	immunization	NOUN
ajis02-1563	118	9	problem	problem	NOUN
ajis02-1563	118	10	as	as	SCONJ
ajis02-1563	118	11	in	in	ADP
ajis02-1563	118	12	influence	influence	NOUN
ajis02-1563	118	13	maximization	maximization	NOUN
ajis02-1563	118	14	problem	problem	NOUN
ajis02-1563	118	15	the	the	DET
ajis02-1563	118	16	goal	goal	NOUN
ajis02-1563	118	17	is	be	AUX
ajis02-1563	118	18	to	to	PART
ajis02-1563	118	19	select	select	VERB
ajis02-1563	118	20	nodes	node	NOUN
ajis02-1563	118	21	for	for	ADP
ajis02-1563	118	22	seeding	seeding	NOUN
ajis02-1563	118	23	which	which	PRON
ajis02-1563	118	24	will	will	AUX
ajis02-1563	118	25	maximize	maximize	VERB
ajis02-1563	118	26	the	the	DET
ajis02-1563	118	27	spread	spread	NOUN
ajis02-1563	118	28	on	on	ADP
ajis02-1563	118	29	new	new	ADJ
ajis02-1563	118	30	idea	idea	NOUN
ajis02-1563	118	31	while	while	SCONJ
ajis02-1563	118	32	in	in	ADP
ajis02-1563	118	33	node	node	ADJ
ajis02-1563	118	34	immunization	immunization	NOUN
ajis02-1563	118	35	problem	problem	NOUN
ajis02-1563	118	36	goal	goal	NOUN
ajis02-1563	118	37	is	be	AUX
ajis02-1563	118	38	to	to	PART
ajis02-1563	118	39	select	select	VERB
ajis02-1563	118	40	nodes	node	NOUN
ajis02-1563	118	41	which	which	PRON
ajis02-1563	118	42	will	will	AUX
ajis02-1563	118	43	help	help	VERB
ajis02-1563	118	44	in	in	ADP
ajis02-1563	118	45	minimal	minimal	ADJ
ajis02-1563	118	46	spread	spread	NOUN
ajis02-1563	118	47	of	of	ADP
ajis02-1563	118	48	virus	virus	NOUN
ajis02-1563	118	49	.	.	PUNCT
ajis02-1563	119	1	4	4	NUM
ajis02-1563	119	2	our	our	PRON
ajis02-1563	119	3	proposed	propose	VERB
ajis02-1563	119	4	algorithm	algorithm	NOUN
ajis02-1563	119	5	in	in	ADP
ajis02-1563	119	6	(	(	PUNCT
ajis02-1563	119	7	chen	chen	PROPN
ajis02-1563	119	8	2016	2016	NUM
ajis02-1563	119	9	)	)	PUNCT
ajis02-1563	119	10	they	they	PRON
ajis02-1563	119	11	defined	define	VERB
ajis02-1563	119	12	shield	shield	NOUN
ajis02-1563	119	13	value	value	NOUN
ajis02-1563	119	14	that	that	PRON
ajis02-1563	119	15	was	be	AUX
ajis02-1563	119	16	an	an	DET
ajis02-1563	119	17	approximation	approximation	NOUN
ajis02-1563	119	18	to	to	ADP
ajis02-1563	119	19	the	the	DET
ajis02-1563	119	20	eigendrop	eigendrop	NOUN
ajis02-1563	119	21	.	.	PUNCT
ajis02-1563	120	1	we	we	PRON
ajis02-1563	120	2	define	define	VERB
ajis02-1563	120	3	our	our	PRON
ajis02-1563	120	4	shield	shield	NOUN
ajis02-1563	120	5	value	value	NOUN
ajis02-1563	120	6	to	to	PART
ajis02-1563	120	7	be	be	AUX
ajis02-1563	120	8	the	the	DET
ajis02-1563	120	9	eigendrop	eigendrop	NOUN
ajis02-1563	120	10	and	and	CCONJ
ajis02-1563	120	11	approximate	approximate	VERB
ajis02-1563	120	12	the	the	DET
ajis02-1563	120	13	eigenvalue	eigenvalue	PROPN
ajis02-1563	120	14	computation	computation	NOUN
ajis02-1563	120	15	instead	instead	ADV
ajis02-1563	120	16	.	.	PUNCT
ajis02-1563	121	1	we	we	PRON
ajis02-1563	121	2	achieve	achieve	VERB
ajis02-1563	121	3	better	well	ADJ
ajis02-1563	121	4	theoretical	theoretical	ADJ
ajis02-1563	121	5	guarantees	guarantee	NOUN
ajis02-1563	121	6	with	with	ADP
ajis02-1563	121	7	our	our	PRON
ajis02-1563	121	8	shield	shield	NOUN
ajis02-1563	121	9	value	value	NOUN
ajis02-1563	121	10	definition	definition	NOUN
ajis02-1563	121	11	.	.	PUNCT
ajis02-1563	122	1	furthermore	furthermore	ADV
ajis02-1563	122	2	,	,	PUNCT
ajis02-1563	122	3	it	it	PRON
ajis02-1563	122	4	is	be	AUX
ajis02-1563	122	5	easy	easy	ADJ
ajis02-1563	122	6	and	and	CCONJ
ajis02-1563	122	7	computationally	computationally	ADV
ajis02-1563	122	8	efficient	efficient	ADJ
ajis02-1563	122	9	to	to	PART
ajis02-1563	122	10	approximate	approximate	VERB
ajis02-1563	122	11	our	our	PRON
ajis02-1563	122	12	shield	shield	NOUN
ajis02-1563	122	13	value	value	NOUN
ajis02-1563	122	14	.	.	PUNCT
ajis02-1563	123	1	4.1	4.1	NUM
ajis02-1563	123	2	our	our	PRON
ajis02-1563	123	3	shield	shield	NOUN
ajis02-1563	123	4	value	value	NOUN
ajis02-1563	123	5	and	and	CCONJ
ajis02-1563	123	6	its	its	PRON
ajis02-1563	123	7	justification	justification	NOUN
ajis02-1563	123	8	we	we	PRON
ajis02-1563	123	9	use	use	VERB
ajis02-1563	123	10	the	the	DET
ajis02-1563	123	11	following	follow	VERB
ajis02-1563	123	12	well	well	ADV
ajis02-1563	123	13	known	know	VERB
ajis02-1563	123	14	facts	fact	NOUN
ajis02-1563	123	15	from	from	ADP
ajis02-1563	123	16	linear	linear	ADJ
ajis02-1563	123	17	algebra	algebra	NOUN
ajis02-1563	123	18	and	and	CCONJ
ajis02-1563	123	19	graph	graph	NOUN
ajis02-1563	123	20	theory	theory	NOUN
ajis02-1563	123	21	.	.	PUNCT
ajis02-1563	124	1	given	give	VERB
ajis02-1563	124	2	an	an	DET
ajis02-1563	124	3	n×n	n×n	PROPN
ajis02-1563	124	4	matrix	matrix	NOUN
ajis02-1563	124	5	a	a	NOUN
ajis02-1563	124	6	,	,	PUNCT
ajis02-1563	124	7	let	let	VERB
ajis02-1563	124	8	trace	trace	NOUN
ajis02-1563	124	9	of	of	ADP
ajis02-1563	124	10	a	a	PRON
ajis02-1563	124	11	be	be	AUX
ajis02-1563	124	12	denoted	denote	VERB
ajis02-1563	124	13	by	by	ADP
ajis02-1563	124	14	tr(a	tr(a	NUM
ajis02-1563	124	15	)	)	PUNCT
ajis02-1563	124	16	,	,	PUNCT
ajis02-1563	124	17	fact	fact	NOUN
ajis02-1563	124	18	3	3	NUM
ajis02-1563	124	19	:	:	PUNCT
ajis02-1563	125	1	[	[	X
ajis02-1563	125	2	c.f	c.f	PROPN
ajis02-1563	125	3	.	.	PROPN
ajis02-1563	125	4	(	(	PUNCT
ajis02-1563	125	5	strang	strang	PROPN
ajis02-1563	125	6	1976	1976	NUM
ajis02-1563	125	7	)	)	PUNCT
ajis02-1563	125	8	]	]	PUNCT
ajis02-1563	125	9	𝑡𝑟(𝐴	𝑡𝑟(𝐴	NOUN
ajis02-1563	125	10	)	)	PUNCT
ajis02-1563	125	11	=	=	PUNCT
ajis02-1563	125	12	∑	∑	PUNCT
ajis02-1563	125	13	𝑎𝑖𝑖	𝑎𝑖𝑖	NOUN
ajis02-1563	125	14	𝑛	𝑛	PRON
ajis02-1563	125	15	𝑖=1	𝑖=1	PUNCT
ajis02-1563	125	16	=	=	PUNCT
ajis02-1563	125	17	∑	∑	PROPN
ajis02-1563	125	18	𝜆𝑖(𝐴	𝜆𝑖(𝐴	NOUN
ajis02-1563	125	19	)	)	PUNCT
ajis02-1563	126	1	𝑛	𝑛	DET
ajis02-1563	126	2	𝑖=1	𝑖=1	PUNCT
ajis02-1563	126	3	fact	fact	NOUN
ajis02-1563	126	4	4	4	NUM
ajis02-1563	126	5	:	:	PUNCT
ajis02-1563	127	1	[	[	X
ajis02-1563	127	2	c.f	c.f	PROPN
ajis02-1563	127	3	.	.	PROPN
ajis02-1563	128	1	(	(	PUNCT
ajis02-1563	128	2	west	west	NOUN
ajis02-1563	128	3	2001	2001	NUM
ajis02-1563	128	4	)	)	PUNCT
ajis02-1563	129	1	p.	p.	NOUN
ajis02-1563	129	2	455	455	NUM
ajis02-1563	130	1	]	]	PUNCT
ajis02-1563	130	2	𝑡𝑟(𝐴𝑝	𝑡𝑟(𝐴𝑝	PROPN
ajis02-1563	130	3	)	)	PUNCT
ajis02-1563	130	4	=	=	SYM
ajis02-1563	130	5	∑	∑	PUNCT
ajis02-1563	130	6	𝜆𝑖(𝐴𝑝	𝜆𝑖(𝐴𝑝	PROPN
ajis02-1563	130	7	)	)	PUNCT
ajis02-1563	130	8	𝑛	𝑛	PROPN
ajis02-1563	130	9	𝑖=1	𝑖=1	PUNCT
ajis02-1563	130	10	=	=	PUNCT
ajis02-1563	130	11	∑	∑	PUNCT
ajis02-1563	130	12	𝜆𝑖(𝐴)𝑝	𝜆𝑖(𝐴)𝑝	NOUN
ajis02-1563	130	13	𝑛	𝑛	PRON
ajis02-1563	130	14	𝑖=1	𝑖=1	PROPN
ajis02-1563	130	15	australasian	australasian	ADJ
ajis02-1563	130	16	journal	journal	NOUN
ajis02-1563	130	17	of	of	ADP
ajis02-1563	130	18	information	information	NOUN
ajis02-1563	130	19	systems	system	NOUN
ajis02-1563	130	20	ahmad	ahmad	PROPN
ajis02-1563	130	21	,	,	PUNCT
ajis02-1563	130	22	traiq	traiq	NOUN
ajis02-1563	130	23	,	,	PUNCT
ajis02-1563	130	24	shabbir	shabbir	PROPN
ajis02-1563	130	25	&	&	CCONJ
ajis02-1563	130	26	khan	khan	PROPN
ajis02-1563	130	27	2017	2017	NUM
ajis02-1563	130	28	,	,	PUNCT
ajis02-1563	130	29	vol	vol	NOUN
ajis02-1563	130	30	21	21	NUM
ajis02-1563	130	31	,	,	PUNCT
ajis02-1563	130	32	selected	select	VERB
ajis02-1563	130	33	papers	paper	NOUN
ajis02-1563	130	34	from	from	ADP
ajis02-1563	130	35	ausdm	ausdm	NOUN
ajis02-1563	130	36	spectral	spectral	ADJ
ajis02-1563	130	37	methods	method	NOUN
ajis02-1563	130	38	for	for	ADP
ajis02-1563	130	39	immunization	immunization	NOUN
ajis02-1563	130	40	of	of	ADP
ajis02-1563	130	41	large	large	ADJ
ajis02-1563	130	42	networks	network	NOUN
ajis02-1563	130	43	6	6	NUM
ajis02-1563	130	44	clearly	clearly	ADV
ajis02-1563	130	45	,	,	PUNCT
ajis02-1563	130	46	for	for	ADP
ajis02-1563	130	47	even	even	ADV
ajis02-1563	130	48	powers	power	NOUN
ajis02-1563	130	49	p	p	NOUN
ajis02-1563	130	50	,	,	PUNCT
ajis02-1563	130	51	tr(ap	tr(ap	PROPN
ajis02-1563	130	52	)	)	PUNCT
ajis02-1563	130	53	is	be	AUX
ajis02-1563	130	54	an	an	DET
ajis02-1563	130	55	upper	upper	ADJ
ajis02-1563	130	56	bound	bind	VERB
ajis02-1563	130	57	on	on	ADP
ajis02-1563	130	58	𝜆1	𝜆1	PROPN
ajis02-1563	130	59	𝑝	𝑝	PROPN
ajis02-1563	130	60	and	and	CCONJ
ajis02-1563	130	61	as	as	SCONJ
ajis02-1563	130	62	p	p	PRON
ajis02-1563	130	63	grows	grow	VERB
ajis02-1563	130	64	tr(ap	tr(ap	PROPN
ajis02-1563	130	65	)	)	PUNCT
ajis02-1563	130	66	approaches	approach	VERB
ajis02-1563	130	67	𝜆𝑚𝑎𝑥	𝜆𝑚𝑎𝑥	PRON
ajis02-1563	130	68	𝑝	𝑝	PROPN
ajis02-1563	130	69	(	(	PUNCT
ajis02-1563	130	70	𝐴	𝐴	PROPN
ajis02-1563	130	71	)	)	PUNCT
ajis02-1563	130	72	where	where	SCONJ
ajis02-1563	130	73	𝜆𝑚𝑎𝑥	𝜆𝑚𝑎𝑥	ADV
ajis02-1563	130	74	=	=	SYM
ajis02-1563	130	75	max{|𝜆𝑖(𝐴)|	max{|𝜆𝑖(𝐴)|	NUM
ajis02-1563	130	76	}	}	PUNCT
ajis02-1563	130	77	.	.	PUNCT
ajis02-1563	131	1	we	we	PRON
ajis02-1563	131	2	therefore	therefore	ADV
ajis02-1563	131	3	,	,	PUNCT
ajis02-1563	131	4	try	try	VERB
ajis02-1563	131	5	to	to	PART
ajis02-1563	131	6	remove	remove	VERB
ajis02-1563	131	7	a	a	DET
ajis02-1563	131	8	set	set	NOUN
ajis02-1563	131	9	s	s	NOUN
ajis02-1563	131	10	of	of	ADP
ajis02-1563	131	11	k	k	PROPN
ajis02-1563	131	12	vertices	vertex	NOUN
ajis02-1563	131	13	from	from	ADP
ajis02-1563	131	14	the	the	DET
ajis02-1563	131	15	graph	graph	NOUN
ajis02-1563	131	16	such	such	ADJ
ajis02-1563	131	17	that	that	DET
ajis02-1563	131	18	𝑡𝑟((𝐴−𝑆)𝑝	𝑡𝑟((𝐴−𝑆)𝑝	NOUN
ajis02-1563	131	19	)	)	PUNCT
ajis02-1563	131	20	is	be	AUX
ajis02-1563	131	21	minimized	minimize	VERB
ajis02-1563	131	22	.	.	PUNCT
ajis02-1563	132	1	the	the	DET
ajis02-1563	132	2	goodness	goodness	NOUN
ajis02-1563	132	3	of	of	ADP
ajis02-1563	132	4	a	a	DET
ajis02-1563	132	5	set	set	NOUN
ajis02-1563	132	6	s	s	NOUN
ajis02-1563	132	7	in	in	ADP
ajis02-1563	132	8	this	this	DET
ajis02-1563	132	9	setting	setting	NOUN
ajis02-1563	132	10	is	be	AUX
ajis02-1563	132	11	defined	define	VERB
ajis02-1563	132	12	as	as	ADP
ajis02-1563	132	13	𝑓𝑝(𝑆	𝑓𝑝(𝑆	NOUN
ajis02-1563	132	14	)	)	PUNCT
ajis02-1563	132	15	=	=	SYM
ajis02-1563	132	16	𝑡𝑟((𝐴−𝑆)𝑝	𝑡𝑟((𝐴−𝑆)𝑝	PROPN
ajis02-1563	132	17	)	)	PUNCT
ajis02-1563	132	18	(	(	PUNCT
ajis02-1563	132	19	1	1	X
ajis02-1563	132	20	)	)	PUNCT
ajis02-1563	132	21	define	define	VERB
ajis02-1563	132	22	𝑔𝑝(𝑆	𝑔𝑝(𝑆	NOUN
ajis02-1563	132	23	)	)	PUNCT
ajis02-1563	132	24	=	=	SYM
ajis02-1563	133	1	𝑡𝑟(𝐴𝑝	𝑡𝑟(𝐴𝑝	PROPN
ajis02-1563	133	2	)	)	PUNCT
ajis02-1563	133	3	−	−	PROPN
ajis02-1563	133	4	𝑡𝑟((𝐴−𝑆)𝑝	𝑡𝑟((𝐴−𝑆)𝑝	PROPN
ajis02-1563	133	5	)	)	PUNCT
ajis02-1563	133	6	(	(	PUNCT
ajis02-1563	133	7	2	2	X
ajis02-1563	133	8	)	)	PUNCT
ajis02-1563	133	9	note	note	NOUN
ajis02-1563	133	10	that	that	SCONJ
ajis02-1563	133	11	minimizing	minimize	VERB
ajis02-1563	133	12	fp(s	fp(s	NOUN
ajis02-1563	133	13	)	)	PUNCT
ajis02-1563	133	14	is	be	AUX
ajis02-1563	133	15	same	same	ADJ
ajis02-1563	133	16	as	as	ADP
ajis02-1563	133	17	maximizing	maximize	VERB
ajis02-1563	133	18	gp(s	gp(s	NOUN
ajis02-1563	133	19	)	)	PUNCT
ajis02-1563	133	20	.	.	PUNCT
ajis02-1563	134	1	given	give	VERB
ajis02-1563	134	2	a	a	DET
ajis02-1563	134	3	graph	graph	NOUN
ajis02-1563	134	4	g=(v	g=(v	NOUN
ajis02-1563	134	5	,	,	PUNCT
ajis02-1563	134	6	e	e	NOUN
ajis02-1563	134	7	)	)	PUNCT
ajis02-1563	134	8	,	,	PUNCT
ajis02-1563	134	9	a	a	DET
ajis02-1563	134	10	walk	walk	NOUN
ajis02-1563	134	11	w	w	ADP
ajis02-1563	134	12	of	of	ADP
ajis02-1563	134	13	length	length	NOUN
ajis02-1563	134	14	l	l	NOUN
ajis02-1563	134	15	in	in	ADP
ajis02-1563	134	16	g	g	PROPN
ajis02-1563	134	17	is	be	AUX
ajis02-1563	134	18	a	a	DET
ajis02-1563	134	19	sequence	sequence	NOUN
ajis02-1563	134	20	of	of	ADP
ajis02-1563	134	21	vertex	vertex	NOUN
ajis02-1563	134	22	𝑣0	𝑣0	PROPN
ajis02-1563	134	23	,	,	PUNCT
ajis02-1563	134	24	𝑣1	𝑣1	NOUN
ajis02-1563	134	25	,	,	PUNCT
ajis02-1563	134	26	…	…	PUNCT
ajis02-1563	134	27	,	,	PUNCT
ajis02-1563	134	28	𝑣𝑙	𝑣𝑙	PROPN
ajis02-1563	134	29	s	s	VERB
ajis02-1563	134	30	such	such	ADJ
ajis02-1563	134	31	that	that	PRON
ajis02-1563	134	32	for	for	ADP
ajis02-1563	134	33	0	0	NUM
ajis02-1563	134	34	≤	≤	NUM
ajis02-1563	134	35	𝑖	𝑖	SYM
ajis02-1563	134	36	≤	≤	NOUN
ajis02-1563	134	37	𝑙	𝑙	PRON
ajis02-1563	135	1	−	−	NUM
ajis02-1563	135	2	1	1	NUM
ajis02-1563	135	3	(	(	PUNCT
ajis02-1563	135	4	𝑣𝑖	𝑣𝑖	NOUN
ajis02-1563	135	5	,	,	PUNCT
ajis02-1563	135	6	𝑣𝑖+1	𝑣𝑖+1	X
ajis02-1563	135	7	)	)	PUNCT
ajis02-1563	135	8	∈	∈	PROPN
ajis02-1563	135	9	𝐸.	𝐸.	NOUN
ajis02-1563	135	10	we	we	PRON
ajis02-1563	135	11	say	say	VERB
ajis02-1563	135	12	that	that	SCONJ
ajis02-1563	135	13	w	w	NOUN
ajis02-1563	135	14	is	be	AUX
ajis02-1563	135	15	a	a	DET
ajis02-1563	135	16	walk	walk	NOUN
ajis02-1563	135	17	from	from	ADP
ajis02-1563	135	18	v0	v0	NOUN
ajis02-1563	135	19	to	to	ADP
ajis02-1563	135	20	vl	vl	PROPN
ajis02-1563	135	21	.	.	PUNCT
ajis02-1563	136	1	if	if	SCONJ
ajis02-1563	136	2	v0	v0	NOUN
ajis02-1563	136	3	=	=	SYM
ajis02-1563	136	4	vl	vl	PROPN
ajis02-1563	136	5	,	,	PUNCT
ajis02-1563	136	6	then	then	ADV
ajis02-1563	136	7	w	w	PROPN
ajis02-1563	136	8	is	be	AUX
ajis02-1563	136	9	called	call	VERB
ajis02-1563	136	10	a	a	DET
ajis02-1563	136	11	closed	closed	ADJ
ajis02-1563	136	12	walk	walk	NOUN
ajis02-1563	136	13	.	.	PUNCT
ajis02-1563	137	1	for	for	ADP
ajis02-1563	137	2	v∈	v∈	PROPN
ajis02-1563	137	3	v	v	NOUN
ajis02-1563	137	4	,	,	PUNCT
ajis02-1563	137	5	let	let	VERB
ajis02-1563	137	6	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	SYM
ajis02-1563	137	7	,	,	PUNCT
ajis02-1563	137	8	𝑣	𝑣	NOUN
ajis02-1563	137	9	)	)	PUNCT
ajis02-1563	137	10	be	be	VERB
ajis02-1563	137	11	the	the	DET
ajis02-1563	137	12	set	set	NOUN
ajis02-1563	137	13	of	of	ADP
ajis02-1563	137	14	closed	closed	ADJ
ajis02-1563	137	15	walks	walk	NOUN
ajis02-1563	137	16	of	of	ADP
ajis02-1563	137	17	length	length	NOUN
ajis02-1563	138	1	i	i	PRON
ajis02-1563	138	2	in	in	ADP
ajis02-1563	138	3	g	g	NOUN
ajis02-1563	138	4	containing	contain	VERB
ajis02-1563	138	5	the	the	DET
ajis02-1563	138	6	vertex	vertex	NOUN
ajis02-1563	138	7	v.	v.	ADP
ajis02-1563	138	8	suppose	suppose	VERB
ajis02-1563	138	9	𝐶𝑊𝑖(𝐺	𝐶𝑊𝑖(𝐺	NOUN
ajis02-1563	138	10	,	,	PUNCT
ajis02-1563	138	11	𝑣	𝑣	NOUN
ajis02-1563	138	12	)	)	PUNCT
ajis02-1563	138	13	=	=	SYM
ajis02-1563	138	14	|ℂ𝕎𝑖(𝐺	|ℂ𝕎𝑖(𝐺	NOUN
ajis02-1563	138	15	,	,	PUNCT
ajis02-1563	138	16	𝑣)|	𝑣)|	NOUN
ajis02-1563	138	17	.	.	PUNCT
ajis02-1563	139	1	when	when	SCONJ
ajis02-1563	139	2	x⊆v	x⊆v	PROPN
ajis02-1563	139	3	,	,	PUNCT
ajis02-1563	139	4	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	NUM
ajis02-1563	139	5	,	,	PUNCT
ajis02-1563	139	6	𝑋	𝑋	NOUN
ajis02-1563	139	7	)	)	PUNCT
ajis02-1563	139	8	=	=	PUNCT
ajis02-1563	139	9	⋃	⋃	NOUN
ajis02-1563	139	10	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	NOUN
ajis02-1563	139	11	,	,	PUNCT
ajis02-1563	139	12	𝑥)𝑥∈𝑋	𝑥)𝑥∈𝑋	PUNCT
ajis02-1563	139	13	.	.	PUNCT
ajis02-1563	140	1	we	we	PRON
ajis02-1563	140	2	similarly	similarly	ADV
ajis02-1563	140	3	denote	denote	VERB
ajis02-1563	140	4	by	by	ADP
ajis02-1563	140	5	𝐶𝑊𝑖(𝐺	𝐶𝑊𝑖(𝐺	NOUN
ajis02-1563	140	6	,	,	PUNCT
ajis02-1563	140	7	𝑋	𝑋	PROPN
ajis02-1563	140	8	)	)	PUNCT
ajis02-1563	140	9	to	to	PART
ajis02-1563	140	10	be	be	AUX
ajis02-1563	140	11	the	the	DET
ajis02-1563	140	12	cardinality	cardinality	NOUN
ajis02-1563	140	13	of	of	ADP
ajis02-1563	140	14	the	the	DET
ajis02-1563	140	15	set	set	NOUN
ajis02-1563	140	16	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	ADP
ajis02-1563	140	17	,	,	PUNCT
ajis02-1563	140	18	𝑋	𝑋	PROPN
ajis02-1563	140	19	)	)	PUNCT
ajis02-1563	140	20	.	.	PUNCT
ajis02-1563	141	1	when	when	SCONJ
ajis02-1563	141	2	x	x	X
ajis02-1563	141	3	=	=	NOUN
ajis02-1563	141	4	v	v	NOUN
ajis02-1563	141	5	,	,	PUNCT
ajis02-1563	141	6	we	we	PRON
ajis02-1563	141	7	refer	refer	VERB
ajis02-1563	141	8	to	to	ADP
ajis02-1563	141	9	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	PRON
ajis02-1563	141	10	,	,	PUNCT
ajis02-1563	141	11	𝑋	𝑋	PROPN
ajis02-1563	141	12	)	)	PUNCT
ajis02-1563	141	13	as	as	ADP
ajis02-1563	141	14	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	NOUN
ajis02-1563	141	15	)	)	PUNCT
ajis02-1563	141	16	.	.	PUNCT
ajis02-1563	142	1	so	so	ADV
ajis02-1563	142	2	ℂ𝕎𝑖(𝐺	ℂ𝕎𝑖(𝐺	NOUN
ajis02-1563	142	3	)	)	PUNCT
ajis02-1563	142	4	is	be	AUX
ajis02-1563	142	5	the	the	DET
ajis02-1563	142	6	set	set	NOUN
ajis02-1563	142	7	of	of	ADP
ajis02-1563	142	8	all	all	DET
ajis02-1563	142	9	closed	closed	ADJ
ajis02-1563	142	10	walks	walk	NOUN
ajis02-1563	142	11	of	of	ADP
ajis02-1563	142	12	length	length	NOUN
ajis02-1563	142	13	i	i	PRON
ajis02-1563	142	14	in	in	ADP
ajis02-1563	142	15	g.	g.	PROPN
ajis02-1563	142	16	we	we	PRON
ajis02-1563	142	17	use	use	VERB
ajis02-1563	142	18	the	the	DET
ajis02-1563	142	19	following	follow	VERB
ajis02-1563	142	20	well	well	ADV
ajis02-1563	142	21	-	-	PUNCT
ajis02-1563	142	22	known	know	VERB
ajis02-1563	142	23	fact	fact	NOUN
ajis02-1563	142	24	from	from	ADP
ajis02-1563	142	25	graph	graph	NOUN
ajis02-1563	142	26	theory	theory	NOUN
ajis02-1563	142	27	fact	fact	NOUN
ajis02-1563	142	28	5:[c.f	5:[c.f	NUM
ajis02-1563	142	29	.	.	PUNCT
ajis02-1563	143	1	(	(	PUNCT
ajis02-1563	143	2	west	west	NOUN
ajis02-1563	143	3	2001	2001	NUM
ajis02-1563	143	4	)	)	PUNCT
ajis02-1563	143	5	p.455	p.455	PROPN
ajis02-1563	143	6	]	]	PUNCT
ajis02-1563	143	7	given	give	VERB
ajis02-1563	143	8	a	a	DET
ajis02-1563	143	9	graph	graph	NOUN
ajis02-1563	143	10	g	g	NOUN
ajis02-1563	143	11	with	with	ADP
ajis02-1563	143	12	adjacency	adjacency	PROPN
ajis02-1563	143	13	matrix	matrix	NOUN
ajis02-1563	143	14	a	a	DET
ajis02-1563	143	15	,	,	PUNCT
ajis02-1563	143	16	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	143	17	)	)	PUNCT
ajis02-1563	143	18	=	=	PUNCT
ajis02-1563	144	1	𝑡𝑟(𝐴𝑝	𝑡𝑟(𝐴𝑝	PROPN
ajis02-1563	144	2	)	)	PUNCT
ajis02-1563	144	3	=	=	PUNCT
ajis02-1563	144	4	∑	∑	PUNCT
ajis02-1563	144	5	𝜆𝑖	𝜆𝑖	PROPN
ajis02-1563	144	6	𝑝	𝑝	PROPN
ajis02-1563	144	7	𝑛	𝑛	PROPN
ajis02-1563	144	8	𝑖=1	𝑖=1	PROPN
ajis02-1563	144	9	.	.	PUNCT
ajis02-1563	145	1	it	it	PRON
ajis02-1563	145	2	is	be	AUX
ajis02-1563	145	3	clear	clear	ADJ
ajis02-1563	145	4	from	from	ADP
ajis02-1563	145	5	the	the	DET
ajis02-1563	145	6	definitions	definition	NOUN
ajis02-1563	145	7	and	and	CCONJ
ajis02-1563	145	8	fact	fact	NOUN
ajis02-1563	145	9	5	5	NUM
ajis02-1563	145	10	that	that	SCONJ
ajis02-1563	145	11	for	for	ADP
ajis02-1563	145	12	⊂	⊂	PROPN
ajis02-1563	145	13	v	v	ADP
ajis02-1563	145	14	,	,	PUNCT
ajis02-1563	145	15	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	145	16	)	)	PUNCT
ajis02-1563	145	17	=	=	SYM
ajis02-1563	145	18	𝐶𝑊𝑝(𝐺−𝑆	𝐶𝑊𝑝(𝐺−𝑆	NOUN
ajis02-1563	145	19	,	,	PUNCT
ajis02-1563	145	20	𝑉	𝑉	PROPN
ajis02-1563	145	21	∖	∖	NOUN
ajis02-1563	145	22	𝑆	𝑆	PROPN
ajis02-1563	145	23	)	)	PUNCT
ajis02-1563	146	1	+	+	CCONJ
ajis02-1563	146	2	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	146	3	,	,	PUNCT
ajis02-1563	146	4	𝑆	𝑆	PROPN
ajis02-1563	146	5	)	)	PUNCT
ajis02-1563	146	6	.	.	PUNCT
ajis02-1563	147	1	(	(	PUNCT
ajis02-1563	147	2	3	3	X
ajis02-1563	147	3	)	)	PUNCT
ajis02-1563	147	4	this	this	DET
ajis02-1563	147	5	identity	identity	NOUN
ajis02-1563	147	6	is	be	AUX
ajis02-1563	147	7	same	same	ADJ
ajis02-1563	147	8	as	as	ADP
ajis02-1563	147	9	the	the	DET
ajis02-1563	147	10	one	one	NOUN
ajis02-1563	147	11	already	already	ADV
ajis02-1563	147	12	mentioned	mention	VERB
ajis02-1563	147	13	in	in	ADP
ajis02-1563	147	14	(	(	PUNCT
ajis02-1563	147	15	3	3	NUM
ajis02-1563	147	16	)	)	PUNCT
ajis02-1563	147	17	.	.	PUNCT
ajis02-1563	148	1	this	this	PRON
ajis02-1563	148	2	similarly	similarly	ADV
ajis02-1563	148	3	suggests	suggest	VERB
ajis02-1563	148	4	a	a	DET
ajis02-1563	148	5	strategy	strategy	NOUN
ajis02-1563	148	6	namely	namely	ADV
ajis02-1563	148	7	one	one	PRON
ajis02-1563	148	8	should	should	AUX
ajis02-1563	148	9	delete	delete	VERB
ajis02-1563	148	10	a	a	DET
ajis02-1563	148	11	set	set	NOUN
ajis02-1563	148	12	s	s	NOUN
ajis02-1563	148	13	of	of	ADP
ajis02-1563	148	14	k	k	PROPN
ajis02-1563	148	15	vertices	vertex	NOUN
ajis02-1563	148	16	such	such	ADJ
ajis02-1563	148	17	that	that	SCONJ
ajis02-1563	148	18	𝐶𝑊𝑝(𝐺−𝑆	𝐶𝑊𝑝(𝐺−𝑆	NOUN
ajis02-1563	148	19	,	,	PUNCT
ajis02-1563	148	20	𝑉	𝑉	PROPN
ajis02-1563	148	21	∖	∖	X
ajis02-1563	148	22	𝑆	𝑆	PROPN
ajis02-1563	148	23	)	)	PUNCT
ajis02-1563	148	24	is	be	AUX
ajis02-1563	148	25	minimized	minimize	VERB
ajis02-1563	148	26	for	for	ADP
ajis02-1563	148	27	a	a	DET
ajis02-1563	148	28	large	large	ADJ
ajis02-1563	148	29	even	even	ADV
ajis02-1563	148	30	integer	integer	NOUN
ajis02-1563	148	31	p	p	X
ajis02-1563	148	32	(	(	PUNCT
ajis02-1563	148	33	equivalently	equivalently	ADV
ajis02-1563	148	34	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	148	35	,	,	PUNCT
ajis02-1563	148	36	𝑆	𝑆	PROPN
ajis02-1563	148	37	)	)	PUNCT
ajis02-1563	148	38	is	be	AUX
ajis02-1563	148	39	maximized	maximize	VERB
ajis02-1563	148	40	)	)	PUNCT
ajis02-1563	148	41	.	.	PUNCT
ajis02-1563	149	1	the	the	DET
ajis02-1563	149	2	goodness	goodness	NOUN
ajis02-1563	149	3	of	of	ADP
ajis02-1563	149	4	a	a	DET
ajis02-1563	149	5	set	set	NOUN
ajis02-1563	149	6	of	of	ADP
ajis02-1563	149	7	vertices	vertex	NOUN
ajis02-1563	149	8	s⊆v	s⊆v	PROPN
ajis02-1563	149	9	,	,	PUNCT
ajis02-1563	149	10	in	in	ADP
ajis02-1563	149	11	terms	term	NOUN
ajis02-1563	149	12	of	of	ADP
ajis02-1563	149	13	number	number	NOUN
ajis02-1563	149	14	of	of	ADP
ajis02-1563	149	15	closed	closed	ADJ
ajis02-1563	149	16	walks	walk	NOUN
ajis02-1563	149	17	is	be	AUX
ajis02-1563	149	18	given	give	VERB
ajis02-1563	149	19	by	by	ADP
ajis02-1563	149	20	𝑔𝑝(𝑆	𝑔𝑝(𝑆	ADJ
ajis02-1563	149	21	)	)	PUNCT
ajis02-1563	149	22	=	=	SYM
ajis02-1563	149	23	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	149	24	,	,	PUNCT
ajis02-1563	149	25	𝑆	𝑆	PROPN
ajis02-1563	149	26	)	)	PUNCT
ajis02-1563	149	27	(	(	PUNCT
ajis02-1563	149	28	4	4	X
ajis02-1563	149	29	)	)	PUNCT
ajis02-1563	149	30	which	which	PRON
ajis02-1563	149	31	as	as	SCONJ
ajis02-1563	149	32	noted	note	VERB
ajis02-1563	149	33	above	above	ADP
ajis02-1563	149	34	we	we	PRON
ajis02-1563	149	35	would	would	AUX
ajis02-1563	149	36	like	like	VERB
ajis02-1563	149	37	to	to	PART
ajis02-1563	149	38	maximize	maximize	VERB
ajis02-1563	149	39	.	.	PUNCT
ajis02-1563	150	1	hence	hence	ADV
ajis02-1563	150	2	we	we	PRON
ajis02-1563	150	3	reduced	reduce	VERB
ajis02-1563	150	4	the	the	DET
ajis02-1563	150	5	problem	problem	NOUN
ajis02-1563	150	6	of	of	ADP
ajis02-1563	150	7	finding	find	VERB
ajis02-1563	150	8	a	a	DET
ajis02-1563	150	9	set	set	NOUN
ajis02-1563	150	10	maximizing	maximize	VERB
ajis02-1563	150	11	the	the	DET
ajis02-1563	150	12	eigendrop	eigendrop	NOUN
ajis02-1563	150	13	to	to	ADP
ajis02-1563	150	14	the	the	DET
ajis02-1563	150	15	problem	problem	NOUN
ajis02-1563	150	16	of	of	ADP
ajis02-1563	150	17	finding	find	VERB
ajis02-1563	150	18	a	a	DET
ajis02-1563	150	19	set	set	NOUN
ajis02-1563	150	20	of	of	ADP
ajis02-1563	150	21	vertices	vertex	NOUN
ajis02-1563	150	22	that	that	PRON
ajis02-1563	150	23	are	be	AUX
ajis02-1563	150	24	part	part	NOUN
ajis02-1563	150	25	of	of	ADP
ajis02-1563	150	26	many	many	ADJ
ajis02-1563	150	27	closed	closed	ADJ
ajis02-1563	150	28	walks	walk	NOUN
ajis02-1563	150	29	.	.	PUNCT
ajis02-1563	151	1	we	we	PRON
ajis02-1563	151	2	note	note	VERB
ajis02-1563	151	3	that	that	SCONJ
ajis02-1563	151	4	this	this	DET
ajis02-1563	151	5	latter	latter	ADJ
ajis02-1563	151	6	problem	problem	NOUN
ajis02-1563	151	7	is	be	AUX
ajis02-1563	151	8	of	of	ADP
ajis02-1563	151	9	a	a	DET
ajis02-1563	151	10	combinatorial	combinatorial	ADJ
ajis02-1563	151	11	nature	nature	NOUN
ajis02-1563	151	12	and	and	CCONJ
ajis02-1563	151	13	more	more	ADV
ajis02-1563	151	14	amenable	amenable	ADJ
ajis02-1563	151	15	to	to	ADP
ajis02-1563	151	16	techniques	technique	NOUN
ajis02-1563	151	17	from	from	ADP
ajis02-1563	151	18	graph	graph	NOUN
ajis02-1563	151	19	theory	theory	NOUN
ajis02-1563	151	20	.	.	PUNCT
ajis02-1563	152	1	algorithm	algorithm	NOUN
ajis02-1563	152	2	2	2	NUM
ajis02-1563	152	3	:	:	PUNCT
ajis02-1563	152	4	greedy-2	greedy-2	PROPN
ajis02-1563	152	5	(	(	PUNCT
ajis02-1563	152	6	𝑮	𝑮	PROPN
ajis02-1563	152	7	,	,	PUNCT
ajis02-1563	152	8	𝒌	𝒌	ADV
ajis02-1563	152	9	,	,	PUNCT
ajis02-1563	152	10	𝒑	𝒑	X
ajis02-1563	152	11	)	)	PUNCT
ajis02-1563	152	12	𝑆	𝑆	PROPN
ajis02-1563	152	13	←	←	NOUN
ajis02-1563	152	14	∅	∅	NOUN
ajis02-1563	152	15	𝒘𝒉𝒊𝒍𝒆	𝒘𝒉𝒊𝒍𝒆	NOUN
ajis02-1563	152	16	|𝑆|	|𝑆|	VERB
ajis02-1563	152	17	<	<	X
ajis02-1563	152	18	𝑘	𝑘	PRON
ajis02-1563	152	19	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	152	20	𝑣	𝑣	PRON
ajis02-1563	152	21	←	←	PROPN
ajis02-1563	152	22	𝑎𝑟𝑔𝑚𝑎𝑥	𝑎𝑟𝑔𝑚𝑎𝑥	PROPN
ajis02-1563	152	23	𝐶𝑊𝑝	𝐶𝑊𝑝	PROPN
ajis02-1563	152	24	v∈v	v∈v	PROPN
ajis02-1563	152	25	∖s	∖s	PROPN
ajis02-1563	152	26	(	(	PUNCT
ajis02-1563	152	27	𝐺𝑆	𝐺𝑆	PROPN
ajis02-1563	152	28	,	,	PUNCT
ajis02-1563	152	29	𝑣	𝑣	NOUN
ajis02-1563	152	30	)	)	PUNCT
ajis02-1563	152	31	𝑆	𝑆	PROPN
ajis02-1563	152	32	←	←	PROPN
ajis02-1563	152	33	𝑆	𝑆	PROPN
ajis02-1563	152	34	∪	∪	NOUN
ajis02-1563	152	35	{	{	PUNCT
ajis02-1563	152	36	𝑣	𝑣	NOUN
ajis02-1563	152	37	}	}	PUNCT
ajis02-1563	152	38	𝒓𝒆𝒕𝒖𝒓𝒏	𝒓𝒆𝒕𝒖𝒓𝒏	VERB
ajis02-1563	152	39	𝑆	𝑆	PROPN
ajis02-1563	152	40	an	an	DET
ajis02-1563	152	41	algorithm	algorithm	NOUN
ajis02-1563	152	42	based	base	VERB
ajis02-1563	152	43	on	on	ADP
ajis02-1563	152	44	this	this	DET
ajis02-1563	152	45	intuition	intuition	NOUN
ajis02-1563	152	46	is	be	AUX
ajis02-1563	152	47	given	give	VERB
ajis02-1563	152	48	in	in	ADP
ajis02-1563	152	49	algorithm	algorithm	NOUN
ajis02-1563	152	50	greedy-2(g	greedy-2(g	NOUN
ajis02-1563	152	51	,	,	PUNCT
ajis02-1563	152	52	k	k	NOUN
ajis02-1563	152	53	,	,	PUNCT
ajis02-1563	152	54	p	p	NOUN
ajis02-1563	152	55	)	)	PUNCT
ajis02-1563	152	56	.	.	PUNCT
ajis02-1563	153	1	quality	quality	NOUN
ajis02-1563	153	2	guarantee	guarantee	NOUN
ajis02-1563	153	3	of	of	ADP
ajis02-1563	153	4	algorithm	algorithm	NOUN
ajis02-1563	153	5	greedy-2(g	greedy-2(g	NOUN
ajis02-1563	153	6	,	,	PUNCT
ajis02-1563	153	7	k	k	NOUN
ajis02-1563	153	8	,	,	PUNCT
ajis02-1563	153	9	p	p	NOUN
ajis02-1563	153	10	)	)	PUNCT
ajis02-1563	153	11	follows	follow	VERB
ajis02-1563	153	12	from	from	ADP
ajis02-1563	153	13	sub	sub	NOUN
ajis02-1563	153	14	-	-	NOUN
ajis02-1563	153	15	modularity	modularity	NOUN
ajis02-1563	153	16	of	of	ADP
ajis02-1563	153	17	the	the	DET
ajis02-1563	153	18	optimization	optimization	NOUN
ajis02-1563	153	19	function	function	NOUN
ajis02-1563	153	20	(	(	PUNCT
ajis02-1563	153	21	4	4	NUM
ajis02-1563	153	22	)	)	PUNCT
ajis02-1563	153	23	and	and	CCONJ
ajis02-1563	153	24	theorem	theorem	VERB
ajis02-1563	153	25	1	1	NUM
ajis02-1563	153	26	.	.	PUNCT
ajis02-1563	154	1	next	next	ADV
ajis02-1563	154	2	we	we	PRON
ajis02-1563	154	3	show	show	VERB
ajis02-1563	154	4	that	that	SCONJ
ajis02-1563	154	5	the	the	DET
ajis02-1563	154	6	objective	objective	ADJ
ajis02-1563	154	7	function	function	NOUN
ajis02-1563	154	8	given	give	VERB
ajis02-1563	154	9	in	in	ADP
ajis02-1563	154	10	(	(	PUNCT
ajis02-1563	154	11	4	4	NUM
ajis02-1563	154	12	)	)	PUNCT
ajis02-1563	154	13	is	be	AUX
ajis02-1563	154	14	nonnegative	nonnegative	ADJ
ajis02-1563	154	15	,	,	PUNCT
ajis02-1563	154	16	monotone	monotone	ADJ
ajis02-1563	154	17	sub	sub	NOUN
ajis02-1563	154	18	-	-	ADJ
ajis02-1563	154	19	modular	modular	ADJ
ajis02-1563	154	20	,	,	PUNCT
ajis02-1563	154	21	i.e.	i.e.	X
ajis02-1563	154	22	we	we	PRON
ajis02-1563	154	23	show	show	VERB
ajis02-1563	154	24	that	that	SCONJ
ajis02-1563	154	25	gp(s	gp(s	NOUN
ajis02-1563	154	26	)	)	PUNCT
ajis02-1563	154	27	has	have	VERB
ajis02-1563	154	28	the	the	DET
ajis02-1563	154	29	property	property	NOUN
ajis02-1563	154	30	of	of	ADP
ajis02-1563	154	31	diminishing	diminish	VERB
ajis02-1563	154	32	return	return	NOUN
ajis02-1563	154	33	.	.	PUNCT
ajis02-1563	155	1	australasian	australasian	ADJ
ajis02-1563	155	2	journal	journal	NOUN
ajis02-1563	155	3	of	of	ADP
ajis02-1563	155	4	information	information	NOUN
ajis02-1563	155	5	systems	system	NOUN
ajis02-1563	155	6	ahmad	ahmad	PROPN
ajis02-1563	155	7	,	,	PUNCT
ajis02-1563	155	8	traiq	traiq	NOUN
ajis02-1563	155	9	,	,	PUNCT
ajis02-1563	155	10	shabbir	shabbir	PROPN
ajis02-1563	155	11	&	&	CCONJ
ajis02-1563	155	12	khan	khan	PROPN
ajis02-1563	155	13	2017	2017	NUM
ajis02-1563	155	14	,	,	PUNCT
ajis02-1563	155	15	vol	vol	NOUN
ajis02-1563	155	16	21	21	NUM
ajis02-1563	155	17	,	,	PUNCT
ajis02-1563	155	18	selected	select	VERB
ajis02-1563	155	19	papers	paper	NOUN
ajis02-1563	155	20	from	from	ADP
ajis02-1563	155	21	ausdm	ausdm	NOUN
ajis02-1563	155	22	spectral	spectral	ADJ
ajis02-1563	155	23	methods	method	NOUN
ajis02-1563	155	24	for	for	ADP
ajis02-1563	155	25	immunization	immunization	NOUN
ajis02-1563	155	26	of	of	ADP
ajis02-1563	155	27	large	large	ADJ
ajis02-1563	155	28	networks	network	NOUN
ajis02-1563	155	29	7	7	NUM
ajis02-1563	155	30	lemma	lemma	PROPN
ajis02-1563	155	31	2	2	NUM
ajis02-1563	155	32	:	:	PUNCT
ajis02-1563	155	33	the	the	DET
ajis02-1563	155	34	function	function	NOUN
ajis02-1563	155	35	gp(s	gp(s	NOUN
ajis02-1563	155	36	)	)	PUNCT
ajis02-1563	155	37	given	give	VERB
ajis02-1563	155	38	in	in	ADP
ajis02-1563	155	39	(	(	PUNCT
ajis02-1563	155	40	4	4	NUM
ajis02-1563	155	41	)	)	PUNCT
ajis02-1563	155	42	is	be	AUX
ajis02-1563	155	43	non	non	ADJ
ajis02-1563	155	44	-	-	ADJ
ajis02-1563	155	45	negative	negative	ADJ
ajis02-1563	155	46	,	,	PUNCT
ajis02-1563	155	47	monotonically	monotonically	ADV
ajis02-1563	155	48	non	non	ADJ
ajis02-1563	155	49	-	-	ADJ
ajis02-1563	155	50	decreasing	decrease	VERB
ajis02-1563	155	51	and	and	CCONJ
ajis02-1563	155	52	sub	sub	ADJ
ajis02-1563	155	53	-	-	ADJ
ajis02-1563	155	54	modular	modular	ADJ
ajis02-1563	155	55	.	.	PUNCT
ajis02-1563	156	1	proof	proof	NOUN
ajis02-1563	156	2	:	:	PUNCT
ajis02-1563	156	3	since	since	SCONJ
ajis02-1563	156	4	gp(s	gp(s	NUM
ajis02-1563	156	5	)	)	PUNCT
ajis02-1563	156	6	counts	count	VERB
ajis02-1563	156	7	the	the	DET
ajis02-1563	156	8	number	number	NOUN
ajis02-1563	156	9	of	of	ADP
ajis02-1563	156	10	closed	closed	ADJ
ajis02-1563	156	11	walks	walk	NOUN
ajis02-1563	156	12	of	of	ADP
ajis02-1563	156	13	length	length	NOUN
ajis02-1563	156	14	p	p	X
ajis02-1563	156	15	,	,	PUNCT
ajis02-1563	156	16	it	it	PRON
ajis02-1563	156	17	is	be	AUX
ajis02-1563	156	18	clearly	clearly	ADV
ajis02-1563	156	19	non	non	ADJ
ajis02-1563	156	20	-	-	ADJ
ajis02-1563	156	21	negative	negative	ADJ
ajis02-1563	156	22	.	.	PUNCT
ajis02-1563	157	1	by	by	ADP
ajis02-1563	157	2	definition	definition	NOUN
ajis02-1563	157	3	of	of	ADP
ajis02-1563	157	4	gp(s	gp(s	NOUN
ajis02-1563	157	5	)	)	PUNCT
ajis02-1563	157	6	for	for	ADP
ajis02-1563	157	7	x⊆	x⊆	PROPN
ajis02-1563	157	8	y	y	PROPN
ajis02-1563	157	9	we	we	PRON
ajis02-1563	157	10	have	have	VERB
ajis02-1563	157	11	𝑔𝑝(𝑌	𝑔𝑝(𝑌	NOUN
ajis02-1563	157	12	)	)	PUNCT
ajis02-1563	158	1	−	−	ADP
ajis02-1563	158	2	𝑔𝑝(𝑋	𝑔𝑝(𝑋	NOUN
ajis02-1563	158	3	)	)	PUNCT
ajis02-1563	158	4	=	=	SYM
ajis02-1563	158	5	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	158	6	,	,	PUNCT
ajis02-1563	158	7	𝑌	𝑌	PROPN
ajis02-1563	158	8	)	)	PUNCT
ajis02-1563	158	9	−	−	PROPN
ajis02-1563	158	10	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	158	11	,	,	PUNCT
ajis02-1563	158	12	𝑌	𝑌	PROPN
ajis02-1563	158	13	)	)	PUNCT
ajis02-1563	158	14	=	=	SYM
ajis02-1563	158	15	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	158	16	,	,	PUNCT
ajis02-1563	158	17	(	(	PUNCT
ajis02-1563	158	18	𝑌	𝑌	PROPN
ajis02-1563	158	19	∖	∖	NOUN
ajis02-1563	158	20	𝑋	𝑋	PROPN
ajis02-1563	158	21	)	)	PUNCT
ajis02-1563	158	22	∪	∪	PROPN
ajis02-1563	158	23	𝑋	𝑋	PROPN
ajis02-1563	158	24	)	)	PUNCT
ajis02-1563	158	25	−	−	PROPN
ajis02-1563	158	26	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	158	27	,	,	PUNCT
ajis02-1563	158	28	𝑋	𝑋	PROPN
ajis02-1563	158	29	)	)	PUNCT
ajis02-1563	158	30	=	=	SYM
ajis02-1563	158	31	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	158	32	,	,	PUNCT
ajis02-1563	158	33	𝑋	𝑋	PROPN
ajis02-1563	158	34	)	)	PUNCT
ajis02-1563	158	35	+	+	NUM
ajis02-1563	158	36	𝐶𝑊𝑝(𝐺−𝑋	𝐶𝑊𝑝(𝐺−𝑋	NOUN
ajis02-1563	158	37	,	,	PUNCT
ajis02-1563	158	38	𝑌	𝑌	PROPN
ajis02-1563	158	39	∖	∖	NOUN
ajis02-1563	158	40	𝑋	𝑋	PROPN
ajis02-1563	158	41	)	)	PUNCT
ajis02-1563	158	42	−	−	PROPN
ajis02-1563	158	43	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	158	44	,	,	PUNCT
ajis02-1563	158	45	𝑋	𝑋	PROPN
ajis02-1563	158	46	)	)	PUNCT
ajis02-1563	158	47	=	=	SYM
ajis02-1563	158	48	𝐶𝑊𝑝(𝐺−𝑋	𝐶𝑊𝑝(𝐺−𝑋	PROPN
ajis02-1563	158	49	,	,	PUNCT
ajis02-1563	158	50	𝑌	𝑌	PROPN
ajis02-1563	158	51	∖	∖	PROPN
ajis02-1563	158	52	𝑋	𝑋	PROPN
ajis02-1563	158	53	)	)	PUNCT
ajis02-1563	158	54	≥	≥	NOUN
ajis02-1563	158	55	0	0	NUM
ajis02-1563	158	56	where	where	SCONJ
ajis02-1563	158	57	the	the	DET
ajis02-1563	158	58	last	last	ADJ
ajis02-1563	158	59	inequality	inequality	NOUN
ajis02-1563	158	60	follows	follow	VERB
ajis02-1563	158	61	from	from	ADP
ajis02-1563	158	62	non	non	ADJ
ajis02-1563	158	63	-	-	NOUN
ajis02-1563	158	64	negativity	negativity	NOUN
ajis02-1563	158	65	of	of	ADP
ajis02-1563	158	66	gp(s	gp(s	NOUN
ajis02-1563	158	67	)	)	PUNCT
ajis02-1563	158	68	.	.	PUNCT
ajis02-1563	159	1	hence	hence	ADV
ajis02-1563	159	2	gp(s	gp(s	NUM
ajis02-1563	159	3	)	)	PUNCT
ajis02-1563	159	4	is	be	AUX
ajis02-1563	159	5	monotonically	monotonically	ADV
ajis02-1563	159	6	non	non	ADJ
ajis02-1563	159	7	-	-	ADJ
ajis02-1563	159	8	decreasing	decrease	VERB
ajis02-1563	159	9	function	function	NOUN
ajis02-1563	159	10	.	.	PUNCT
ajis02-1563	160	1	for	for	ADP
ajis02-1563	160	2	sub	sub	NOUN
ajis02-1563	160	3	-	-	NOUN
ajis02-1563	160	4	modularity	modularity	NOUN
ajis02-1563	160	5	of	of	ADP
ajis02-1563	160	6	gp(s	gp(s	NOUN
ajis02-1563	160	7	)	)	PUNCT
ajis02-1563	160	8	,	,	PUNCT
ajis02-1563	160	9	let	let	VERB
ajis02-1563	160	10	x	x	PRON
ajis02-1563	160	11	,	,	PUNCT
ajis02-1563	160	12	y	y	PROPN
ajis02-1563	160	13	,	,	PUNCT
ajis02-1563	160	14	z⊂v	z⊂v	NOUN
ajis02-1563	160	15	such	such	ADJ
ajis02-1563	160	16	that	that	SCONJ
ajis02-1563	160	17	x⊂y	x⊂y	NOUN
ajis02-1563	160	18	and	and	CCONJ
ajis02-1563	160	19	z∩y=∅.	z∩y=∅.	NUM
ajis02-1563	160	20	let	let	VERB
ajis02-1563	160	21	l	l	NOUN
ajis02-1563	160	22	=	=	NOUN
ajis02-1563	160	23	x∪z	x∪z	NOUN
ajis02-1563	160	24	and	and	CCONJ
ajis02-1563	160	25	r	r	NOUN
ajis02-1563	160	26	=	=	NOUN
ajis02-1563	160	27	y∪z	y∪z	NOUN
ajis02-1563	160	28	.	.	PUNCT
ajis02-1563	161	1	we	we	PRON
ajis02-1563	161	2	have	have	VERB
ajis02-1563	161	3	(	(	PUNCT
ajis02-1563	161	4	𝑔𝑝(𝑅	𝑔𝑝(𝑅	PROPN
ajis02-1563	161	5	)	)	PUNCT
ajis02-1563	161	6	−	−	PROPN
ajis02-1563	161	7	𝑔𝑝(𝑌	𝑔𝑝(𝑌	PROPN
ajis02-1563	161	8	)	)	PUNCT
ajis02-1563	161	9	)	)	PUNCT
ajis02-1563	162	1	−	−	PROPN
ajis02-1563	162	2	(	(	PUNCT
ajis02-1563	162	3	𝑔𝑝(𝐿	𝑔𝑝(𝐿	NOUN
ajis02-1563	162	4	)	)	PUNCT
ajis02-1563	162	5	−	−	PROPN
ajis02-1563	162	6	𝑔𝑝(𝑋	𝑔𝑝(𝑋	NOUN
ajis02-1563	162	7	)	)	PUNCT
ajis02-1563	162	8	)	)	PUNCT
ajis02-1563	163	1	=	=	SYM
ajis02-1563	163	2	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	163	3	,	,	PUNCT
ajis02-1563	163	4	𝑅	𝑅	NOUN
ajis02-1563	163	5	)	)	PUNCT
ajis02-1563	163	6	−	−	PROPN
ajis02-1563	163	7	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	163	8	,	,	PUNCT
ajis02-1563	163	9	𝑌	𝑌	PROPN
ajis02-1563	163	10	)	)	PUNCT
ajis02-1563	163	11	−	−	PROPN
ajis02-1563	163	12	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	163	13	,	,	PUNCT
ajis02-1563	163	14	𝐿	𝐿	PROPN
ajis02-1563	163	15	)	)	PUNCT
ajis02-1563	163	16	+	+	CCONJ
ajis02-1563	163	17	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	163	18	,	,	PUNCT
ajis02-1563	163	19	𝑋	𝑋	PROPN
ajis02-1563	163	20	=	=	SYM
ajis02-1563	163	21	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	163	22	,	,	PUNCT
ajis02-1563	163	23	𝑌	𝑌	PROPN
ajis02-1563	163	24	∪	∪	ADJ
ajis02-1563	163	25	𝑍	𝑍	NOUN
ajis02-1563	163	26	)	)	PUNCT
ajis02-1563	163	27	−	−	PROPN
ajis02-1563	163	28	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	163	29	,	,	PUNCT
ajis02-1563	163	30	𝑌	𝑌	PROPN
ajis02-1563	163	31	)	)	PUNCT
ajis02-1563	163	32	−	−	PROPN
ajis02-1563	163	33	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	163	34	,	,	PUNCT
ajis02-1563	163	35	𝑋	𝑋	PROPN
ajis02-1563	163	36	∪	∪	ADJ
ajis02-1563	163	37	𝑍	𝑍	NOUN
ajis02-1563	163	38	)	)	PUNCT
ajis02-1563	164	1	+	+	CCONJ
ajis02-1563	164	2	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	164	3	,	,	PUNCT
ajis02-1563	164	4	𝑋	𝑋	PROPN
ajis02-1563	164	5	)	)	PUNCT
ajis02-1563	164	6	=	=	SYM
ajis02-1563	164	7	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	164	8	,	,	PUNCT
ajis02-1563	164	9	𝑌	𝑌	PROPN
ajis02-1563	164	10	)	)	PUNCT
ajis02-1563	164	11	+	+	CCONJ
ajis02-1563	164	12	𝐶𝑊𝑝(𝐺−𝑌	𝐶𝑊𝑝(𝐺−𝑌	NOUN
ajis02-1563	164	13	,	,	PUNCT
ajis02-1563	164	14	𝑍	𝑍	NOUN
ajis02-1563	164	15	)	)	PUNCT
ajis02-1563	164	16	−	−	PROPN
ajis02-1563	164	17	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	164	18	,	,	PUNCT
ajis02-1563	164	19	𝑌	𝑌	PROPN
ajis02-1563	164	20	)	)	PUNCT
ajis02-1563	164	21	−	−	PROPN
ajis02-1563	164	22	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	164	23	,	,	PUNCT
ajis02-1563	164	24	𝑋	𝑋	PROPN
ajis02-1563	164	25	)	)	PUNCT
ajis02-1563	164	26	−	−	PROPN
ajis02-1563	164	27	𝐶𝑊𝑝(𝐺−𝑋	𝐶𝑊𝑝(𝐺−𝑋	PROPN
ajis02-1563	164	28	,	,	PUNCT
ajis02-1563	164	29	𝑍	𝑍	PROPN
ajis02-1563	164	30	)	)	PUNCT
ajis02-1563	164	31	+	+	CCONJ
ajis02-1563	164	32	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	PROPN
ajis02-1563	164	33	,	,	PUNCT
ajis02-1563	164	34	𝑋	𝑋	PROPN
ajis02-1563	164	35	)	)	PUNCT
ajis02-1563	164	36	=	=	SYM
ajis02-1563	164	37	𝐶𝑊𝑝(𝐺−𝑌	𝐶𝑊𝑝(𝐺−𝑌	NOUN
ajis02-1563	164	38	,	,	PUNCT
ajis02-1563	164	39	𝑍	𝑍	NOUN
ajis02-1563	164	40	)	)	PUNCT
ajis02-1563	164	41	−	−	NOUN
ajis02-1563	164	42	𝐶𝑊𝑝(𝐺𝑋	𝐶𝑊𝑝(𝐺𝑋	NOUN
ajis02-1563	164	43	,	,	PUNCT
ajis02-1563	164	44	𝑍	𝑍	PROPN
ajis02-1563	164	45	)	)	PUNCT
ajis02-1563	164	46	≤	≤	NOUN
ajis02-1563	164	47	0	0	NUM
ajis02-1563	164	48	where	where	SCONJ
ajis02-1563	164	49	the	the	DET
ajis02-1563	164	50	last	last	ADJ
ajis02-1563	164	51	inequality	inequality	NOUN
ajis02-1563	164	52	follows	follow	VERB
ajis02-1563	164	53	from	from	ADP
ajis02-1563	164	54	the	the	DET
ajis02-1563	164	55	fact	fact	NOUN
ajis02-1563	164	56	that	that	SCONJ
ajis02-1563	164	57	by	by	ADP
ajis02-1563	164	58	definition	definition	NOUN
ajis02-1563	164	59	ℂ𝕎𝑝(𝐺−𝑌	ℂ𝕎𝑝(𝐺−𝑌	NOUN
ajis02-1563	164	60	,	,	PUNCT
ajis02-1563	164	61	𝑍	𝑍	PROPN
ajis02-1563	164	62	)	)	PUNCT
ajis02-1563	164	63	⊆	⊆	NUM
ajis02-1563	164	64	ℂ𝕎𝑝(𝐺−𝑋	ℂ𝕎𝑝(𝐺−𝑋	NOUN
ajis02-1563	164	65	,	,	PUNCT
ajis02-1563	164	66	𝑍	𝑍	PROPN
ajis02-1563	164	67	)	)	PUNCT
ajis02-1563	164	68	,	,	PUNCT
ajis02-1563	164	69	hence	hence	ADV
ajis02-1563	164	70	𝐶𝑊𝑝(𝐺−𝑌	𝐶𝑊𝑝(𝐺−𝑌	NOUN
ajis02-1563	164	71	,	,	PUNCT
ajis02-1563	164	72	𝑍	𝑍	PROPN
ajis02-1563	164	73	)	)	PUNCT
ajis02-1563	164	74	≤	≤	NOUN
ajis02-1563	164	75	𝐶𝑊𝑝(𝐺−𝑋	𝐶𝑊𝑝(𝐺−𝑋	NOUN
ajis02-1563	164	76	,	,	PUNCT
ajis02-1563	164	77	𝑍	𝑍	PROPN
ajis02-1563	164	78	)	)	PUNCT
ajis02-1563	164	79	for	for	ADP
ajis02-1563	164	80	a	a	DET
ajis02-1563	164	81	vertex	vertex	NOUN
ajis02-1563	164	82	v	v	NOUN
ajis02-1563	164	83	,	,	PUNCT
ajis02-1563	164	84	𝐶𝑊𝑝(𝐺	𝐶𝑊𝑝(𝐺	NOUN
ajis02-1563	164	85	,	,	PUNCT
ajis02-1563	164	86	𝑣	𝑣	NOUN
ajis02-1563	164	87	)	)	PUNCT
ajis02-1563	164	88	can	can	AUX
ajis02-1563	164	89	be	be	AUX
ajis02-1563	164	90	computed	compute	VERB
ajis02-1563	164	91	by	by	ADP
ajis02-1563	164	92	the	the	DET
ajis02-1563	164	93	powers	power	NOUN
ajis02-1563	164	94	of	of	ADP
ajis02-1563	164	95	a	a	DET
ajis02-1563	164	96	i.e	i.e	PROPN
ajis02-1563	164	97	𝐴2	𝐴2	PROPN
ajis02-1563	164	98	,	,	PUNCT
ajis02-1563	164	99	𝐴3	𝐴3	PROPN
ajis02-1563	164	100	,	,	PUNCT
ajis02-1563	164	101	⋯	⋯	PROPN
ajis02-1563	164	102	,	,	PUNCT
ajis02-1563	164	103	𝐴𝑝.	𝐴𝑝.	PROPN
ajis02-1563	164	104	clearly	clearly	ADV
ajis02-1563	164	105	computing	compute	VERB
ajis02-1563	164	106	all	all	DET
ajis02-1563	164	107	these	these	DET
ajis02-1563	164	108	matrices	matrix	NOUN
ajis02-1563	164	109	for	for	ADP
ajis02-1563	164	110	large	large	ADJ
ajis02-1563	164	111	p	p	NOUN
ajis02-1563	164	112	when	when	SCONJ
ajis02-1563	164	113	g	g	PROPN
ajis02-1563	164	114	is	be	AUX
ajis02-1563	164	115	significantly	significantly	ADV
ajis02-1563	164	116	large	large	ADJ
ajis02-1563	164	117	as	as	ADV
ajis02-1563	164	118	well	well	ADV
ajis02-1563	164	119	is	be	AUX
ajis02-1563	164	120	computationally	computationally	ADV
ajis02-1563	164	121	expensive	expensive	ADJ
ajis02-1563	164	122	.	.	PUNCT
ajis02-1563	165	1	so	so	ADV
ajis02-1563	165	2	the	the	DET
ajis02-1563	165	3	algorithm	algorithm	NOUN
ajis02-1563	165	4	greedy-2(g	greedy-2(g	NOUN
ajis02-1563	165	5	,	,	PUNCT
ajis02-1563	165	6	k	k	NOUN
ajis02-1563	165	7	,	,	PUNCT
ajis02-1563	165	8	p	p	NOUN
ajis02-1563	165	9	)	)	PUNCT
ajis02-1563	165	10	is	be	AUX
ajis02-1563	165	11	practically	practically	ADV
ajis02-1563	165	12	impossible	impossible	ADJ
ajis02-1563	165	13	to	to	PART
ajis02-1563	165	14	be	be	AUX
ajis02-1563	165	15	executed	execute	VERB
ajis02-1563	165	16	.	.	PUNCT
ajis02-1563	166	1	so	so	ADV
ajis02-1563	166	2	we	we	PRON
ajis02-1563	166	3	set	set	VERB
ajis02-1563	166	4	p=4	p=4	ADP
ajis02-1563	166	5	to	to	PART
ajis02-1563	166	6	approximate	approximate	VERB
ajis02-1563	166	7	the	the	DET
ajis02-1563	166	8	result	result	NOUN
ajis02-1563	166	9	and	and	CCONJ
ajis02-1563	166	10	our	our	PRON
ajis02-1563	166	11	practical	practical	ADJ
ajis02-1563	166	12	experimentation	experimentation	NOUN
ajis02-1563	166	13	shows	show	VERB
ajis02-1563	166	14	that	that	SCONJ
ajis02-1563	166	15	p=4	p=4	PRON
ajis02-1563	166	16	gives	give	VERB
ajis02-1563	166	17	good	good	ADJ
ajis02-1563	166	18	enough	enough	ADJ
ajis02-1563	166	19	quality	quality	NOUN
ajis02-1563	166	20	guarantee	guarantee	NOUN
ajis02-1563	166	21	.	.	PUNCT
ajis02-1563	167	1	although	although	SCONJ
ajis02-1563	167	2	we	we	PRON
ajis02-1563	167	3	have	have	AUX
ajis02-1563	167	4	also	also	ADV
ajis02-1563	167	5	done	do	VERB
ajis02-1563	167	6	approximation	approximation	NOUN
ajis02-1563	167	7	using	use	VERB
ajis02-1563	167	8	p=6	p=6	PROPN
ajis02-1563	167	9	in	in	ADP
ajis02-1563	167	10	(	(	PUNCT
ajis02-1563	167	11	tariq	tariq	PROPN
ajis02-1563	167	12	2017	2017	NUM
ajis02-1563	167	13	)	)	PUNCT
ajis02-1563	167	14	,	,	PUNCT
ajis02-1563	167	15	which	which	PRON
ajis02-1563	167	16	certainly	certainly	ADV
ajis02-1563	167	17	gives	give	VERB
ajis02-1563	167	18	better	well	ADJ
ajis02-1563	167	19	results	result	NOUN
ajis02-1563	167	20	,	,	PUNCT
ajis02-1563	167	21	we	we	PRON
ajis02-1563	167	22	focus	focus	VERB
ajis02-1563	167	23	on	on	ADP
ajis02-1563	167	24	p=4	p=4	ADP
ajis02-1563	167	25	only	only	ADV
ajis02-1563	167	26	in	in	ADP
ajis02-1563	167	27	this	this	DET
ajis02-1563	167	28	paper	paper	NOUN
ajis02-1563	167	29	.	.	PUNCT
ajis02-1563	168	1	first	first	ADV
ajis02-1563	168	2	we	we	PRON
ajis02-1563	168	3	give	give	VERB
ajis02-1563	168	4	a	a	DET
ajis02-1563	168	5	closed	closed	ADJ
ajis02-1563	168	6	form	form	NOUN
ajis02-1563	168	7	expression	expression	NOUN
ajis02-1563	168	8	for	for	ADP
ajis02-1563	168	9	𝐶𝑊4(𝐺	𝐶𝑊4(𝐺	PROPN
ajis02-1563	168	10	,	,	PUNCT
ajis02-1563	168	11	𝑣	𝑣	NOUN
ajis02-1563	168	12	)	)	PUNCT
ajis02-1563	168	13	in	in	ADP
ajis02-1563	168	14	terms	term	NOUN
ajis02-1563	168	15	of	of	ADP
ajis02-1563	168	16	degrees	degree	NOUN
ajis02-1563	168	17	and	and	CCONJ
ajis02-1563	168	18	codegrees	codegree	NOUN
ajis02-1563	168	19	.	.	PUNCT
ajis02-1563	169	1	for	for	ADP
ajis02-1563	169	2	a	a	DET
ajis02-1563	169	3	given	give	VERB
ajis02-1563	169	4	graph	graph	NOUN
ajis02-1563	169	5	g	g	NOUN
ajis02-1563	169	6	,	,	PUNCT
ajis02-1563	169	7	𝑁𝐺(𝑥	𝑁𝐺(𝑥	PROPN
ajis02-1563	169	8	)	)	PUNCT
ajis02-1563	169	9	=	=	PRON
ajis02-1563	169	10	{	{	PUNCT
ajis02-1563	169	11	𝑦	𝑦	NOUN
ajis02-1563	169	12	∈	∈	PROPN
ajis02-1563	169	13	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	169	14	):	):	PUNCT
ajis02-1563	169	15	𝐴𝐺(𝑥	𝐴𝐺(𝑥	PROPN
ajis02-1563	169	16	,	,	PUNCT
ajis02-1563	169	17	𝑦	𝑦	NOUN
ajis02-1563	169	18	)	)	PUNCT
ajis02-1563	169	19	=	=	SYM
ajis02-1563	169	20	1	1	X
ajis02-1563	169	21	}	}	PUNCT
ajis02-1563	169	22	and	and	CCONJ
ajis02-1563	169	23	𝑑𝐺(𝑥	𝑑𝐺(𝑥	NOUN
ajis02-1563	169	24	)	)	PUNCT
ajis02-1563	169	25	=	=	PUNCT
ajis02-1563	169	26	|𝑁𝐺(𝑥)|	|𝑁𝐺(𝑥)|	PRON
ajis02-1563	169	27	.	.	PUNCT
ajis02-1563	170	1	define	define	VERB
ajis02-1563	170	2	𝑁𝐺(𝑥	𝑁𝐺(𝑥	PROPN
ajis02-1563	170	3	,	,	PUNCT
ajis02-1563	170	4	𝑦	𝑦	NOUN
ajis02-1563	170	5	)	)	PUNCT
ajis02-1563	170	6	=	=	SYM
ajis02-1563	170	7	{	{	PUNCT
ajis02-1563	170	8	𝑧	𝑧	DET
ajis02-1563	170	9	∈	∈	PROPN
ajis02-1563	170	10	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	170	11	):	):	PUNCT
ajis02-1563	170	12	𝐴𝐺(𝑥	𝐴𝐺(𝑥	NOUN
ajis02-1563	170	13	,	,	PUNCT
ajis02-1563	170	14	𝑧	𝑧	NOUN
ajis02-1563	170	15	)	)	PUNCT
ajis02-1563	170	16	=	=	SYM
ajis02-1563	170	17	1	1	NUM
ajis02-1563	170	18	∧	∧	PROPN
ajis02-1563	170	19	𝐴𝐺(𝑦	𝐴𝐺(𝑦	NOUN
ajis02-1563	170	20	,	,	PUNCT
ajis02-1563	170	21	𝑧	𝑧	NOUN
ajis02-1563	170	22	)	)	PUNCT
ajis02-1563	170	23	=	=	SYM
ajis02-1563	170	24	1	1	X
ajis02-1563	170	25	}	}	PUNCT
ajis02-1563	170	26	to	to	PART
ajis02-1563	170	27	be	be	AUX
ajis02-1563	170	28	the	the	DET
ajis02-1563	170	29	common	common	ADJ
ajis02-1563	170	30	neighborhood	neighborhood	NOUN
ajis02-1563	170	31	of	of	ADP
ajis02-1563	170	32	x	x	X
ajis02-1563	170	33	and	and	CCONJ
ajis02-1563	170	34	y	y	PROPN
ajis02-1563	170	35	in	in	ADP
ajis02-1563	170	36	g.	g.	PROPN
ajis02-1563	170	37	let	let	VERB
ajis02-1563	170	38	𝑑𝐺(𝑥	𝑑𝐺(𝑥	NOUN
ajis02-1563	170	39	,	,	PUNCT
ajis02-1563	170	40	𝑦	𝑦	NOUN
ajis02-1563	170	41	)	)	PUNCT
ajis02-1563	170	42	=	=	SYM
ajis02-1563	170	43	|𝑁𝐺(𝑥	|𝑁𝐺(𝑥	NOUN
ajis02-1563	170	44	,	,	PUNCT
ajis02-1563	170	45	𝑦)|	𝑦)|	PROPN
ajis02-1563	170	46	,	,	PUNCT
ajis02-1563	170	47	note	note	VERB
ajis02-1563	170	48	that	that	SCONJ
ajis02-1563	170	49	𝑁𝐺(𝑥	𝑁𝐺(𝑥	PROPN
ajis02-1563	170	50	,	,	PUNCT
ajis02-1563	170	51	𝑥	𝑥	NOUN
ajis02-1563	170	52	)	)	PUNCT
ajis02-1563	170	53	=	=	SYM
ajis02-1563	170	54	𝑁𝐺(𝑥	𝑁𝐺(𝑥	X
ajis02-1563	170	55	)	)	PUNCT
ajis02-1563	170	56	and	and	CCONJ
ajis02-1563	170	57	𝑑𝐺(𝑥	𝑑𝐺(𝑥	PROPN
ajis02-1563	170	58	,	,	PUNCT
ajis02-1563	170	59	𝑥	𝑥	NOUN
ajis02-1563	170	60	)	)	PUNCT
ajis02-1563	170	61	=	=	SYM
ajis02-1563	170	62	𝑑𝐺(𝑥	𝑑𝐺(𝑥	NOUN
ajis02-1563	170	63	)	)	PUNCT
ajis02-1563	170	64	.	.	PUNCT
ajis02-1563	171	1	when	when	SCONJ
ajis02-1563	171	2	g	g	PROPN
ajis02-1563	171	3	is	be	AUX
ajis02-1563	171	4	clear	clear	ADJ
ajis02-1563	171	5	in	in	ADP
ajis02-1563	171	6	the	the	DET
ajis02-1563	171	7	context	context	NOUN
ajis02-1563	171	8	,	,	PUNCT
ajis02-1563	171	9	we	we	PRON
ajis02-1563	171	10	refer	refer	VERB
ajis02-1563	171	11	to	to	ADP
ajis02-1563	171	12	𝑁𝐺(𝑥	𝑁𝐺(𝑥	PROPN
ajis02-1563	171	13	,	,	PUNCT
ajis02-1563	171	14	𝑦	𝑦	NOUN
ajis02-1563	171	15	)	)	PUNCT
ajis02-1563	171	16	as	as	ADP
ajis02-1563	171	17	n(x	n(x	PROPN
ajis02-1563	171	18	,	,	PUNCT
ajis02-1563	171	19	y	y	PROPN
ajis02-1563	171	20	)	)	PUNCT
ajis02-1563	171	21	and	and	CCONJ
ajis02-1563	171	22	similarly	similarly	ADV
ajis02-1563	171	23	to	to	ADP
ajis02-1563	171	24	dg	dg	PROPN
ajis02-1563	171	25	(	(	PUNCT
ajis02-1563	171	26	x	x	X
ajis02-1563	171	27	,	,	PUNCT
ajis02-1563	171	28	y	y	PROPN
ajis02-1563	171	29	)	)	PUNCT
ajis02-1563	171	30	as	as	ADP
ajis02-1563	171	31	d(x	d(x	PROPN
ajis02-1563	171	32	,	,	PUNCT
ajis02-1563	171	33	y	y	NOUN
ajis02-1563	171	34	)	)	PUNCT
ajis02-1563	171	35	.	.	PUNCT
ajis02-1563	172	1	lemma	lemma	PROPN
ajis02-1563	172	2	3	3	NUM
ajis02-1563	172	3	:	:	PUNCT
ajis02-1563	172	4	for	for	ADP
ajis02-1563	172	5	any	any	DET
ajis02-1563	172	6	vertex	vertex	NOUN
ajis02-1563	172	7	v∈	v∈	PROPN
ajis02-1563	172	8	v	v	NOUN
ajis02-1563	172	9	,	,	PUNCT
ajis02-1563	172	10	𝐶𝑊4(𝐺	𝐶𝑊4(𝐺	PROPN
ajis02-1563	172	11	,	,	PUNCT
ajis02-1563	172	12	𝑣	𝑣	NOUN
ajis02-1563	172	13	)	)	PUNCT
ajis02-1563	172	14	=	=	PUNCT
ajis02-1563	173	1	2𝑑(𝑣)2	2𝑑(𝑣)2	NOUN
ajis02-1563	174	1	+	+	CCONJ
ajis02-1563	174	2	4	4	NUM
ajis02-1563	174	3	∑	∑	PUNCT
ajis02-1563	174	4	𝑑(𝑢	𝑑(𝑢	NUM
ajis02-1563	174	5	,	,	PUNCT
ajis02-1563	174	6	𝑣)2	𝑣)2	PROPN
ajis02-1563	174	7	{	{	PUNCT
ajis02-1563	174	8	𝑢∈𝑉	𝑢∈𝑉	PROPN
ajis02-1563	174	9	,	,	PUNCT
ajis02-1563	174	10	𝑢≠	𝑢≠	VERB
ajis02-1563	174	11	𝑣	𝑣	NOUN
ajis02-1563	174	12	}	}	PUNCT
ajis02-1563	174	13	.	.	PUNCT
ajis02-1563	175	1	proof	proof	NOUN
ajis02-1563	175	2	:	:	PUNCT
ajis02-1563	175	3	a	a	DET
ajis02-1563	175	4	closed	closed	ADJ
ajis02-1563	175	5	walk	walk	NOUN
ajis02-1563	175	6	w:(v	w:(v	PROPN
ajis02-1563	175	7	,	,	PUNCT
ajis02-1563	175	8	x	x	NOUN
ajis02-1563	175	9	,	,	PUNCT
ajis02-1563	175	10	u	u	NOUN
ajis02-1563	175	11	,	,	PUNCT
ajis02-1563	175	12	y	y	PROPN
ajis02-1563	175	13	,	,	PUNCT
ajis02-1563	175	14	v	v	NOUN
ajis02-1563	175	15	)	)	PUNCT
ajis02-1563	175	16	of	of	ADP
ajis02-1563	175	17	length	length	NOUN
ajis02-1563	175	18	4	4	NUM
ajis02-1563	175	19	can	can	AUX
ajis02-1563	175	20	be	be	AUX
ajis02-1563	175	21	interpreted	interpret	VERB
ajis02-1563	175	22	as	as	ADP
ajis02-1563	175	23	the	the	DET
ajis02-1563	175	24	concatenation	concatenation	NOUN
ajis02-1563	175	25	of	of	ADP
ajis02-1563	175	26	two	two	NUM
ajis02-1563	175	27	walks	walk	NOUN
ajis02-1563	175	28	of	of	ADP
ajis02-1563	175	29	length	length	NOUN
ajis02-1563	175	30	2	2	NUM
ajis02-1563	175	31	with	with	ADP
ajis02-1563	175	32	same	same	ADJ
ajis02-1563	175	33	end	end	NOUN
ajis02-1563	175	34	points	point	NOUN
ajis02-1563	175	35	u	u	NOUN
ajis02-1563	175	36	and	and	CCONJ
ajis02-1563	175	37	v.	v.	ADP
ajis02-1563	175	38	the	the	DET
ajis02-1563	175	39	number	number	NOUN
ajis02-1563	175	40	of	of	ADP
ajis02-1563	175	41	walks	walk	NOUN
ajis02-1563	175	42	of	of	ADP
ajis02-1563	175	43	length	length	NOUN
ajis02-1563	175	44	2	2	NUM
ajis02-1563	175	45	with	with	ADP
ajis02-1563	175	46	the	the	DET
ajis02-1563	175	47	end	end	NOUN
ajis02-1563	175	48	points	point	NOUN
ajis02-1563	175	49	u	u	PROPN
ajis02-1563	175	50	,	,	PUNCT
ajis02-1563	175	51	v	v	NOUN
ajis02-1563	175	52	is	be	AUX
ajis02-1563	175	53	𝐴𝐺	𝐴𝐺	PROPN
ajis02-1563	175	54	2	2	NUM
ajis02-1563	175	55	(	(	PUNCT
ajis02-1563	175	56	𝑢	𝑢	X
ajis02-1563	175	57	,	,	PUNCT
ajis02-1563	175	58	𝑣	𝑣	NOUN
ajis02-1563	175	59	)	)	PUNCT
ajis02-1563	175	60	.	.	PUNCT
ajis02-1563	176	1	we	we	PRON
ajis02-1563	176	2	want	want	VERB
ajis02-1563	176	3	to	to	PART
ajis02-1563	176	4	count	count	VERB
ajis02-1563	176	5	the	the	DET
ajis02-1563	176	6	closed	close	VERB
ajis02-1563	176	7	walks	walk	NOUN
ajis02-1563	176	8	of	of	ADP
ajis02-1563	176	9	length	length	NOUN
ajis02-1563	176	10	4	4	NUM
ajis02-1563	176	11	that	that	PRON
ajis02-1563	176	12	contain	contain	VERB
ajis02-1563	176	13	a	a	DET
ajis02-1563	176	14	fixed	fix	VERB
ajis02-1563	176	15	vertex	vertex	NOUN
ajis02-1563	176	16	v	v	NOUN
ajis02-1563	176	17	atleast	atleast	ADV
ajis02-1563	176	18	once	once	ADV
ajis02-1563	176	19	.	.	PUNCT
ajis02-1563	177	1	note	note	VERB
ajis02-1563	177	2	that	that	SCONJ
ajis02-1563	177	3	v	v	NOUN
ajis02-1563	177	4	can	can	AUX
ajis02-1563	177	5	occur	occur	VERB
ajis02-1563	177	6	at	at	ADV
ajis02-1563	177	7	most	most	ADV
ajis02-1563	177	8	twice	twice	ADV
ajis02-1563	177	9	in	in	ADP
ajis02-1563	177	10	a	a	DET
ajis02-1563	177	11	closed	closed	ADJ
ajis02-1563	177	12	walk	walk	NOUN
ajis02-1563	177	13	of	of	ADP
ajis02-1563	177	14	length	length	NOUN
ajis02-1563	177	15	4	4	NUM
ajis02-1563	177	16	.	.	PUNCT
ajis02-1563	178	1	in	in	ADP
ajis02-1563	178	2	a	a	DET
ajis02-1563	178	3	closed	closed	ADJ
ajis02-1563	178	4	walk	walk	NOUN
ajis02-1563	178	5	of	of	ADP
ajis02-1563	178	6	length	length	NOUN
ajis02-1563	178	7	4	4	NUM
ajis02-1563	178	8	there	there	PRON
ajis02-1563	178	9	are	be	VERB
ajis02-1563	178	10	4	4	NUM
ajis02-1563	178	11	positions	position	NOUN
ajis02-1563	178	12	for	for	ADP
ajis02-1563	178	13	vertices	vertex	NOUN
ajis02-1563	178	14	(	(	PUNCT
ajis02-1563	178	15	since	since	SCONJ
ajis02-1563	178	16	first	first	ADV
ajis02-1563	178	17	and	and	CCONJ
ajis02-1563	178	18	last	last	ADJ
ajis02-1563	178	19	vertex	vertex	NOUN
ajis02-1563	178	20	is	be	AUX
ajis02-1563	178	21	same	same	ADJ
ajis02-1563	178	22	,	,	PUNCT
ajis02-1563	178	23	we	we	PRON
ajis02-1563	178	24	consider	consider	VERB
ajis02-1563	178	25	it	it	PRON
ajis02-1563	178	26	one	one	NUM
ajis02-1563	178	27	position	position	NOUN
ajis02-1563	178	28	)	)	PUNCT
ajis02-1563	178	29	.	.	PUNCT
ajis02-1563	179	1	first	first	ADV
ajis02-1563	179	2	we	we	PRON
ajis02-1563	179	3	count	count	VERB
ajis02-1563	179	4	the	the	DET
ajis02-1563	179	5	closed	close	VERB
ajis02-1563	179	6	walks	walk	NOUN
ajis02-1563	179	7	of	of	ADP
ajis02-1563	179	8	length	length	NOUN
ajis02-1563	179	9	4	4	NUM
ajis02-1563	179	10	that	that	PRON
ajis02-1563	179	11	contain	contain	VERB
ajis02-1563	179	12	v	v	NOUN
ajis02-1563	179	13	exactly	exactly	ADV
ajis02-1563	179	14	in	in	ADP
ajis02-1563	179	15	one	one	NUM
ajis02-1563	179	16	position	position	NOUN
ajis02-1563	179	17	.	.	PUNCT
ajis02-1563	180	1	call	call	VERB
ajis02-1563	180	2	the	the	DET
ajis02-1563	180	3	set	set	NOUN
ajis02-1563	180	4	of	of	ADP
ajis02-1563	180	5	closed	closed	ADJ
ajis02-1563	180	6	walks	walk	NOUN
ajis02-1563	180	7	of	of	ADP
ajis02-1563	180	8	length	length	NOUN
ajis02-1563	180	9	4	4	NUM
ajis02-1563	180	10	with	with	ADP
ajis02-1563	180	11	v	v	NOUN
ajis02-1563	180	12	at	at	ADP
ajis02-1563	180	13	ith	ith	PROPN
ajis02-1563	180	14	position	position	NOUN
ajis02-1563	180	15	as	as	ADP
ajis02-1563	180	16	𝐶4	𝐶4	NOUN
ajis02-1563	180	17	(	(	PUNCT
ajis02-1563	180	18	𝑣	𝑣	NOUN
ajis02-1563	180	19	,	,	PUNCT
ajis02-1563	180	20	𝑖	𝑖	NOUN
ajis02-1563	180	21	)	)	PUNCT
ajis02-1563	180	22	.	.	PUNCT
ajis02-1563	181	1	this	this	PRON
ajis02-1563	181	2	gives	give	VERB
ajis02-1563	181	3	the	the	DET
ajis02-1563	181	4	total	total	ADJ
ajis02-1563	181	5	number	number	NOUN
ajis02-1563	181	6	of	of	ADP
ajis02-1563	181	7	closed	closed	ADJ
ajis02-1563	181	8	walks	walk	NOUN
ajis02-1563	181	9	of	of	ADP
ajis02-1563	181	10	length	length	NOUN
ajis02-1563	181	11	4	4	NUM
ajis02-1563	181	12	with	with	ADP
ajis02-1563	181	13	appearance	appearance	NOUN
ajis02-1563	181	14	of	of	ADP
ajis02-1563	181	15	v	v	NOUN
ajis02-1563	181	16	exactly	exactly	ADV
ajis02-1563	181	17	once	once	ADV
ajis02-1563	181	18	as	as	ADP
ajis02-1563	181	19	∑	∑	PROPN
ajis02-1563	181	20	|𝐶4(𝑣	|𝐶4(𝑣	X
ajis02-1563	181	21	,	,	PUNCT
ajis02-1563	181	22	𝑖)|4	𝑖)|4	PUNCT
ajis02-1563	181	23	{	{	PUNCT
ajis02-1563	181	24	𝑖=1	𝑖=1	NOUN
ajis02-1563	181	25	}	}	PUNCT
ajis02-1563	181	26	.	.	PUNCT
ajis02-1563	182	1	any	any	DET
ajis02-1563	182	2	closed	closed	ADJ
ajis02-1563	182	3	walk	walk	NOUN
ajis02-1563	182	4	in	in	ADP
ajis02-1563	182	5	𝐶4(𝑣	𝐶4(𝑣	NUM
ajis02-1563	182	6	,	,	PUNCT
ajis02-1563	182	7	1	1	NUM
ajis02-1563	182	8	)	)	PUNCT
ajis02-1563	182	9	is	be	AUX
ajis02-1563	182	10	of	of	ADP
ajis02-1563	182	11	the	the	DET
ajis02-1563	182	12	form	form	NOUN
ajis02-1563	182	13	(	(	PUNCT
ajis02-1563	182	14	v	v	NOUN
ajis02-1563	182	15	,	,	PUNCT
ajis02-1563	182	16	a	a	DET
ajis02-1563	182	17	,	,	PUNCT
ajis02-1563	182	18	b	b	NOUN
ajis02-1563	182	19	,	,	PUNCT
ajis02-1563	182	20	c	c	NOUN
ajis02-1563	182	21	,	,	PUNCT
ajis02-1563	182	22	v	v	NOUN
ajis02-1563	182	23	)	)	PUNCT
ajis02-1563	182	24	,	,	PUNCT
ajis02-1563	182	25	where	where	SCONJ
ajis02-1563	182	26	a	a	DET
ajis02-1563	182	27	,	,	PUNCT
ajis02-1563	182	28	b	b	NOUN
ajis02-1563	182	29	,	,	PUNCT
ajis02-1563	182	30	c	c	PROPN
ajis02-1563	182	31	are	be	AUX
ajis02-1563	182	32	vertices	vertex	NOUN
ajis02-1563	182	33	in	in	ADP
ajis02-1563	182	34	v(g	v(g	NUM
ajis02-1563	182	35	)	)	PUNCT
ajis02-1563	182	36	.	.	PUNCT
ajis02-1563	183	1	number	number	NOUN
ajis02-1563	183	2	of	of	ADP
ajis02-1563	183	3	these	these	DET
ajis02-1563	183	4	walks	walk	NOUN
ajis02-1563	183	5	is	be	AUX
ajis02-1563	183	6	∑	∑	PUNCT
ajis02-1563	183	7	(	(	PUNCT
ajis02-1563	183	8	𝐴2(𝑣	𝐴2(𝑣	NOUN
ajis02-1563	183	9	,	,	PUNCT
ajis02-1563	183	10	𝑏))2	𝑏))2	NOUN
ajis02-1563	183	11	{	{	PUNCT
ajis02-1563	183	12	𝑏≠	𝑏≠	VERB
ajis02-1563	183	13	𝑣	𝑣	PRON
ajis02-1563	183	14	}	}	PUNCT
ajis02-1563	183	15	.	.	PUNCT
ajis02-1563	184	1	clearly	clearly	ADV
ajis02-1563	184	2	(	(	PUNCT
ajis02-1563	184	3	c	c	X
ajis02-1563	184	4	,	,	PUNCT
ajis02-1563	184	5	v	v	NOUN
ajis02-1563	184	6	,	,	PUNCT
ajis02-1563	184	7	a	a	DET
ajis02-1563	184	8	,	,	PUNCT
ajis02-1563	184	9	b	b	NOUN
ajis02-1563	184	10	,	,	PUNCT
ajis02-1563	184	11	c	c	NOUN
ajis02-1563	184	12	)	)	PUNCT
ajis02-1563	184	13	represents	represent	VERB
ajis02-1563	184	14	any	any	DET
ajis02-1563	184	15	closed	closed	ADJ
ajis02-1563	184	16	walk	walk	NOUN
ajis02-1563	184	17	in	in	ADP
ajis02-1563	184	18	𝐶4(𝑣	𝐶4(𝑣	NUM
ajis02-1563	184	19	,	,	PUNCT
ajis02-1563	184	20	2	2	NUM
ajis02-1563	184	21	)	)	PUNCT
ajis02-1563	184	22	.	.	PUNCT
ajis02-1563	185	1	note	note	VERB
ajis02-1563	185	2	that	that	SCONJ
ajis02-1563	185	3	for	for	ADP
ajis02-1563	185	4	a	a	DET
ajis02-1563	185	5	fixed	fix	VERB
ajis02-1563	185	6	a	a	PRON
ajis02-1563	185	7	,	,	PUNCT
ajis02-1563	185	8	b	b	NOUN
ajis02-1563	185	9	and	and	CCONJ
ajis02-1563	185	10	c	c	NOUN
ajis02-1563	185	11	,	,	PUNCT
ajis02-1563	185	12	(	(	PUNCT
ajis02-1563	185	13	c	c	X
ajis02-1563	185	14	,	,	PUNCT
ajis02-1563	185	15	v	v	NOUN
ajis02-1563	185	16	,	,	PUNCT
ajis02-1563	185	17	a	a	DET
ajis02-1563	185	18	,	,	PUNCT
ajis02-1563	185	19	b	b	NOUN
ajis02-1563	185	20	,	,	PUNCT
ajis02-1563	185	21	c	c	NOUN
ajis02-1563	185	22	)	)	PUNCT
ajis02-1563	185	23	is	be	AUX
ajis02-1563	185	24	one	one	NUM
ajis02-1563	185	25	position	position	NOUN
ajis02-1563	185	26	clockwise	clockwise	NOUN
ajis02-1563	185	27	rotation	rotation	NOUN
ajis02-1563	185	28	of	of	ADP
ajis02-1563	185	29	closed	closed	ADJ
ajis02-1563	185	30	walk	walk	NOUN
ajis02-1563	185	31	(	(	PUNCT
ajis02-1563	185	32	v	v	NOUN
ajis02-1563	185	33	,	,	PUNCT
ajis02-1563	185	34	a	a	DET
ajis02-1563	185	35	,	,	PUNCT
ajis02-1563	185	36	b	b	NOUN
ajis02-1563	185	37	,	,	PUNCT
ajis02-1563	185	38	c	c	NOUN
ajis02-1563	185	39	,	,	PUNCT
ajis02-1563	185	40	v	v	NOUN
ajis02-1563	185	41	)	)	PUNCT
ajis02-1563	185	42	.	.	PUNCT
ajis02-1563	186	1	this	this	PRON
ajis02-1563	186	2	implies	imply	VERB
ajis02-1563	186	3	that	that	SCONJ
ajis02-1563	186	4	corresponding	correspond	VERB
ajis02-1563	186	5	to	to	ADP
ajis02-1563	186	6	every	every	DET
ajis02-1563	186	7	closed	closed	ADJ
ajis02-1563	186	8	walk	walk	NOUN
ajis02-1563	186	9	in	in	ADP
ajis02-1563	186	10	𝐶4(𝑣	𝐶4(𝑣	NUM
ajis02-1563	186	11	,	,	PUNCT
ajis02-1563	186	12	1	1	NUM
ajis02-1563	186	13	)	)	PUNCT
ajis02-1563	186	14	there	there	PRON
ajis02-1563	186	15	is	be	VERB
ajis02-1563	186	16	a	a	DET
ajis02-1563	186	17	closed	closed	ADJ
ajis02-1563	186	18	walk	walk	NOUN
ajis02-1563	186	19	in	in	ADP
ajis02-1563	186	20	𝑖𝑛	𝑖𝑛	NOUN
ajis02-1563	186	21	𝐶4(𝑣	𝐶4(𝑣	PROPN
ajis02-1563	186	22	,	,	PUNCT
ajis02-1563	186	23	2	2	NUM
ajis02-1563	186	24	)	)	PUNCT
ajis02-1563	186	25	and	and	CCONJ
ajis02-1563	186	26	vice	vice	ADV
ajis02-1563	186	27	versa	versa	ADV
ajis02-1563	186	28	.	.	PUNCT
ajis02-1563	187	1	hence	hence	ADV
ajis02-1563	187	2	the	the	DET
ajis02-1563	187	3	number	number	NOUN
ajis02-1563	187	4	of	of	ADP
ajis02-1563	187	5	walks	walk	NOUN
ajis02-1563	187	6	in	in	ADP
ajis02-1563	187	7	𝑖𝑛	𝑖𝑛	NOUN
ajis02-1563	187	8	𝐶4(𝑣	𝐶4(𝑣	PROPN
ajis02-1563	187	9	,	,	PUNCT
ajis02-1563	187	10	2	2	NUM
ajis02-1563	187	11	)	)	PUNCT
ajis02-1563	187	12	is	be	AUX
ajis02-1563	187	13	also	also	ADV
ajis02-1563	187	14	∑	∑	PROPN
ajis02-1563	187	15	(	(	PUNCT
ajis02-1563	187	16	𝐴2(𝑣	𝐴2(𝑣	NOUN
ajis02-1563	187	17	,	,	PUNCT
ajis02-1563	187	18	𝑏	𝑏	NOUN
ajis02-1563	187	19	)	)	PUNCT
ajis02-1563	187	20	)	)	PUNCT
ajis02-1563	187	21	2	2	NUM
ajis02-1563	187	22	{	{	PUNCT
ajis02-1563	187	23	𝑏≠	𝑏≠	VERB
ajis02-1563	187	24	𝑣	𝑣	NOUN
ajis02-1563	187	25	}	}	PUNCT
ajis02-1563	187	26	.	.	PUNCT
ajis02-1563	188	1	similarly	similarly	ADV
ajis02-1563	188	2	we	we	PRON
ajis02-1563	188	3	get	get	VERB
ajis02-1563	188	4	australasian	australasian	ADJ
ajis02-1563	188	5	journal	journal	NOUN
ajis02-1563	188	6	of	of	ADP
ajis02-1563	188	7	information	information	NOUN
ajis02-1563	188	8	systems	system	NOUN
ajis02-1563	188	9	ahmad	ahmad	PROPN
ajis02-1563	188	10	,	,	PUNCT
ajis02-1563	188	11	traiq	traiq	NOUN
ajis02-1563	188	12	,	,	PUNCT
ajis02-1563	188	13	shabbir	shabbir	PROPN
ajis02-1563	188	14	&	&	CCONJ
ajis02-1563	188	15	khan	khan	PROPN
ajis02-1563	188	16	2017	2017	NUM
ajis02-1563	188	17	,	,	PUNCT
ajis02-1563	188	18	vol	vol	NOUN
ajis02-1563	188	19	21	21	NUM
ajis02-1563	188	20	,	,	PUNCT
ajis02-1563	188	21	selected	select	VERB
ajis02-1563	188	22	papers	paper	NOUN
ajis02-1563	188	23	from	from	ADP
ajis02-1563	188	24	ausdm	ausdm	NOUN
ajis02-1563	188	25	spectral	spectral	ADJ
ajis02-1563	188	26	methods	method	NOUN
ajis02-1563	188	27	for	for	ADP
ajis02-1563	188	28	immunization	immunization	NOUN
ajis02-1563	188	29	of	of	ADP
ajis02-1563	188	30	large	large	ADJ
ajis02-1563	188	31	networks	network	NOUN
ajis02-1563	188	32	8	8	NUM
ajis02-1563	188	33	that	that	SCONJ
ajis02-1563	188	34	the	the	DET
ajis02-1563	188	35	number	number	NOUN
ajis02-1563	188	36	of	of	ADP
ajis02-1563	188	37	walks	walk	NOUN
ajis02-1563	188	38	in	in	ADP
ajis02-1563	188	39	𝐶4(𝑣	𝐶4(𝑣	NUM
ajis02-1563	188	40	,	,	PUNCT
ajis02-1563	188	41	3	3	NUM
ajis02-1563	188	42	)	)	PUNCT
ajis02-1563	188	43	and	and	CCONJ
ajis02-1563	188	44	𝐶4(𝑣	𝐶4(𝑣	NUM
ajis02-1563	188	45	,	,	PUNCT
ajis02-1563	188	46	4	4	NUM
ajis02-1563	188	47	)	)	PUNCT
ajis02-1563	188	48	is	be	AUX
ajis02-1563	188	49	also	also	ADV
ajis02-1563	188	50	the	the	DET
ajis02-1563	188	51	same	same	ADJ
ajis02-1563	188	52	.	.	PUNCT
ajis02-1563	189	1	so	so	ADV
ajis02-1563	189	2	we	we	PRON
ajis02-1563	189	3	have	have	VERB
ajis02-1563	189	4	∑	∑	ADV
ajis02-1563	189	5	|𝐶4(𝑣	|𝐶4(𝑣	X
ajis02-1563	189	6	,	,	PUNCT
ajis02-1563	189	7	𝑖	𝑖	PRON
ajis02-1563	189	8	)	)	PUNCT
ajis02-1563	189	9	|4	|4	X
ajis02-1563	189	10	{	{	PUNCT
ajis02-1563	189	11	𝑖=1	𝑖=1	PROPN
ajis02-1563	189	12	}	}	PUNCT
ajis02-1563	189	13	=	=	SYM
ajis02-1563	189	14	4	4	NUM
ajis02-1563	189	15	∑	∑	PUNCT
ajis02-1563	189	16	(	(	PUNCT
ajis02-1563	189	17	𝐴2(𝑢	𝐴2(𝑢	PROPN
ajis02-1563	189	18	,	,	PUNCT
ajis02-1563	189	19	𝑣	𝑣	NOUN
ajis02-1563	189	20	)	)	PUNCT
ajis02-1563	189	21	)	)	PUNCT
ajis02-1563	189	22	2	2	NUM
ajis02-1563	189	23	{	{	PUNCT
ajis02-1563	189	24	𝑢≠	𝑢≠	VERB
ajis02-1563	189	25	𝑣	𝑣	PRON
ajis02-1563	189	26	}	}	PUNCT
ajis02-1563	189	27	.	.	PUNCT
ajis02-1563	190	1	second	second	ADV
ajis02-1563	190	2	we	we	PRON
ajis02-1563	190	3	consider	consider	VERB
ajis02-1563	190	4	closed	closed	ADJ
ajis02-1563	190	5	walks	walk	NOUN
ajis02-1563	190	6	in	in	ADP
ajis02-1563	190	7	which	which	PRON
ajis02-1563	190	8	v	v	NOUN
ajis02-1563	190	9	appears	appear	VERB
ajis02-1563	190	10	twice	twice	ADV
ajis02-1563	190	11	.	.	PUNCT
ajis02-1563	191	1	now	now	ADV
ajis02-1563	191	2	it	it	PRON
ajis02-1563	191	3	is	be	AUX
ajis02-1563	191	4	possible	possible	ADJ
ajis02-1563	191	5	in	in	ADP
ajis02-1563	191	6	two	two	NUM
ajis02-1563	191	7	ways	way	NOUN
ajis02-1563	191	8	:	:	PUNCT
ajis02-1563	191	9	1	1	NUM
ajis02-1563	191	10	)	)	PUNCT
ajis02-1563	191	11	v	v	NOUN
ajis02-1563	191	12	appears	appear	VERB
ajis02-1563	191	13	in	in	ADP
ajis02-1563	191	14	1st	1st	ADJ
ajis02-1563	191	15	and	and	CCONJ
ajis02-1563	191	16	3rd	3rd	ADJ
ajis02-1563	191	17	position	position	NOUN
ajis02-1563	191	18	as	as	ADP
ajis02-1563	191	19	(	(	PUNCT
ajis02-1563	191	20	v	v	NOUN
ajis02-1563	191	21	,	,	PUNCT
ajis02-1563	191	22	a	a	DET
ajis02-1563	191	23	,	,	PUNCT
ajis02-1563	191	24	v	v	NOUN
ajis02-1563	191	25	,	,	PUNCT
ajis02-1563	191	26	c	c	NOUN
ajis02-1563	191	27	,	,	PUNCT
ajis02-1563	191	28	v	v	NOUN
ajis02-1563	191	29	)	)	PUNCT
ajis02-1563	191	30	or	or	CCONJ
ajis02-1563	191	31	2	2	NUM
ajis02-1563	191	32	)	)	PUNCT
ajis02-1563	191	33	v	v	NOUN
ajis02-1563	191	34	takes	take	VERB
ajis02-1563	191	35	2nd	2nd	ADJ
ajis02-1563	191	36	and	and	CCONJ
ajis02-1563	191	37	4th	4th	ADJ
ajis02-1563	191	38	position	position	NOUN
ajis02-1563	191	39	as	as	ADP
ajis02-1563	191	40	(	(	PUNCT
ajis02-1563	191	41	a	a	PRON
ajis02-1563	191	42	,	,	PUNCT
ajis02-1563	191	43	v	v	NOUN
ajis02-1563	191	44	,	,	PUNCT
ajis02-1563	191	45	c	c	NOUN
ajis02-1563	191	46	,	,	PUNCT
ajis02-1563	191	47	v	v	NOUN
ajis02-1563	191	48	,	,	PUNCT
ajis02-1563	191	49	a	a	PRON
ajis02-1563	191	50	)	)	PUNCT
ajis02-1563	191	51	.	.	PUNCT
ajis02-1563	192	1	clearly	clearly	ADV
ajis02-1563	192	2	there	there	PRON
ajis02-1563	192	3	are	be	VERB
ajis02-1563	192	4	2(𝐴2(𝑣	2(𝐴2(𝑣	NUM
ajis02-1563	192	5	,	,	PUNCT
ajis02-1563	192	6	𝑣))2	𝑣))2	ADP
ajis02-1563	192	7	such	such	ADJ
ajis02-1563	192	8	walks	walk	NOUN
ajis02-1563	192	9	.	.	PUNCT
ajis02-1563	193	1	this	this	PRON
ajis02-1563	193	2	gives	give	VERB
ajis02-1563	193	3	total	total	ADJ
ajis02-1563	193	4	number	number	NOUN
ajis02-1563	193	5	of	of	ADP
ajis02-1563	193	6	closed	closed	ADJ
ajis02-1563	193	7	walks	walk	NOUN
ajis02-1563	193	8	of	of	ADP
ajis02-1563	193	9	length	length	NOUN
ajis02-1563	193	10	4	4	NUM
ajis02-1563	193	11	containing	contain	VERB
ajis02-1563	193	12	a	a	DET
ajis02-1563	193	13	vertex	vertex	NOUN
ajis02-1563	193	14	v	v	NOUN
ajis02-1563	193	15	as	as	ADP
ajis02-1563	193	16	𝐶𝑊4(𝐺	𝐶𝑊4(𝐺	PROPN
ajis02-1563	193	17	,	,	PUNCT
ajis02-1563	193	18	𝑣	𝑣	NOUN
ajis02-1563	193	19	)	)	PUNCT
ajis02-1563	193	20	=	=	SYM
ajis02-1563	193	21	2(𝐴2(𝑣	2(𝐴2(𝑣	NUM
ajis02-1563	193	22	,	,	PUNCT
ajis02-1563	193	23	𝑣))2	𝑣))2	NOUN
ajis02-1563	193	24	+	+	CCONJ
ajis02-1563	193	25	4	4	NUM
ajis02-1563	193	26	∑	∑	ADV
ajis02-1563	193	27	𝐴2(𝑢	𝐴2(𝑢	PROPN
ajis02-1563	193	28	,	,	PUNCT
ajis02-1563	193	29	𝑣)2	𝑣)2	PROPN
ajis02-1563	193	30	{	{	PUNCT
ajis02-1563	193	31	𝑢≠	𝑢≠	VERB
ajis02-1563	193	32	𝑣	𝑣	PROPN
ajis02-1563	193	33	}	}	PUNCT
ajis02-1563	193	34	which	which	PRON
ajis02-1563	193	35	is	be	AUX
ajis02-1563	193	36	same	same	ADJ
ajis02-1563	193	37	as	as	ADP
ajis02-1563	193	38	what	what	PRON
ajis02-1563	193	39	we	we	PRON
ajis02-1563	193	40	required	require	VERB
ajis02-1563	193	41	.	.	PUNCT
ajis02-1563	194	1	we	we	PRON
ajis02-1563	194	2	incorporate	incorporate	VERB
ajis02-1563	194	3	the	the	DET
ajis02-1563	194	4	above	above	ADJ
ajis02-1563	194	5	formula	formula	NOUN
ajis02-1563	194	6	in	in	ADP
ajis02-1563	194	7	the	the	DET
ajis02-1563	194	8	following	following	ADJ
ajis02-1563	194	9	algorithm	algorithm	NOUN
ajis02-1563	194	10	.	.	PUNCT
ajis02-1563	195	1	for	for	ADP
ajis02-1563	195	2	a	a	DET
ajis02-1563	195	3	given	give	VERB
ajis02-1563	195	4	vertex	vertex	NOUN
ajis02-1563	195	5	v	v	NOUN
ajis02-1563	195	6	,	,	PUNCT
ajis02-1563	195	7	𝑠𝑐𝑜𝑟𝑒𝐺(𝑣	𝑠𝑐𝑜𝑟𝑒𝐺(𝑣	PROPN
ajis02-1563	195	8	)	)	PUNCT
ajis02-1563	195	9	=	=	SYM
ajis02-1563	195	10	4	4	NUM
ajis02-1563	195	11	∑	∑	PUNCT
ajis02-1563	195	12	𝑑(𝑢	𝑑(𝑢	ADJ
ajis02-1563	195	13	,	,	PUNCT
ajis02-1563	195	14	𝑣)^2	𝑣)^2	PROPN
ajis02-1563	195	15	−	−	PROPN
ajis02-1563	195	16	2𝑑(𝑣)^2{𝑢∈	2𝑑(𝑣)^2{𝑢∈	NUM
ajis02-1563	195	17	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	195	18	)	)	PUNCT
ajis02-1563	195	19	}	}	PUNCT
ajis02-1563	195	20	then	then	ADV
ajis02-1563	195	21	∑	∑	PUNCT
ajis02-1563	195	22	𝑑(𝑢	𝑑(𝑢	PROPN
ajis02-1563	195	23	,	,	PUNCT
ajis02-1563	195	24	𝑣)2	𝑣)2	PROPN
ajis02-1563	195	25	{	{	PUNCT
ajis02-1563	195	26	𝑢≠	𝑢≠	VERB
ajis02-1563	195	27	𝑣	𝑣	PROPN
ajis02-1563	195	28	}	}	PUNCT
ajis02-1563	195	29	can	can	AUX
ajis02-1563	195	30	be	be	AUX
ajis02-1563	195	31	computed	compute	VERB
ajis02-1563	195	32	by	by	ADP
ajis02-1563	195	33	taking	take	VERB
ajis02-1563	195	34	the	the	DET
ajis02-1563	195	35	characteristic	characteristic	ADJ
ajis02-1563	195	36	vector	vector	NOUN
ajis02-1563	195	37	𝜒𝑣	𝜒𝑣	NOUN
ajis02-1563	195	38	of	of	ADP
ajis02-1563	195	39	n(v	n(v	PROPN
ajis02-1563	195	40	)	)	PUNCT
ajis02-1563	195	41	(	(	PUNCT
ajis02-1563	195	42	a	a	DET
ajis02-1563	195	43	binary	binary	ADJ
ajis02-1563	195	44	vector	vector	NOUN
ajis02-1563	195	45	of	of	ADP
ajis02-1563	195	46	length	length	NOUN
ajis02-1563	195	47	n	n	PROPN
ajis02-1563	195	48	where	where	SCONJ
ajis02-1563	195	49	the	the	DET
ajis02-1563	195	50	𝜒𝑣[𝑖	𝜒𝑣[𝑖	NOUN
ajis02-1563	195	51	]	]	X
ajis02-1563	195	52	=	=	SYM
ajis02-1563	195	53	1	1	NUM
ajis02-1563	195	54	↔	↔	PROPN
ajis02-1563	195	55	(	(	PUNCT
ajis02-1563	195	56	𝑣	𝑣	NOUN
ajis02-1563	195	57	,	,	PUNCT
ajis02-1563	195	58	𝑣𝑖	𝑣𝑖	NOUN
ajis02-1563	195	59	)	)	PUNCT
ajis02-1563	195	60	∈	∈	PROPN
ajis02-1563	195	61	𝐸	𝐸	PROPN
ajis02-1563	195	62	)	)	PUNCT
ajis02-1563	195	63	.	.	PUNCT
ajis02-1563	196	1	then	then	ADV
ajis02-1563	196	2	for	for	SCONJ
ajis02-1563	196	3	each	each	DET
ajis02-1563	196	4	𝑣𝑒𝑟𝑡𝑒𝑥	𝑣𝑒𝑟𝑡𝑒𝑥	NOUN
ajis02-1563	196	5	𝑢	𝑢	ADP
ajis02-1563	196	6	∈	∈	PROPN
ajis02-1563	196	7	𝑉	𝑉	PROPN
ajis02-1563	196	8	∖	∖	NOUN
ajis02-1563	196	9	{	{	PUNCT
ajis02-1563	196	10	𝑣	𝑣	AUX
ajis02-1563	196	11	}	}	PUNCT
ajis02-1563	196	12	we	we	PRON
ajis02-1563	196	13	go	go	VERB
ajis02-1563	196	14	through	through	ADP
ajis02-1563	196	15	each	each	DET
ajis02-1563	196	16	neighbour	neighbour	NOUN
ajis02-1563	196	17	x	x	PUNCT
ajis02-1563	196	18	of	of	ADP
ajis02-1563	196	19	u	u	PROPN
ajis02-1563	196	20	in	in	ADP
ajis02-1563	196	21	its	its	PRON
ajis02-1563	196	22	adjacency	adjacency	NOUN
ajis02-1563	196	23	list	list	NOUN
ajis02-1563	196	24	and	and	CCONJ
ajis02-1563	196	25	check	check	VERB
ajis02-1563	196	26	if	if	SCONJ
ajis02-1563	196	27	𝜒𝑣[𝑥	𝜒𝑣[𝑥	PROPN
ajis02-1563	196	28	]	]	X
ajis02-1563	196	29	=	=	SYM
ajis02-1563	196	30	1	1	NUM
ajis02-1563	196	31	to	to	PART
ajis02-1563	196	32	increment	increment	VERB
ajis02-1563	196	33	d(v	d(v	PROPN
ajis02-1563	196	34	,	,	PUNCT
ajis02-1563	196	35	u	u	NOUN
ajis02-1563	196	36	)	)	PUNCT
ajis02-1563	196	37	.	.	PUNCT
ajis02-1563	197	1	it	it	PRON
ajis02-1563	197	2	takes	take	VERB
ajis02-1563	197	3	o(m	o(m	NOUN
ajis02-1563	197	4	)	)	PUNCT
ajis02-1563	197	5	time	time	NOUN
ajis02-1563	197	6	to	to	PART
ajis02-1563	197	7	compute	compute	VERB
ajis02-1563	197	8	the	the	DET
ajis02-1563	197	9	𝑠𝑐𝑜𝑟𝑒𝐺(𝑥	𝑠𝑐𝑜𝑟𝑒𝐺(𝑥	NOUN
ajis02-1563	197	10	)	)	PUNCT
ajis02-1563	197	11	for	for	ADP
ajis02-1563	197	12	a	a	DET
ajis02-1563	197	13	vertex	vertex	NOUN
ajis02-1563	197	14	x	x	NOUN
ajis02-1563	197	15	,	,	PUNCT
ajis02-1563	197	16	to	to	PART
ajis02-1563	197	17	get	get	VERB
ajis02-1563	197	18	the	the	DET
ajis02-1563	197	19	vertex	vertex	NOUN
ajis02-1563	197	20	with	with	ADP
ajis02-1563	197	21	maximum	maximum	ADJ
ajis02-1563	197	22	score	score	NOUN
ajis02-1563	197	23	it	it	PRON
ajis02-1563	197	24	takes	take	VERB
ajis02-1563	197	25	o(nm	o(nm	NOUN
ajis02-1563	197	26	)	)	PUNCT
ajis02-1563	197	27	time	time	NOUN
ajis02-1563	197	28	.	.	PUNCT
ajis02-1563	198	1	note	note	VERB
ajis02-1563	198	2	that	that	SCONJ
ajis02-1563	198	3	after	after	ADP
ajis02-1563	198	4	removing	remove	VERB
ajis02-1563	198	5	k	k	PROPN
ajis02-1563	198	6	vertices	vertex	NOUN
ajis02-1563	198	7	(	(	PUNCT
ajis02-1563	198	8	for	for	ADP
ajis02-1563	198	9	constant	constant	ADJ
ajis02-1563	198	10	k	k	NOUN
ajis02-1563	198	11	)	)	PUNCT
ajis02-1563	198	12	the	the	DET
ajis02-1563	198	13	graph	graph	NOUN
ajis02-1563	198	14	still	still	ADV
ajis02-1563	198	15	has	have	VERB
ajis02-1563	198	16	o(m	o(m	NOUN
ajis02-1563	198	17	)	)	PUNCT
ajis02-1563	198	18	edges	edge	NOUN
ajis02-1563	198	19	.	.	PUNCT
ajis02-1563	199	1	now	now	ADV
ajis02-1563	199	2	we	we	PRON
ajis02-1563	199	3	give	give	VERB
ajis02-1563	199	4	an	an	DET
ajis02-1563	199	5	efficient	efficient	ADJ
ajis02-1563	199	6	approximation	approximation	NOUN
ajis02-1563	199	7	to	to	ADP
ajis02-1563	199	8	𝑠𝑐𝑜𝑟𝑒𝐺(𝑥	𝑠𝑐𝑜𝑟𝑒𝐺(𝑥	PROPN
ajis02-1563	199	9	)	)	PUNCT
ajis02-1563	199	10	that	that	SCONJ
ajis02-1563	199	11	not	not	PART
ajis02-1563	199	12	only	only	ADV
ajis02-1563	199	13	can	can	AUX
ajis02-1563	199	14	be	be	AUX
ajis02-1563	199	15	computed	compute	VERB
ajis02-1563	199	16	in	in	ADP
ajis02-1563	199	17	linear	linear	ADJ
ajis02-1563	199	18	time	time	NOUN
ajis02-1563	199	19	but	but	CCONJ
ajis02-1563	199	20	also	also	ADV
ajis02-1563	199	21	can	can	AUX
ajis02-1563	199	22	be	be	AUX
ajis02-1563	199	23	updated	update	VERB
ajis02-1563	199	24	after	after	ADP
ajis02-1563	199	25	removing	remove	VERB
ajis02-1563	199	26	a	a	DET
ajis02-1563	199	27	vertex	vertex	NOUN
ajis02-1563	199	28	y	y	NOUN
ajis02-1563	199	29	in	in	ADP
ajis02-1563	199	30	time	time	NOUN
ajis02-1563	199	31	proportional	proportional	ADJ
ajis02-1563	199	32	to	to	ADP
ajis02-1563	199	33	d(x	d(x	PROPN
ajis02-1563	199	34	)	)	PUNCT
ajis02-1563	199	35	.	.	PUNCT
ajis02-1563	200	1	we	we	PRON
ajis02-1563	200	2	have	have	VERB
ajis02-1563	200	3	(	(	PUNCT
ajis02-1563	200	4	∑	∑	ADV
ajis02-1563	200	5	𝑑(𝑢,𝑣){𝑢≠𝑣	𝑑(𝑢,𝑣){𝑢≠𝑣	PROPN
ajis02-1563	200	6	}	}	PUNCT
ajis02-1563	200	7	𝑛	𝑛	NOUN
ajis02-1563	200	8	)	)	PUNCT
ajis02-1563	200	9	2	2	NUM
ajis02-1563	200	10	≤	≤	NOUN
ajis02-1563	200	11	(	(	PUNCT
ajis02-1563	200	12	∑	∑	PROPN
ajis02-1563	200	13	𝑑(𝑢,𝑣)2	𝑑(𝑢,𝑣)2	PROPN
ajis02-1563	200	14	{	{	PUNCT
ajis02-1563	200	15	𝑢≠𝑣	𝑢≠𝑣	NOUN
ajis02-1563	200	16	}	}	PUNCT
ajis02-1563	200	17	)	)	PUNCT
ajis02-1563	200	18	𝑛	𝑛	DET
ajis02-1563	200	19	≤	≤	NUM
ajis02-1563	200	20	(	(	PUNCT
ajis02-1563	200	21	∑	∑	PROPN
ajis02-1563	200	22	𝑑(𝑢,𝑣)2	𝑑(𝑢,𝑣)2	PROPN
ajis02-1563	200	23	{	{	PUNCT
ajis02-1563	200	24	𝑢≠𝑣	𝑢≠𝑣	NOUN
ajis02-1563	200	25	}	}	PUNCT
ajis02-1563	200	26	𝑛	𝑛	NOUN
ajis02-1563	200	27	)	)	PUNCT
ajis02-1563	200	28	(	(	PUNCT
ajis02-1563	200	29	5	5	X
ajis02-1563	200	30	)	)	PUNCT
ajis02-1563	200	31	the	the	DET
ajis02-1563	200	32	first	first	ADJ
ajis02-1563	200	33	inequality	inequality	NOUN
ajis02-1563	200	34	is	be	AUX
ajis02-1563	200	35	the	the	DET
ajis02-1563	200	36	cauchy	cauchy	PROPN
ajis02-1563	200	37	-	-	PUNCT
ajis02-1563	200	38	schwarz	schwarz	PROPN
ajis02-1563	200	39	inequality	inequality	NOUN
ajis02-1563	200	40	,	,	PUNCT
ajis02-1563	200	41	[	[	X
ajis02-1563	200	42	c.f	c.f	PROPN
ajis02-1563	200	43	(	(	PUNCT
ajis02-1563	200	44	kreyszig	kreyszig	PROPN
ajis02-1563	200	45	1989	1989	NUM
ajis02-1563	200	46	)	)	PUNCT
ajis02-1563	200	47	]	]	PUNCT
ajis02-1563	200	48	,	,	PUNCT
ajis02-1563	200	49	while	while	SCONJ
ajis02-1563	200	50	the	the	DET
ajis02-1563	200	51	second	second	NOUN
ajis02-1563	200	52	follows	follow	VERB
ajis02-1563	200	53	from	from	ADP
ajis02-1563	200	54	the	the	DET
ajis02-1563	200	55	fact	fact	NOUN
ajis02-1563	200	56	that	that	SCONJ
ajis02-1563	200	57	d(u	d(u	PROPN
ajis02-1563	200	58	,	,	PUNCT
ajis02-1563	200	59	v	v	NOUN
ajis02-1563	200	60	)	)	PUNCT
ajis02-1563	200	61	is	be	AUX
ajis02-1563	200	62	non	non	ADJ
ajis02-1563	200	63	-	-	ADJ
ajis02-1563	200	64	negative	negative	ADJ
ajis02-1563	200	65	for	for	ADP
ajis02-1563	200	66	each	each	DET
ajis02-1563	200	67	u	u	NOUN
ajis02-1563	200	68	,	,	PUNCT
ajis02-1563	200	69	v.	v.	CCONJ
ajis02-1563	200	70	in	in	ADP
ajis02-1563	200	71	view	view	NOUN
ajis02-1563	200	72	of	of	ADP
ajis02-1563	200	73	the	the	DET
ajis02-1563	200	74	above	above	ADJ
ajis02-1563	200	75	inequality	inequality	NOUN
ajis02-1563	200	76	,	,	PUNCT
ajis02-1563	200	77	we	we	PRON
ajis02-1563	200	78	approximate	approximate	VERB
ajis02-1563	200	79	the	the	DET
ajis02-1563	200	80	𝑠𝑐𝑜𝑟𝑒_𝐺(𝑣	𝑠𝑐𝑜𝑟𝑒_𝐺(𝑣	PROPN
ajis02-1563	200	81	)	)	PUNCT
ajis02-1563	200	82	by	by	ADP
ajis02-1563	200	83	𝑠𝑐𝑜𝑟𝑒_𝐺′(𝑣	𝑠𝑐𝑜𝑟𝑒_𝐺′(𝑣	NOUN
ajis02-1563	200	84	)	)	PUNCT
ajis02-1563	200	85	given	give	VERB
ajis02-1563	200	86	as	as	ADP
ajis02-1563	200	87	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	200	88	′	′	NUM
ajis02-1563	200	89	(	(	PUNCT
ajis02-1563	200	90	𝑣	𝑣	X
ajis02-1563	200	91	)	)	PUNCT
ajis02-1563	200	92	=	=	SYM
ajis02-1563	200	93	2𝑑𝐺	2𝑑𝐺	NUM
ajis02-1563	200	94	2	2	NUM
ajis02-1563	200	95	(	(	PUNCT
ajis02-1563	200	96	𝑣	𝑣	NOUN
ajis02-1563	200	97	)	)	PUNCT
ajis02-1563	200	98	+	+	CCONJ
ajis02-1563	200	99	4(∑	4(∑	NUM
ajis02-1563	200	100	𝑑𝐺(𝑢,𝑣){𝑢≠	𝑑𝐺(𝑢,𝑣){𝑢≠	PROPN
ajis02-1563	200	101	𝑣	𝑣	PROPN
ajis02-1563	200	102	}	}	PUNCT
ajis02-1563	200	103	)	)	PUNCT
ajis02-1563	200	104	2	2	NUM
ajis02-1563	200	105	.	.	PUNCT
ajis02-1563	201	1	(	(	PUNCT
ajis02-1563	201	2	6	6	X
ajis02-1563	201	3	)	)	PUNCT
ajis02-1563	201	4	our	our	PRON
ajis02-1563	201	5	motivation	motivation	NOUN
ajis02-1563	201	6	to	to	PART
ajis02-1563	201	7	use	use	VERB
ajis02-1563	201	8	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	202	1	′	′	NUM
ajis02-1563	202	2	(	(	PUNCT
ajis02-1563	202	3	𝑥	𝑥	NOUN
ajis02-1563	202	4	)	)	PUNCT
ajis02-1563	202	5	is	be	AUX
ajis02-1563	202	6	that	that	SCONJ
ajis02-1563	202	7	not	not	PART
ajis02-1563	202	8	only	only	ADV
ajis02-1563	202	9	it	it	PRON
ajis02-1563	202	10	is	be	AUX
ajis02-1563	202	11	easy	easy	ADJ
ajis02-1563	202	12	to	to	PART
ajis02-1563	202	13	compute	compute	VERB
ajis02-1563	202	14	but	but	CCONJ
ajis02-1563	202	15	also	also	ADV
ajis02-1563	202	16	after	after	SCONJ
ajis02-1563	202	17	a	a	DET
ajis02-1563	202	18	vertex	vertex	NOUN
ajis02-1563	202	19	is	be	AUX
ajis02-1563	202	20	deleted	delete	VERB
ajis02-1563	202	21	it	it	PRON
ajis02-1563	202	22	is	be	AUX
ajis02-1563	202	23	easy	easy	ADJ
ajis02-1563	202	24	to	to	PART
ajis02-1563	202	25	update	update	VERB
ajis02-1563	202	26	the	the	DET
ajis02-1563	202	27	scores	score	NOUN
ajis02-1563	202	28	of	of	ADP
ajis02-1563	202	29	all	all	DET
ajis02-1563	202	30	vertices	vertex	NOUN
ajis02-1563	202	31	in	in	ADP
ajis02-1563	202	32	the	the	DET
ajis02-1563	202	33	remaining	remain	VERB
ajis02-1563	202	34	subgraph	subgraph	NOUN
ajis02-1563	202	35	.	.	PUNCT
ajis02-1563	203	1	4.2	4.2	NUM
ajis02-1563	203	2	algorithm	algorithm	NOUN
ajis02-1563	203	3	now	now	ADV
ajis02-1563	203	4	we	we	PRON
ajis02-1563	203	5	give	give	VERB
ajis02-1563	203	6	the	the	DET
ajis02-1563	203	7	algorithm	algorithm	NOUN
ajis02-1563	203	8	to	to	PART
ajis02-1563	203	9	compute	compute	VERB
ajis02-1563	203	10	the	the	DET
ajis02-1563	203	11	results	result	NOUN
ajis02-1563	203	12	.	.	PUNCT
ajis02-1563	204	1	first	first	ADV
ajis02-1563	204	2	we	we	PRON
ajis02-1563	204	3	show	show	VERB
ajis02-1563	204	4	procedure	procedure	NOUN
ajis02-1563	204	5	to	to	PART
ajis02-1563	204	6	find	find	VERB
ajis02-1563	204	7	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	204	8	′	′	NUM
ajis02-1563	204	9	(	(	PUNCT
ajis02-1563	204	10	𝑣	𝑣	NOUN
ajis02-1563	204	11	)	)	PUNCT
ajis02-1563	204	12	for	for	ADP
ajis02-1563	204	13	graph	graph	NOUN
ajis02-1563	204	14	g	g	PROPN
ajis02-1563	204	15	in	in	ADP
ajis02-1563	204	16	algorithm	algorithm	PROPN
ajis02-1563	204	17	compute	compute	PROPN
ajis02-1563	204	18	-	-	PUNCT
ajis02-1563	204	19	score(g	score(g	NOUN
ajis02-1563	204	20	)	)	PUNCT
ajis02-1563	204	21	,	,	PUNCT
ajis02-1563	204	22	then	then	ADV
ajis02-1563	204	23	in	in	ADP
ajis02-1563	204	24	algorithm	algorithm	NOUN
ajis02-1563	204	25	update	update	NOUN
ajis02-1563	204	26	-	-	PUNCT
ajis02-1563	204	27	score(g	score(g	PROPN
ajis02-1563	204	28	,	,	PUNCT
ajis02-1563	204	29	vi)we	vi)we	PRON
ajis02-1563	204	30	give	give	VERB
ajis02-1563	204	31	algorithm	algorithm	NOUN
ajis02-1563	204	32	to	to	PART
ajis02-1563	204	33	update	update	VERB
ajis02-1563	204	34	the	the	DET
ajis02-1563	204	35	scores	score	NOUN
ajis02-1563	204	36	of	of	ADP
ajis02-1563	204	37	vertices	vertex	NOUN
ajis02-1563	204	38	when	when	SCONJ
ajis02-1563	204	39	a	a	DET
ajis02-1563	204	40	certain	certain	ADJ
ajis02-1563	204	41	vertex	vertex	NOUN
ajis02-1563	204	42	vi	vi	PROPN
ajis02-1563	204	43	is	be	AUX
ajis02-1563	204	44	deleted	delete	VERB
ajis02-1563	204	45	from	from	ADP
ajis02-1563	204	46	the	the	DET
ajis02-1563	204	47	graph	graph	NOUN
ajis02-1563	204	48	and	and	CCONJ
ajis02-1563	204	49	finally	finally	ADV
ajis02-1563	204	50	we	we	PRON
ajis02-1563	204	51	discuss	discuss	VERB
ajis02-1563	204	52	the	the	DET
ajis02-1563	204	53	greedy	greedy	ADJ
ajis02-1563	204	54	approach	approach	NOUN
ajis02-1563	204	55	to	to	PART
ajis02-1563	204	56	approximate	approximate	VERB
ajis02-1563	204	57	that	that	PRON
ajis02-1563	204	58	which	which	DET
ajis02-1563	204	59	vertices	vertice	VERB
ajis02-1563	204	60	should	should	AUX
ajis02-1563	204	61	be	be	AUX
ajis02-1563	204	62	deleted	delete	VERB
ajis02-1563	204	63	in	in	ADP
ajis02-1563	204	64	order	order	NOUN
ajis02-1563	204	65	to	to	PART
ajis02-1563	204	66	immunize	immunize	VERB
ajis02-1563	204	67	the	the	DET
ajis02-1563	204	68	graph	graph	NOUN
ajis02-1563	204	69	in	in	ADP
ajis02-1563	204	70	algorithm	algorithm	NOUN
ajis02-1563	204	71	greedy-3(g	greedy-3(g	NOUN
ajis02-1563	204	72	,	,	PUNCT
ajis02-1563	204	73	k	k	NOUN
ajis02-1563	204	74	)	)	PUNCT
ajis02-1563	204	75	and	and	CCONJ
ajis02-1563	204	76	along	along	ADP
ajis02-1563	204	77	with	with	ADP
ajis02-1563	204	78	these	these	PRON
ajis02-1563	204	79	we	we	PRON
ajis02-1563	204	80	discuss	discuss	VERB
ajis02-1563	204	81	the	the	DET
ajis02-1563	204	82	time	time	NOUN
ajis02-1563	204	83	and	and	CCONJ
ajis02-1563	204	84	space	space	NOUN
ajis02-1563	204	85	complexity	complexity	NOUN
ajis02-1563	204	86	in	in	ADP
ajis02-1563	204	87	this	this	DET
ajis02-1563	204	88	section	section	NOUN
ajis02-1563	204	89	.	.	PUNCT
ajis02-1563	205	1	now	now	ADV
ajis02-1563	205	2	we	we	PRON
ajis02-1563	205	3	give	give	VERB
ajis02-1563	205	4	algorithm	algorithm	NOUN
ajis02-1563	205	5	to	to	PART
ajis02-1563	205	6	compute	compute	VERB
ajis02-1563	205	7	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	205	8	′	′	NUM
ajis02-1563	205	9	(	(	PUNCT
ajis02-1563	205	10	𝑣	𝑣	NOUN
ajis02-1563	205	11	)	)	PUNCT
ajis02-1563	205	12	;	;	PUNCT
ajis02-1563	205	13	australasian	australasian	ADJ
ajis02-1563	205	14	journal	journal	NOUN
ajis02-1563	205	15	of	of	ADP
ajis02-1563	205	16	information	information	NOUN
ajis02-1563	205	17	systems	system	NOUN
ajis02-1563	205	18	ahmad	ahmad	PROPN
ajis02-1563	205	19	,	,	PUNCT
ajis02-1563	205	20	traiq	traiq	NOUN
ajis02-1563	205	21	,	,	PUNCT
ajis02-1563	205	22	shabbir	shabbir	PROPN
ajis02-1563	205	23	&	&	CCONJ
ajis02-1563	205	24	khan	khan	PROPN
ajis02-1563	205	25	2017	2017	NUM
ajis02-1563	205	26	,	,	PUNCT
ajis02-1563	205	27	vol	vol	NOUN
ajis02-1563	205	28	21	21	NUM
ajis02-1563	205	29	,	,	PUNCT
ajis02-1563	205	30	selected	select	VERB
ajis02-1563	205	31	papers	paper	NOUN
ajis02-1563	205	32	from	from	ADP
ajis02-1563	205	33	ausdm	ausdm	NOUN
ajis02-1563	205	34	spectral	spectral	ADJ
ajis02-1563	205	35	methods	method	NOUN
ajis02-1563	205	36	for	for	ADP
ajis02-1563	205	37	immunization	immunization	NOUN
ajis02-1563	205	38	of	of	ADP
ajis02-1563	205	39	large	large	ADJ
ajis02-1563	205	40	networks	network	NOUN
ajis02-1563	205	41	9	9	NUM
ajis02-1563	205	42	algorithm	algorithm	NOUN
ajis02-1563	205	43	3	3	NUM
ajis02-1563	205	44	:	:	PUNCT
ajis02-1563	205	45	compute	compute	NOUN
ajis02-1563	205	46	-	-	PUNCT
ajis02-1563	205	47	score	score	NOUN
ajis02-1563	205	48	(	(	PUNCT
ajis02-1563	205	49	g	g	NOUN
ajis02-1563	205	50	)	)	PUNCT
ajis02-1563	205	51	1	1	NUM
ajis02-1563	205	52	:	:	PUNCT
ajis02-1563	205	53	deg	deg	PROPN
ajis02-1563	205	54	←	←	PROPN
ajis02-1563	205	55	𝑍𝐸𝑅𝑂𝑆(𝑛	𝑍𝐸𝑅𝑂𝑆(𝑛	PROPN
ajis02-1563	205	56	)	)	PUNCT
ajis02-1563	205	57	⊳	⊳	PROPN
ajis02-1563	205	58	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	PROPN
ajis02-1563	205	59	𝑡ℎ𝑒	𝑡ℎ𝑒	VERB
ajis02-1563	205	60	𝑑𝑒𝑔𝑟𝑒𝑒	𝑑𝑒𝑔𝑟𝑒𝑒	VERB
ajis02-1563	205	61	𝑎𝑟𝑟𝑎𝑦	𝑎𝑟𝑟𝑎𝑦	ADJ
ajis02-1563	205	62	𝑡𝑜	𝑡𝑜	PROPN
ajis02-1563	205	63	𝑛	𝑛	PROPN
ajis02-1563	205	64	𝑧𝑒𝑟𝑜𝑠	𝑧𝑒𝑟𝑜𝑠	VERB
ajis02-1563	205	65	2	2	NUM
ajis02-1563	205	66	:	:	PUNCT
ajis02-1563	205	67	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚	PROPN
ajis02-1563	205	68	←	←	PROPN
ajis02-1563	205	69	𝑍𝐸𝑅𝑂𝑆(𝑛	𝑍𝐸𝑅𝑂𝑆(𝑛	X
ajis02-1563	205	70	)	)	PUNCT
ajis02-1563	205	71	⊳	⊳	PROPN
ajis02-1563	205	72	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	PROPN
ajis02-1563	205	73	𝑡ℎ𝑒	𝑡ℎ𝑒	VERB
ajis02-1563	205	74	𝑐𝑜𝑑𝑒𝑔𝑟𝑒𝑒	𝑐𝑜𝑑𝑒𝑔𝑟𝑒𝑒	ADJ
ajis02-1563	205	75	𝑠𝑢𝑚	𝑠𝑢𝑚	NOUN
ajis02-1563	205	76	𝑎𝑟𝑟𝑎𝑦	𝑎𝑟𝑟𝑎𝑦	ADJ
ajis02-1563	206	1	𝑡𝑜	𝑡𝑜	PRON
ajis02-1563	206	2	𝑛	𝑛	PROPN
ajis02-1563	206	3	𝑧𝑒𝑟𝑜𝑠	𝑧𝑒𝑟𝑜𝑠	VERB
ajis02-1563	206	4	3	3	NUM
ajis02-1563	206	5	:	:	PUNCT
ajis02-1563	206	6	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	206	7	′	′	NUM
ajis02-1563	206	8	←	←	PROPN
ajis02-1563	206	9	𝑍𝐸𝑅𝑂𝑆(𝑛	𝑍𝐸𝑅𝑂𝑆(𝑛	PROPN
ajis02-1563	206	10	)	)	PUNCT
ajis02-1563	207	1	⊳	⊳	NOUN
ajis02-1563	207	2	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒	PROPN
ajis02-1563	207	3	𝑎𝑙𝑙	𝑎𝑙𝑙	VERB
ajis02-1563	207	4	𝑠𝑐𝑜𝑟𝑒𝑠	𝑠𝑐𝑜𝑟𝑒𝑠	PROPN
ajis02-1563	207	5	𝑡𝑜	𝑡𝑜	PROPN
ajis02-1563	207	6	𝑧𝑒𝑟𝑜𝑠	𝑧𝑒𝑟𝑜𝑠	VERB
ajis02-1563	207	7	4	4	NUM
ajis02-1563	207	8	:	:	SYM
ajis02-1563	207	9	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	207	10	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	PROPN
ajis02-1563	207	11	𝑣𝑒𝑟𝑡𝑒𝑥	𝑣𝑒𝑟𝑡𝑒𝑥	PROPN
ajis02-1563	207	12	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	207	13	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	207	14	5	5	NUM
ajis02-1563	207	15	:	:	SYM
ajis02-1563	207	16	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	207	17	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	207	18	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	207	19	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	207	20	𝑜𝑓	𝑜𝑓	ADP
ajis02-1563	207	21	𝑣𝑖	𝑣𝑖	ADV
ajis02-1563	207	22	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	207	23	6	6	NUM
ajis02-1563	207	24	:	:	PUNCT
ajis02-1563	207	25	degg	degg	NOUN
ajis02-1563	207	26	[	[	PUNCT
ajis02-1563	207	27	𝑣𝑖	𝑣𝑖	PROPN
ajis02-1563	207	28	]	]	PUNCT
ajis02-1563	207	29	←	←	PROPN
ajis02-1563	207	30	degg	degg	PROPN
ajis02-1563	207	31	[	[	PUNCT
ajis02-1563	207	32	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	207	33	]	]	X
ajis02-1563	207	34	+	+	CCONJ
ajis02-1563	207	35	1	1	NUM
ajis02-1563	207	36	7	7	NUM
ajis02-1563	207	37	:	:	SYM
ajis02-1563	207	38	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	207	39	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	PROPN
ajis02-1563	207	40	𝑣𝑒𝑟𝑡𝑒𝑥	𝑣𝑒𝑟𝑡𝑒𝑥	PROPN
ajis02-1563	207	41	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	207	42	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	207	43	8	8	NUM
ajis02-1563	207	44	:	:	SYM
ajis02-1563	207	45	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	207	46	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	207	47	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	207	48	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	207	49	𝑜𝑓	𝑜𝑓	ADP
ajis02-1563	207	50	𝑣𝑖	𝑣𝑖	ADV
ajis02-1563	207	51	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	207	52	9	9	NUM
ajis02-1563	207	53	:	:	PUNCT
ajis02-1563	207	54	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	PROPN
ajis02-1563	207	55	]	]	X
ajis02-1563	207	56	←	←	PROPN
ajis02-1563	207	57	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	PROPN
ajis02-1563	207	58	]	]	PUNCT
ajis02-1563	207	59	+	+	CCONJ
ajis02-1563	207	60	degg[𝑣𝑖	degg[𝑣𝑖	PROPN
ajis02-1563	207	61	]	]	X
ajis02-1563	207	62	−	−	PROPN
ajis02-1563	207	63	1	1	NUM
ajis02-1563	207	64	10	10	NUM
ajis02-1563	207	65	:	:	SYM
ajis02-1563	207	66	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	207	67	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	PROPN
ajis02-1563	207	68	𝑣𝑒𝑟𝑡𝑒𝑥	𝑣𝑒𝑟𝑡𝑒𝑥	NOUN
ajis02-1563	207	69	𝑣𝑖𝒅𝒐	𝑣𝑖𝒅𝒐	NOUN
ajis02-1563	207	70	11	11	NUM
ajis02-1563	207	71	:	:	PUNCT
ajis02-1563	207	72	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	207	73	′	′	NUM
ajis02-1563	208	1	[	[	X
ajis02-1563	208	2	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	208	3	]	]	PUNCT
ajis02-1563	208	4	←	←	PROPN
ajis02-1563	208	5	2	2	NUM
ajis02-1563	208	6	∗	∗	NOUN
ajis02-1563	208	7	degg[𝑣𝑖	degg[𝑣𝑖	PROPN
ajis02-1563	208	8	]	]	X
ajis02-1563	208	9	2	2	NUM
ajis02-1563	208	10	+	+	SYM
ajis02-1563	208	11	4	4	NUM
ajis02-1563	208	12	∗	∗	NOUN
ajis02-1563	208	13	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑖]2	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑖]2	NOUN
ajis02-1563	208	14	lemma	lemma	PROPN
ajis02-1563	208	15	4	4	NUM
ajis02-1563	208	16	:	:	PUNCT
ajis02-1563	208	17	runtime	runtime	NOUN
ajis02-1563	208	18	of	of	ADP
ajis02-1563	208	19	algorithm	algorithm	PROPN
ajis02-1563	208	20	compute	compute	PROPN
ajis02-1563	208	21	-	-	PUNCT
ajis02-1563	208	22	score(g	score(g	NOUN
ajis02-1563	208	23	)	)	PUNCT
ajis02-1563	208	24	is	be	AUX
ajis02-1563	208	25	o(m	o(m	PROPN
ajis02-1563	208	26	)	)	PUNCT
ajis02-1563	208	27	.	.	PUNCT
ajis02-1563	209	1	proof	proof	NOUN
ajis02-1563	209	2	:	:	PUNCT
ajis02-1563	209	3	it	it	PRON
ajis02-1563	209	4	is	be	AUX
ajis02-1563	209	5	clear	clear	ADJ
ajis02-1563	209	6	that	that	SCONJ
ajis02-1563	209	7	line	line	NOUN
ajis02-1563	209	8	6	6	NUM
ajis02-1563	209	9	of	of	ADP
ajis02-1563	209	10	algorithm	algorithm	NOUN
ajis02-1563	209	11	compute	compute	PROPN
ajis02-1563	209	12	-	-	PUNCT
ajis02-1563	209	13	score(g	score(g	NOUN
ajis02-1563	209	14	)	)	PUNCT
ajis02-1563	209	15	takes	take	VERB
ajis02-1563	209	16	o(1	o(1	NOUN
ajis02-1563	209	17	)	)	PUNCT
ajis02-1563	209	18	time	time	NOUN
ajis02-1563	209	19	and	and	CCONJ
ajis02-1563	209	20	it	it	PRON
ajis02-1563	209	21	is	be	AUX
ajis02-1563	209	22	executed	execute	VERB
ajis02-1563	209	23	o(m	o(m	NUM
ajis02-1563	209	24	)	)	PUNCT
ajis02-1563	209	25	times	time	NOUN
ajis02-1563	209	26	.	.	PUNCT
ajis02-1563	210	1	since	since	SCONJ
ajis02-1563	210	2	loop	loop	NOUN
ajis02-1563	210	3	at	at	ADP
ajis02-1563	210	4	line	line	NOUN
ajis02-1563	210	5	5	5	NUM
ajis02-1563	210	6	is	be	AUX
ajis02-1563	210	7	iterated	iterate	VERB
ajis02-1563	210	8	over	over	ADP
ajis02-1563	210	9	all	all	DET
ajis02-1563	210	10	neighbours	neighbour	NOUN
ajis02-1563	210	11	of	of	ADP
ajis02-1563	210	12	a	a	DET
ajis02-1563	210	13	fixed	fix	VERB
ajis02-1563	210	14	vertex	vertex	NOUN
ajis02-1563	210	15	,	,	PUNCT
ajis02-1563	210	16	vi	vi	NOUN
ajis02-1563	210	17	.	.	NOUN
ajis02-1563	210	18	hence	hence	ADV
ajis02-1563	210	19	for	for	ADP
ajis02-1563	210	20	vi	vi	NOUN
ajis02-1563	210	21	,	,	PUNCT
ajis02-1563	210	22	line	line	NOUN
ajis02-1563	210	23	6	6	NUM
ajis02-1563	210	24	is	be	AUX
ajis02-1563	210	25	executed	execute	VERB
ajis02-1563	210	26	𝑑𝐺(𝑣𝑖	𝑑𝐺(𝑣𝑖	PROPN
ajis02-1563	210	27	)	)	PUNCT
ajis02-1563	210	28	times	time	NOUN
ajis02-1563	210	29	.	.	PUNCT
ajis02-1563	211	1	thus	thus	ADV
ajis02-1563	211	2	for	for	ADP
ajis02-1563	211	3	all	all	DET
ajis02-1563	211	4	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	211	5	∈	∈	PROPN
ajis02-1563	211	6	𝐺	𝐺	PROPN
ajis02-1563	211	7	,	,	PUNCT
ajis02-1563	211	8	line	line	NOUN
ajis02-1563	211	9	6	6	NUM
ajis02-1563	211	10	runs	run	NOUN
ajis02-1563	211	11	for	for	ADP
ajis02-1563	211	12	∑	∑	ADV
ajis02-1563	211	13	𝑑_𝐺(𝑣_𝑖){𝑣𝑖∈𝑉(𝐺	𝑑_𝐺(𝑣_𝑖){𝑣𝑖∈𝑉(𝐺	NOUN
ajis02-1563	211	14	)	)	PUNCT
ajis02-1563	211	15	}	}	PUNCT
ajis02-1563	212	1	=	=	SYM
ajis02-1563	212	2	2𝑚	2𝑚	NOUN
ajis02-1563	212	3	(	(	PUNCT
ajis02-1563	212	4	bondy	bondy	NOUN
ajis02-1563	212	5	1976	1976	NUM
ajis02-1563	212	6	)	)	PUNCT
ajis02-1563	212	7	.	.	PUNCT
ajis02-1563	213	1	same	same	ADJ
ajis02-1563	213	2	is	be	AUX
ajis02-1563	213	3	true	true	ADJ
ajis02-1563	213	4	for	for	ADP
ajis02-1563	213	5	line	line	NOUN
ajis02-1563	213	6	9	9	NUM
ajis02-1563	213	7	.	.	PUNCT
ajis02-1563	213	8	line	line	NOUN
ajis02-1563	213	9	11	11	NUM
ajis02-1563	213	10	has	have	VERB
ajis02-1563	213	11	constant	constant	ADJ
ajis02-1563	213	12	time	time	NOUN
ajis02-1563	213	13	computation	computation	NOUN
ajis02-1563	213	14	while	while	SCONJ
ajis02-1563	213	15	it	it	PRON
ajis02-1563	213	16	is	be	AUX
ajis02-1563	213	17	computed	compute	VERB
ajis02-1563	213	18	for	for	ADP
ajis02-1563	213	19	every	every	DET
ajis02-1563	213	20	vertex	vertex	NOUN
ajis02-1563	213	21	,	,	PUNCT
ajis02-1563	213	22	thus	thus	ADV
ajis02-1563	213	23	it	it	PRON
ajis02-1563	213	24	takes	take	VERB
ajis02-1563	213	25	o(n	o(n	NOUN
ajis02-1563	213	26	)	)	PUNCT
ajis02-1563	213	27	time	time	NOUN
ajis02-1563	213	28	.	.	PUNCT
ajis02-1563	214	1	so	so	ADV
ajis02-1563	214	2	total	total	ADJ
ajis02-1563	214	3	time	time	NOUN
ajis02-1563	214	4	taken	take	VERB
ajis02-1563	214	5	to	to	PART
ajis02-1563	214	6	compute	compute	VERB
ajis02-1563	214	7	score	score	NOUN
ajis02-1563	214	8	of	of	ADP
ajis02-1563	214	9	every	every	DET
ajis02-1563	214	10	vertex	vertex	NOUN
ajis02-1563	214	11	is	be	AUX
ajis02-1563	214	12	o(m	o(m	NOUN
ajis02-1563	214	13	)	)	PUNCT
ajis02-1563	214	14	.	.	PUNCT
ajis02-1563	215	1	for	for	ADP
ajis02-1563	215	2	a	a	DET
ajis02-1563	215	3	given	give	VERB
ajis02-1563	215	4	vertex	vertex	NOUN
ajis02-1563	215	5	v	v	NOUN
ajis02-1563	215	6	of	of	ADP
ajis02-1563	215	7	g	g	NOUN
ajis02-1563	215	8	,	,	PUNCT
ajis02-1563	215	9	we	we	PRON
ajis02-1563	215	10	update	update	VERB
ajis02-1563	215	11	the	the	DET
ajis02-1563	215	12	score	score	NOUN
ajis02-1563	215	13	of	of	ADP
ajis02-1563	215	14	vertices	vertex	NOUN
ajis02-1563	215	15	after	after	ADP
ajis02-1563	215	16	removing	remove	VERB
ajis02-1563	215	17	v	v	NOUN
ajis02-1563	215	18	in	in	ADP
ajis02-1563	215	19	the	the	DET
ajis02-1563	215	20	following	following	ADJ
ajis02-1563	215	21	way	way	NOUN
ajis02-1563	215	22	;	;	PUNCT
ajis02-1563	215	23	algorithm	algorithm	NOUN
ajis02-1563	215	24	4	4	NUM
ajis02-1563	215	25	:	:	PUNCT
ajis02-1563	215	26	update	update	NOUN
ajis02-1563	215	27	-	-	PUNCT
ajis02-1563	215	28	score	score	NOUN
ajis02-1563	215	29	(	(	PUNCT
ajis02-1563	215	30	𝑮,𝒗𝒊	𝑮,𝒗𝒊	NOUN
ajis02-1563	215	31	)	)	PUNCT
ajis02-1563	215	32	1	1	NUM
ajis02-1563	215	33	:	:	SYM
ajis02-1563	215	34	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	215	35	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	215	36	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	215	37	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	215	38	𝑜𝑓	𝑜𝑓	ADP
ajis02-1563	215	39	𝑣𝑖	𝑣𝑖	ADV
ajis02-1563	215	40	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	215	41	2	2	NUM
ajis02-1563	215	42	:	:	PUNCT
ajis02-1563	215	43	degg	degg	NOUN
ajis02-1563	215	44	[	[	PUNCT
ajis02-1563	215	45	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	215	46	]	]	PUNCT
ajis02-1563	215	47	←	←	PROPN
ajis02-1563	215	48	degg	degg	NOUN
ajis02-1563	215	49	[	[	PUNCT
ajis02-1563	215	50	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	215	51	]	]	PUNCT
ajis02-1563	215	52	−	−	NUM
ajis02-1563	215	53	1	1	NUM
ajis02-1563	215	54	3	3	NUM
ajis02-1563	215	55	:	:	PUNCT
ajis02-1563	215	56	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	PROPN
ajis02-1563	215	57	]	]	X
ajis02-1563	215	58	←	←	PROPN
ajis02-1563	215	59	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	PROPN
ajis02-1563	215	60	]	]	X
ajis02-1563	215	61	−	−	PROPN
ajis02-1563	215	62	(	(	PUNCT
ajis02-1563	215	63	degg[𝑣𝑖	degg[𝑣𝑖	PROPN
ajis02-1563	215	64	]	]	X
ajis02-1563	215	65	−	−	PROPN
ajis02-1563	215	66	1	1	NUM
ajis02-1563	215	67	)	)	PUNCT
ajis02-1563	215	68	4	4	NUM
ajis02-1563	215	69	:	:	SYM
ajis02-1563	215	70	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	215	71	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	215	72	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	215	73	𝑣𝑘	𝑣𝑘	INTJ
ajis02-1563	215	74	𝑜𝑓	𝑜𝑓	INTJ
ajis02-1563	215	75	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	215	76	𝒅𝒐	𝒅𝒐	NOUN
ajis02-1563	215	77	5	5	NUM
ajis02-1563	215	78	:	:	PUNCT
ajis02-1563	215	79	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘	PROPN
ajis02-1563	215	80	]	]	PUNCT
ajis02-1563	215	81	←	←	PROPN
ajis02-1563	215	82	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘	PROPN
ajis02-1563	215	83	]	]	X
ajis02-1563	215	84	−	−	PROPN
ajis02-1563	215	85	1	1	NUM
ajis02-1563	215	86	6	6	NUM
ajis02-1563	215	87	:	:	PUNCT
ajis02-1563	215	88	degg	degg	NOUN
ajis02-1563	215	89	[	[	PUNCT
ajis02-1563	215	90	𝑣𝑖	𝑣𝑖	PROPN
ajis02-1563	215	91	]	]	PUNCT
ajis02-1563	215	92	←	←	PROPN
ajis02-1563	215	93	0	0	NUM
ajis02-1563	215	94	7	7	NUM
ajis02-1563	215	95	:	:	PUNCT
ajis02-1563	215	96	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚	PROPN
ajis02-1563	215	97	[	[	PUNCT
ajis02-1563	215	98	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	215	99	]	]	PUNCT
ajis02-1563	215	100	←	←	PROPN
ajis02-1563	215	101	0	0	NUM
ajis02-1563	215	102	8	8	NUM
ajis02-1563	215	103	:	:	PUNCT
ajis02-1563	216	1	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	216	2	′	′	NUM
ajis02-1563	217	1	[	[	X
ajis02-1563	217	2	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	217	3	]	]	PUNCT
ajis02-1563	217	4	←	←	PROPN
ajis02-1563	217	5	0	0	NUM
ajis02-1563	217	6	9	9	NUM
ajis02-1563	217	7	:	:	SYM
ajis02-1563	217	8	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	217	9	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	217	10	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	217	11	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	217	12	𝑜𝑓	𝑜𝑓	ADP
ajis02-1563	217	13	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	217	14	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	217	15	10	10	NUM
ajis02-1563	217	16	:	:	PUNCT
ajis02-1563	217	17	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	217	18	′	′	NUM
ajis02-1563	218	1	[	[	X
ajis02-1563	218	2	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	218	3	]	]	PUNCT
ajis02-1563	218	4	←	←	PROPN
ajis02-1563	218	5	2	2	NUM
ajis02-1563	218	6	∗	∗	NOUN
ajis02-1563	218	7	degg[𝑣𝑗	degg[𝑣𝑗	PROPN
ajis02-1563	218	8	]	]	PUNCT
ajis02-1563	218	9	2	2	NUM
ajis02-1563	218	10	+	+	SYM
ajis02-1563	219	1	4	4	NUM
ajis02-1563	219	2	∗	∗	NOUN
ajis02-1563	219	3	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑗	PROPN
ajis02-1563	219	4	]	]	X
ajis02-1563	219	5	2	2	NUM
ajis02-1563	219	6	11	11	NUM
ajis02-1563	219	7	:	:	SYM
ajis02-1563	219	8	𝒇𝒐𝒓	𝒇𝒐𝒓	NUM
ajis02-1563	219	9	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	NOUN
ajis02-1563	219	10	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟	NOUN
ajis02-1563	219	11	𝑣𝑘	𝑣𝑘	INTJ
ajis02-1563	219	12	𝑜𝑓	𝑜𝑓	INTJ
ajis02-1563	219	13	𝑣𝑗	𝑣𝑗	ADP
ajis02-1563	219	14	𝒅𝒐	𝒅𝒐	NOUN
ajis02-1563	219	15	12	12	NUM
ajis02-1563	219	16	:	:	PUNCT
ajis02-1563	220	1	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	220	2	′	′	NUM
ajis02-1563	221	1	[	[	X
ajis02-1563	221	2	𝑣𝑘	𝑣𝑘	X
ajis02-1563	221	3	]	]	PUNCT
ajis02-1563	221	4	←	←	PROPN
ajis02-1563	221	5	2	2	NUM
ajis02-1563	221	6	∗	∗	NOUN
ajis02-1563	221	7	degg[𝑣𝑘]2	degg[𝑣𝑘]2	PUNCT
ajis02-1563	221	8	+	+	CCONJ
ajis02-1563	221	9	4	4	NUM
ajis02-1563	221	10	∗	∗	NOUN
ajis02-1563	221	11	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘]2	𝑐𝑜𝑑𝑒𝑔𝑆𝑢𝑚[𝑣𝑘]2	PROPN
ajis02-1563	222	1	lemma	lemma	PROPN
ajis02-1563	222	2	5	5	NUM
ajis02-1563	222	3	:	:	PUNCT
ajis02-1563	222	4	algorithm	algorithm	NOUN
ajis02-1563	222	5	update	update	NOUN
ajis02-1563	222	6	-	-	PUNCT
ajis02-1563	222	7	score(g	score(g	PROPN
ajis02-1563	222	8	,	,	PUNCT
ajis02-1563	222	9	vi	vi	NOUN
ajis02-1563	222	10	)	)	PUNCT
ajis02-1563	222	11	takes	take	VERB
ajis02-1563	222	12	o(m	o(m	NOUN
ajis02-1563	222	13	)	)	PUNCT
ajis02-1563	222	14	time	time	NOUN
ajis02-1563	222	15	to	to	PART
ajis02-1563	222	16	update	update	VERB
ajis02-1563	222	17	score	score	NOUN
ajis02-1563	222	18	with	with	ADP
ajis02-1563	222	19	respect	respect	NOUN
ajis02-1563	222	20	to	to	ADP
ajis02-1563	222	21	parameter	parameter	PROPN
ajis02-1563	222	22	vi	vi	PROPN
ajis02-1563	222	23	.	.	PUNCT
ajis02-1563	223	1	proof	proof	NOUN
ajis02-1563	223	2	:	:	PUNCT
ajis02-1563	223	3	in	in	ADP
ajis02-1563	223	4	algorithm	algorithm	NOUN
ajis02-1563	223	5	,	,	PUNCT
ajis02-1563	223	6	line	line	NOUN
ajis02-1563	223	7	2	2	NUM
ajis02-1563	223	8	,	,	PUNCT
ajis02-1563	223	9	3	3	NUM
ajis02-1563	223	10	and	and	CCONJ
ajis02-1563	223	11	8	8	NUM
ajis02-1563	223	12	takes	take	VERB
ajis02-1563	223	13	constant	constant	ADJ
ajis02-1563	223	14	time	time	NOUN
ajis02-1563	223	15	steps	step	NOUN
ajis02-1563	223	16	and	and	CCONJ
ajis02-1563	223	17	both	both	PRON
ajis02-1563	223	18	are	be	AUX
ajis02-1563	223	19	computed	compute	VERB
ajis02-1563	223	20	𝑑𝐺(𝑣_𝑖	𝑑𝐺(𝑣_𝑖	PRON
ajis02-1563	223	21	)	)	PUNCT
ajis02-1563	223	22	times	time	NOUN
ajis02-1563	223	23	.	.	PUNCT
ajis02-1563	224	1	however	however	ADV
ajis02-1563	224	2	line	line	NOUN
ajis02-1563	224	3	5	5	NUM
ajis02-1563	224	4	and	and	CCONJ
ajis02-1563	224	5	12	12	NUM
ajis02-1563	224	6	are	be	AUX
ajis02-1563	224	7	computed	compute	VERB
ajis02-1563	224	8	∑	∑	ADV
ajis02-1563	224	9	𝑑𝐺(𝑣𝑗){𝑣𝑗∈	𝑑𝐺(𝑣𝑗){𝑣𝑗∈	PUNCT
ajis02-1563	224	10	𝑁𝐺(𝑣𝑖	𝑁𝐺(𝑣𝑖	NUM
ajis02-1563	224	11	)	)	PUNCT
ajis02-1563	224	12	}	}	PUNCT
ajis02-1563	224	13	times	time	NOUN
ajis02-1563	224	14	which	which	PRON
ajis02-1563	224	15	is	be	AUX
ajis02-1563	224	16	upper	upper	ADJ
ajis02-1563	224	17	bounded	bound	VERB
ajis02-1563	224	18	by	by	ADP
ajis02-1563	224	19	m.	m.	NOUN
ajis02-1563	224	20	hence	hence	ADV
ajis02-1563	224	21	for	for	ADP
ajis02-1563	224	22	a	a	DET
ajis02-1563	224	23	fixed	fix	VERB
ajis02-1563	224	24	vertex	vertex	NOUN
ajis02-1563	224	25	vi	vi	NOUN
ajis02-1563	224	26	runtime	runtime	NOUN
ajis02-1563	224	27	of	of	ADP
ajis02-1563	224	28	algorithm	algorithm	NOUN
ajis02-1563	224	29	is	be	AUX
ajis02-1563	224	30	o(m	o(m	NOUN
ajis02-1563	224	31	)	)	PUNCT
ajis02-1563	224	32	.	.	PUNCT
ajis02-1563	225	1	we	we	PRON
ajis02-1563	225	2	give	give	VERB
ajis02-1563	225	3	here	here	ADV
ajis02-1563	225	4	the	the	DET
ajis02-1563	225	5	proof	proof	NOUN
ajis02-1563	225	6	of	of	ADP
ajis02-1563	225	7	correctness	correctness	NOUN
ajis02-1563	225	8	of	of	ADP
ajis02-1563	225	9	the	the	DET
ajis02-1563	225	10	algorithms	algorithm	NOUN
ajis02-1563	225	11	compute	compute	NOUN
ajis02-1563	225	12	-	-	PUNCT
ajis02-1563	225	13	score(g	score(g	NOUN
ajis02-1563	225	14	)	)	PUNCT
ajis02-1563	225	15	and	and	CCONJ
ajis02-1563	225	16	updatescore(g	updatescore(g	NOUN
ajis02-1563	225	17	,	,	PUNCT
ajis02-1563	225	18	vi	vi	NOUN
ajis02-1563	225	19	)	)	PUNCT
ajis02-1563	225	20	.	.	PUNCT
ajis02-1563	226	1	australasian	australasian	ADJ
ajis02-1563	226	2	journal	journal	NOUN
ajis02-1563	226	3	of	of	ADP
ajis02-1563	226	4	information	information	NOUN
ajis02-1563	226	5	systems	system	NOUN
ajis02-1563	226	6	ahmad	ahmad	PROPN
ajis02-1563	226	7	,	,	PUNCT
ajis02-1563	226	8	traiq	traiq	NOUN
ajis02-1563	226	9	,	,	PUNCT
ajis02-1563	226	10	shabbir	shabbir	PROPN
ajis02-1563	226	11	&	&	CCONJ
ajis02-1563	226	12	khan	khan	PROPN
ajis02-1563	226	13	2017	2017	NUM
ajis02-1563	226	14	,	,	PUNCT
ajis02-1563	226	15	vol	vol	NOUN
ajis02-1563	226	16	21	21	NUM
ajis02-1563	226	17	,	,	PUNCT
ajis02-1563	226	18	selected	select	VERB
ajis02-1563	226	19	papers	paper	NOUN
ajis02-1563	226	20	from	from	ADP
ajis02-1563	226	21	ausdm	ausdm	NOUN
ajis02-1563	226	22	spectral	spectral	ADJ
ajis02-1563	226	23	methods	method	NOUN
ajis02-1563	226	24	for	for	ADP
ajis02-1563	226	25	immunization	immunization	NOUN
ajis02-1563	226	26	of	of	ADP
ajis02-1563	226	27	large	large	ADJ
ajis02-1563	226	28	networks	network	NOUN
ajis02-1563	226	29	10	10	NUM
ajis02-1563	226	30	lemma	lemma	PROPN
ajis02-1563	226	31	6	6	NUM
ajis02-1563	226	32	:	:	PUNCT
ajis02-1563	226	33	for	for	ADP
ajis02-1563	226	34	each	each	DET
ajis02-1563	226	35	vertex	vertex	NOUN
ajis02-1563	226	36	𝑣	𝑣	ADP
ajis02-1563	226	37	∈	∈	PROPN
ajis02-1563	226	38	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	226	39	)	)	PUNCT
ajis02-1563	226	40	algorithm	algorithm	PROPN
ajis02-1563	226	41	compute	compute	NOUN
ajis02-1563	226	42	-	-	PUNCT
ajis02-1563	226	43	score(g	score(g	NOUN
ajis02-1563	226	44	)	)	PUNCT
ajis02-1563	226	45	computes	compute	VERB
ajis02-1563	226	46	the	the	DET
ajis02-1563	226	47	score	score	NOUN
ajis02-1563	226	48	𝐺	𝐺	PROPN
ajis02-1563	226	49	,	,	PUNCT
ajis02-1563	226	50	𝑣𝑖	𝑣𝑖	ADP
ajis02-1563	226	51	as	as	ADV
ajis02-1563	226	52	defined	define	VERB
ajis02-1563	226	53	in	in	ADP
ajis02-1563	226	54	(	(	PUNCT
ajis02-1563	226	55	5	5	NUM
ajis02-1563	226	56	)	)	PUNCT
ajis02-1563	226	57	.	.	PUNCT
ajis02-1563	227	1	proof	proof	NOUN
ajis02-1563	227	2	:	:	PUNCT
ajis02-1563	227	3	it	it	PRON
ajis02-1563	227	4	is	be	AUX
ajis02-1563	227	5	clear	clear	ADJ
ajis02-1563	227	6	that	that	SCONJ
ajis02-1563	227	7	the	the	DET
ajis02-1563	227	8	algorithm	algorithm	NOUN
ajis02-1563	227	9	compute	compute	NOUN
ajis02-1563	227	10	-	-	PUNCT
ajis02-1563	227	11	score(g	score(g	NOUN
ajis02-1563	227	12	)	)	PUNCT
ajis02-1563	227	13	computes	compute	VERB
ajis02-1563	227	14	the	the	DET
ajis02-1563	227	15	first	first	ADJ
ajis02-1563	227	16	term	term	NOUN
ajis02-1563	227	17	correctly	correctly	ADV
ajis02-1563	227	18	,	,	PUNCT
ajis02-1563	227	19	as	as	SCONJ
ajis02-1563	227	20	each	each	DET
ajis02-1563	227	21	neighbour	neighbour	NOUN
ajis02-1563	227	22	vi	vi	PROPN
ajis02-1563	227	23	of	of	ADP
ajis02-1563	227	24	v	v	NOUN
ajis02-1563	227	25	contributes	contribute	VERB
ajis02-1563	227	26	1	1	NUM
ajis02-1563	227	27	to	to	ADP
ajis02-1563	227	28	the	the	DET
ajis02-1563	227	29	degree	degree	NOUN
ajis02-1563	227	30	of	of	ADP
ajis02-1563	227	31	v.	v.	ADP
ajis02-1563	227	32	to	to	PART
ajis02-1563	227	33	see	see	VERB
ajis02-1563	227	34	why	why	SCONJ
ajis02-1563	227	35	the	the	DET
ajis02-1563	227	36	second	second	ADJ
ajis02-1563	227	37	term	term	NOUN
ajis02-1563	227	38	is	be	AUX
ajis02-1563	227	39	computed	compute	VERB
ajis02-1563	227	40	correctly	correctly	ADV
ajis02-1563	227	41	,	,	PUNCT
ajis02-1563	227	42	consider	consider	VERB
ajis02-1563	227	43	the	the	DET
ajis02-1563	227	44	following	follow	VERB
ajis02-1563	227	45	fact	fact	NOUN
ajis02-1563	227	46	:	:	PUNCT
ajis02-1563	227	47	fact	fact	NOUN
ajis02-1563	227	48	6	6	NUM
ajis02-1563	227	49	:	:	PUNCT
ajis02-1563	227	50	for	for	ADP
ajis02-1563	227	51	∈	∈	PROPN
ajis02-1563	227	52	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	227	53	)	)	PUNCT
ajis02-1563	227	54	,	,	PUNCT
ajis02-1563	227	55	∑	∑	PROPN
ajis02-1563	227	56	𝑑𝐺(𝑢	𝑑𝐺(𝑢	PROPN
ajis02-1563	227	57	,	,	PUNCT
ajis02-1563	227	58	𝑣){𝑢≠	𝑣){𝑢≠	PROPN
ajis02-1563	227	59	𝑣	𝑣	NOUN
ajis02-1563	227	60	}	}	PUNCT
ajis02-1563	227	61	=	=	PUNCT
ajis02-1563	227	62	∑	∑	PUNCT
ajis02-1563	227	63	(	(	PUNCT
ajis02-1563	227	64	𝑑𝐺(𝑤	𝑑𝐺(𝑤	PROPN
ajis02-1563	227	65	)	)	PUNCT
ajis02-1563	227	66	−	−	PROPN
ajis02-1563	228	1	1){𝑤∈	1){𝑤∈	NUM
ajis02-1563	228	2	𝑁𝐺(𝑣	𝑁𝐺(𝑣	NOUN
ajis02-1563	228	3	)	)	PUNCT
ajis02-1563	228	4	}	}	PUNCT
ajis02-1563	228	5	proof	proof	NOUN
ajis02-1563	228	6	:	:	PUNCT
ajis02-1563	228	7	the	the	DET
ajis02-1563	228	8	left	left	ADJ
ajis02-1563	228	9	hand	hand	NOUN
ajis02-1563	228	10	side	side	NOUN
ajis02-1563	228	11	is	be	AUX
ajis02-1563	228	12	counting	count	VERB
ajis02-1563	228	13	all	all	DET
ajis02-1563	228	14	occurrences	occurrence	NOUN
ajis02-1563	228	15	of	of	ADP
ajis02-1563	228	16	all	all	DET
ajis02-1563	228	17	vertices	vertex	NOUN
ajis02-1563	228	18	w	w	ADP
ajis02-1563	228	19	such	such	ADJ
ajis02-1563	228	20	that	that	PRON
ajis02-1563	228	21	w	w	NOUN
ajis02-1563	228	22	is	be	AUX
ajis02-1563	228	23	a	a	DET
ajis02-1563	228	24	common	common	ADJ
ajis02-1563	228	25	neighbour	neighbour	NOUN
ajis02-1563	228	26	of	of	ADP
ajis02-1563	228	27	u	u	NOUN
ajis02-1563	228	28	and	and	CCONJ
ajis02-1563	228	29	some	some	DET
ajis02-1563	228	30	vertex	vertex	NOUN
ajis02-1563	228	31	v.	v.	ADP
ajis02-1563	228	32	essentially	essentially	ADV
ajis02-1563	228	33	counting	count	VERB
ajis02-1563	228	34	all	all	DET
ajis02-1563	228	35	paths	path	NOUN
ajis02-1563	228	36	of	of	ADP
ajis02-1563	228	37	length	length	NOUN
ajis02-1563	228	38	2	2	NUM
ajis02-1563	228	39	from	from	ADP
ajis02-1563	228	40	u	u	PRON
ajis02-1563	228	41	to	to	ADP
ajis02-1563	228	42	v	v	NUM
ajis02-1563	228	43	where	where	SCONJ
ajis02-1563	228	44	w	w	NOUN
ajis02-1563	228	45	is	be	AUX
ajis02-1563	228	46	the	the	DET
ajis02-1563	228	47	center	center	ADJ
ajis02-1563	228	48	vertex	vertex	NOUN
ajis02-1563	228	49	.	.	PUNCT
ajis02-1563	229	1	we	we	PRON
ajis02-1563	229	2	count	count	VERB
ajis02-1563	229	3	these	these	DET
ajis02-1563	229	4	structures	structure	NOUN
ajis02-1563	229	5	by	by	ADP
ajis02-1563	229	6	counting	count	VERB
ajis02-1563	229	7	the	the	DET
ajis02-1563	229	8	number	number	NOUN
ajis02-1563	229	9	of	of	ADP
ajis02-1563	229	10	times	time	NOUN
ajis02-1563	229	11	each	each	DET
ajis02-1563	229	12	center	center	ADJ
ajis02-1563	229	13	vertex	vertex	NOUN
ajis02-1563	229	14	thus	thus	ADV
ajis02-1563	229	15	appear	appear	VERB
ajis02-1563	229	16	.	.	PUNCT
ajis02-1563	230	1	since	since	SCONJ
ajis02-1563	230	2	v	v	NOUN
ajis02-1563	230	3	is	be	AUX
ajis02-1563	230	4	fixed	fix	VERB
ajis02-1563	230	5	,	,	PUNCT
ajis02-1563	230	6	the	the	DET
ajis02-1563	230	7	number	number	NOUN
ajis02-1563	230	8	of	of	ADP
ajis02-1563	230	9	times	time	NOUN
ajis02-1563	230	10	a	a	DET
ajis02-1563	230	11	vertex	vertex	NOUN
ajis02-1563	230	12	w	w	NOUN
ajis02-1563	230	13	appears	appear	VERB
ajis02-1563	230	14	in	in	ADP
ajis02-1563	230	15	such	such	DET
ajis02-1563	230	16	a	a	DET
ajis02-1563	230	17	structure	structure	NOUN
ajis02-1563	230	18	is	be	AUX
ajis02-1563	230	19	exactly	exactly	ADV
ajis02-1563	230	20	the	the	DET
ajis02-1563	230	21	number	number	NOUN
ajis02-1563	230	22	of	of	ADP
ajis02-1563	230	23	neighbours	neighbour	NOUN
ajis02-1563	230	24	of	of	ADP
ajis02-1563	230	25	w	w	PROPN
ajis02-1563	230	26	,	,	PUNCT
ajis02-1563	230	27	i.e.	i.e.	X
ajis02-1563	230	28	𝑑𝐺(𝑤	𝑑𝐺(𝑤	ADJ
ajis02-1563	230	29	)	)	PUNCT
ajis02-1563	230	30	times	time	NOUN
ajis02-1563	230	31	.	.	PUNCT
ajis02-1563	231	1	now	now	ADV
ajis02-1563	231	2	since	since	SCONJ
ajis02-1563	231	3	v	v	NOUN
ajis02-1563	231	4	is	be	AUX
ajis02-1563	231	5	fixed	fix	VERB
ajis02-1563	231	6	and	and	CCONJ
ajis02-1563	231	7	it	it	PRON
ajis02-1563	231	8	is	be	AUX
ajis02-1563	231	9	also	also	ADV
ajis02-1563	231	10	a	a	DET
ajis02-1563	231	11	neighbour	neighbour	NOUN
ajis02-1563	231	12	of	of	ADP
ajis02-1563	231	13	w	w	PROPN
ajis02-1563	231	14	,	,	PUNCT
ajis02-1563	231	15	we	we	PRON
ajis02-1563	231	16	subtract	subtract	VERB
ajis02-1563	231	17	one	one	NUM
ajis02-1563	231	18	from	from	ADP
ajis02-1563	231	19	it	it	PRON
ajis02-1563	231	20	.	.	PUNCT
ajis02-1563	232	1	hence	hence	ADV
ajis02-1563	232	2	the	the	DET
ajis02-1563	232	3	expression	expression	NOUN
ajis02-1563	232	4	on	on	ADP
ajis02-1563	232	5	the	the	DET
ajis02-1563	232	6	right	right	ADJ
ajis02-1563	232	7	hand	hand	NOUN
ajis02-1563	232	8	side	side	NOUN
ajis02-1563	232	9	follows	follow	VERB
ajis02-1563	232	10	.	.	PUNCT
ajis02-1563	233	1	lemma	lemma	PROPN
ajis02-1563	233	2	7	7	NUM
ajis02-1563	233	3	:	:	PUNCT
ajis02-1563	233	4	for	for	ADP
ajis02-1563	233	5	all	all	DET
ajis02-1563	233	6	vertices	vertex	NOUN
ajis02-1563	233	7	𝑢	𝑢	PART
ajis02-1563	233	8	,	,	PUNCT
ajis02-1563	233	9	𝑣	𝑣	PRON
ajis02-1563	233	10	∈	∈	PROPN
ajis02-1563	233	11	𝑉(𝐺	𝑉(𝐺	NOUN
ajis02-1563	233	12	)	)	PUNCT
ajis02-1563	233	13	algorithm	algorithm	NOUN
ajis02-1563	233	14	update	update	NOUN
ajis02-1563	233	15	-	-	PUNCT
ajis02-1563	233	16	score(𝐺	score(𝐺	PROPN
ajis02-1563	233	17	,	,	PUNCT
ajis02-1563	233	18	𝑣𝑖	𝑣𝑖	PRON
ajis02-1563	233	19	)	)	PUNCT
ajis02-1563	233	20	computes	compute	VERB
ajis02-1563	233	21	the	the	DET
ajis02-1563	233	22	𝑠𝑐𝑜𝑟𝑒𝐺−{𝑢	𝑠𝑐𝑜𝑟𝑒𝐺−{𝑢	PROPN
ajis02-1563	233	23	}	}	PUNCT
ajis02-1563	233	24	′	′	NUM
ajis02-1563	233	25	(	(	PUNCT
ajis02-1563	233	26	𝑣	𝑣	NOUN
ajis02-1563	233	27	)	)	PUNCT
ajis02-1563	233	28	as	as	SCONJ
ajis02-1563	233	29	defined	define	VERB
ajis02-1563	233	30	in	in	ADP
ajis02-1563	233	31	(	(	PUNCT
ajis02-1563	233	32	5	5	NUM
ajis02-1563	233	33	)	)	PUNCT
ajis02-1563	233	34	.	.	PUNCT
ajis02-1563	234	1	proof	proof	NOUN
ajis02-1563	234	2	.	.	PUNCT
ajis02-1563	235	1	to	to	PART
ajis02-1563	235	2	see	see	VERB
ajis02-1563	235	3	this	this	PRON
ajis02-1563	235	4	,	,	PUNCT
ajis02-1563	235	5	consider	consider	VERB
ajis02-1563	235	6	a	a	DET
ajis02-1563	235	7	vertex	vertex	NOUN
ajis02-1563	235	8	v	v	ADP
ajis02-1563	235	9	which	which	PRON
ajis02-1563	235	10	is	be	AUX
ajis02-1563	235	11	neighbour	neighbour	NOUN
ajis02-1563	235	12	of	of	ADP
ajis02-1563	235	13	u.	u.	NOUN
ajis02-1563	235	14	we	we	PRON
ajis02-1563	235	15	note	note	VERB
ajis02-1563	235	16	that	that	SCONJ
ajis02-1563	235	17	first	first	ADJ
ajis02-1563	235	18	contribution	contribution	NOUN
ajis02-1563	235	19	of	of	ADP
ajis02-1563	235	20	u	u	NOUN
ajis02-1563	235	21	in	in	ADP
ajis02-1563	235	22	score	score	NOUN
ajis02-1563	235	23	'	'	PUNCT
ajis02-1563	235	24	of	of	ADP
ajis02-1563	235	25	v	v	NOUN
ajis02-1563	235	26	is	be	AUX
ajis02-1563	235	27	in	in	ADP
ajis02-1563	235	28	the	the	DET
ajis02-1563	235	29	first	first	ADJ
ajis02-1563	235	30	term	term	NOUN
ajis02-1563	235	31	i.e.	i.e.	X
ajis02-1563	235	32	degree	degree	NOUN
ajis02-1563	235	33	of	of	ADP
ajis02-1563	235	34	v	v	NOUN
ajis02-1563	235	35	,	,	PUNCT
ajis02-1563	235	36	so	so	SCONJ
ajis02-1563	235	37	we	we	PRON
ajis02-1563	235	38	decrease	decrease	VERB
ajis02-1563	235	39	the	the	DET
ajis02-1563	235	40	degree	degree	NOUN
ajis02-1563	235	41	of	of	ADP
ajis02-1563	235	42	v	v	NUM
ajis02-1563	235	43	by	by	ADP
ajis02-1563	235	44	one	one	NUM
ajis02-1563	235	45	.	.	PUNCT
ajis02-1563	236	1	clearly	clearly	ADV
ajis02-1563	236	2	from	from	ADP
ajis02-1563	236	3	the	the	DET
ajis02-1563	236	4	figure	figure	NOUN
ajis02-1563	236	5	below	below	ADV
ajis02-1563	236	6	,	,	PUNCT
ajis02-1563	236	7	u	u	NOUN
ajis02-1563	236	8	adds	add	VERB
ajis02-1563	236	9	𝑑𝐺(𝑢	𝑑𝐺(𝑢	PROPN
ajis02-1563	236	10	)	)	PUNCT
ajis02-1563	236	11	−	−	PROPN
ajis02-1563	236	12	1	1	NUM
ajis02-1563	236	13	in	in	ADP
ajis02-1563	236	14	codegree	codegree	NOUN
ajis02-1563	236	15	sum	sum	NOUN
ajis02-1563	236	16	of	of	ADP
ajis02-1563	236	17	v	v	NOUN
ajis02-1563	236	18	,	,	PUNCT
ajis02-1563	236	19	which	which	PRON
ajis02-1563	236	20	is	be	AUX
ajis02-1563	236	21	the	the	DET
ajis02-1563	236	22	second	second	ADJ
ajis02-1563	236	23	term	term	NOUN
ajis02-1563	236	24	of	of	ADP
ajis02-1563	236	25	the	the	DET
ajis02-1563	236	26	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	236	27	′	′	NUM
ajis02-1563	236	28	(	(	PUNCT
ajis02-1563	236	29	𝑣	𝑣	NOUN
ajis02-1563	236	30	)	)	PUNCT
ajis02-1563	236	31	,	,	PUNCT
ajis02-1563	236	32	given	give	VERB
ajis02-1563	236	33	as	as	ADP
ajis02-1563	236	34	∑	∑	PROPN
ajis02-1563	236	35	𝑑𝐺(𝑢	𝑑𝐺(𝑢	PROPN
ajis02-1563	236	36	,	,	PUNCT
ajis02-1563	236	37	𝑣){𝑢≠	𝑣){𝑢≠	PROPN
ajis02-1563	236	38	𝑣	𝑣	NOUN
ajis02-1563	236	39	}	}	PUNCT
ajis02-1563	236	40	.	.	PUNCT
ajis02-1563	237	1	now	now	ADV
ajis02-1563	237	2	consider	consider	VERB
ajis02-1563	237	3	the	the	DET
ajis02-1563	237	4	vertices	vertex	NOUN
ajis02-1563	237	5	vi	vi	PROPN
ajis02-1563	237	6	,	,	PUNCT
ajis02-1563	237	7	which	which	PRON
ajis02-1563	237	8	are	be	AUX
ajis02-1563	237	9	neighbours	neighbour	NOUN
ajis02-1563	237	10	of	of	ADP
ajis02-1563	237	11	neighbours	neighbour	NOUN
ajis02-1563	237	12	of	of	ADP
ajis02-1563	237	13	u.	u.	NOUN
ajis02-1563	237	14	score	score	NOUN
ajis02-1563	237	15	of	of	ADP
ajis02-1563	237	16	these	these	DET
ajis02-1563	237	17	vertices	vertex	NOUN
ajis02-1563	237	18	is	be	AUX
ajis02-1563	237	19	also	also	ADV
ajis02-1563	237	20	effected	effect	VERB
ajis02-1563	237	21	by	by	ADP
ajis02-1563	237	22	removing	remove	VERB
ajis02-1563	237	23	u	u	NOUN
ajis02-1563	237	24	since	since	SCONJ
ajis02-1563	237	25	u	u	PRON
ajis02-1563	237	26	contribute	contribute	VERB
ajis02-1563	237	27	one	one	NUM
ajis02-1563	237	28	to	to	ADP
ajis02-1563	237	29	codegree	codegree	NOUN
ajis02-1563	237	30	sum	sum	NOUN
ajis02-1563	237	31	of	of	ADP
ajis02-1563	237	32	vi	vi	PROPN
ajis02-1563	237	33	.	.	PUNCT
ajis02-1563	238	1	here	here	ADV
ajis02-1563	238	2	is	be	AUX
ajis02-1563	238	3	the	the	DET
ajis02-1563	238	4	algorithm	algorithm	NOUN
ajis02-1563	238	5	to	to	PART
ajis02-1563	238	6	select	select	VERB
ajis02-1563	238	7	k	k	PROPN
ajis02-1563	238	8	vertices	vertex	NOUN
ajis02-1563	238	9	in	in	ADP
ajis02-1563	238	10	the	the	DET
ajis02-1563	238	11	given	give	VERB
ajis02-1563	238	12	graph	graph	NOUN
ajis02-1563	238	13	g	g	ADP
ajis02-1563	238	14	such	such	ADJ
ajis02-1563	238	15	that	that	SCONJ
ajis02-1563	238	16	approximated	approximate	VERB
ajis02-1563	238	17	eigendrop	eigendrop	NOUN
ajis02-1563	238	18	is	be	AUX
ajis02-1563	238	19	maximized	maximize	VERB
ajis02-1563	238	20	after	after	ADP
ajis02-1563	238	21	deleting	delete	VERB
ajis02-1563	238	22	those	those	DET
ajis02-1563	238	23	vertices	vertex	NOUN
ajis02-1563	238	24	.	.	PUNCT
ajis02-1563	239	1	algorithm	algorithm	NOUN
ajis02-1563	239	2	5	5	NUM
ajis02-1563	239	3	:	:	PUNCT
ajis02-1563	239	4	greedy-3	greedy-3	PROPN
ajis02-1563	239	5	(	(	PUNCT
ajis02-1563	239	6	𝑮	𝑮	PROPN
ajis02-1563	239	7	,	,	PUNCT
ajis02-1563	239	8	𝒌	𝒌	ADJ
ajis02-1563	239	9	)	)	PUNCT
ajis02-1563	239	10	1	1	NUM
ajis02-1563	239	11	:	:	PUNCT
ajis02-1563	239	12	𝑆	𝑆	PROPN
ajis02-1563	239	13	←	←	PROPN
ajis02-1563	239	14	∅	∅	NOUN
ajis02-1563	239	15	2	2	NUM
ajis02-1563	239	16	:	:	PUNCT
ajis02-1563	239	17	compute	compute	NOUN
ajis02-1563	239	18	-	-	PUNCT
ajis02-1563	239	19	score(g	score(g	NOUN
ajis02-1563	239	20	)	)	PUNCT
ajis02-1563	239	21	3	3	NUM
ajis02-1563	239	22	:	:	PUNCT
ajis02-1563	239	23	𝒘𝒉𝒊𝒍𝒆	𝒘𝒉𝒊𝒍𝒆	NOUN
ajis02-1563	239	24	|𝑆|	|𝑆|	VERB
ajis02-1563	239	25	<	<	X
ajis02-1563	239	26	𝑘	𝑘	PRON
ajis02-1563	239	27	𝒅𝒐	𝒅𝒐	PROPN
ajis02-1563	239	28	4	4	NUM
ajis02-1563	239	29	:	:	PUNCT
ajis02-1563	239	30	𝑣	𝑣	ADP
ajis02-1563	239	31	←	←	PROPN
ajis02-1563	239	32	𝑎𝑟𝑔𝑚𝑎𝑥	𝑎𝑟𝑔𝑚𝑎𝑥	NOUN
ajis02-1563	239	33	𝑢∈𝑉∖𝑆	𝑢∈𝑉∖𝑆	PROPN
ajis02-1563	239	34	𝑠𝑐𝑜𝑟𝑒𝐺	𝑠𝑐𝑜𝑟𝑒𝐺	PROPN
ajis02-1563	239	35	′	′	NOUN
ajis02-1563	240	1	[	[	X
ajis02-1563	240	2	𝑢	𝑢	X
ajis02-1563	240	3	]	]	X
ajis02-1563	240	4	5	5	NUM
ajis02-1563	240	5	:	:	PUNCT
ajis02-1563	240	6	𝑆	𝑆	PROPN
ajis02-1563	240	7	←	←	PROPN
ajis02-1563	240	8	𝑆	𝑆	PROPN
ajis02-1563	240	9	∪	∪	X
ajis02-1563	240	10	{	{	PUNCT
ajis02-1563	240	11	𝑣	𝑣	NOUN
ajis02-1563	240	12	}	}	PUNCT
ajis02-1563	240	13	6	6	NUM
ajis02-1563	240	14	:	:	PUNCT
ajis02-1563	240	15	update	update	NOUN
ajis02-1563	240	16	-	-	PUNCT
ajis02-1563	240	17	score(g	score(g	NOUN
ajis02-1563	240	18	,	,	PUNCT
ajis02-1563	240	19	v	v	NOUN
ajis02-1563	240	20	)	)	PUNCT
ajis02-1563	240	21	7	7	NUM
ajis02-1563	240	22	:	:	PUNCT
ajis02-1563	240	23	𝒓𝒆𝒕𝒖𝒓𝒏	𝒓𝒆𝒕𝒖𝒓𝒏	PROPN
ajis02-1563	240	24	𝑆	𝑆	PROPN
ajis02-1563	240	25	theorem	theorem	VERB
ajis02-1563	240	26	2	2	NUM
ajis02-1563	240	27	:	:	PUNCT
ajis02-1563	240	28	the	the	DET
ajis02-1563	240	29	computational	computational	ADJ
ajis02-1563	240	30	complexity	complexity	NOUN
ajis02-1563	240	31	of	of	ADP
ajis02-1563	240	32	the	the	DET
ajis02-1563	240	33	algorithm	algorithm	NOUN
ajis02-1563	240	34	greedy-3(g	greedy-3(g	NOUN
ajis02-1563	240	35	,	,	PUNCT
ajis02-1563	240	36	k	k	NOUN
ajis02-1563	240	37	)	)	PUNCT
ajis02-1563	240	38	is	be	AUX
ajis02-1563	240	39	𝑂(𝑛	𝑂(𝑛	PROPN
ajis02-1563	240	40	+	+	NUM
ajis02-1563	240	41	𝑘𝑚	𝑘𝑚	NOUN
ajis02-1563	241	1	+	+	CCONJ
ajis02-1563	241	2	𝑘	𝑘	DET
ajis02-1563	241	3	log	log	NOUN
ajis02-1563	241	4	(	(	PUNCT
ajis02-1563	241	5	𝑛	𝑛	NOUN
ajis02-1563	241	6	)	)	PUNCT
ajis02-1563	241	7	)	)	PUNCT
ajis02-1563	241	8	,	,	PUNCT
ajis02-1563	241	9	while	while	SCONJ
ajis02-1563	241	10	the	the	DET
ajis02-1563	241	11	space	space	NOUN
ajis02-1563	241	12	complexity	complexity	NOUN
ajis02-1563	241	13	is	be	AUX
ajis02-1563	241	14	o(m+n+k	o(m+n+k	NOUN
ajis02-1563	241	15	)	)	PUNCT
ajis02-1563	241	16	.	.	PUNCT
ajis02-1563	242	1	australasian	australasian	ADJ
ajis02-1563	242	2	journal	journal	NOUN
ajis02-1563	242	3	of	of	ADP
ajis02-1563	242	4	information	information	NOUN
ajis02-1563	242	5	systems	system	NOUN
ajis02-1563	242	6	ahmad	ahmad	PROPN
ajis02-1563	242	7	,	,	PUNCT
ajis02-1563	242	8	traiq	traiq	NOUN
ajis02-1563	242	9	,	,	PUNCT
ajis02-1563	242	10	shabbir	shabbir	PROPN
ajis02-1563	242	11	&	&	CCONJ
ajis02-1563	242	12	khan	khan	PROPN
ajis02-1563	242	13	2017	2017	NUM
ajis02-1563	242	14	,	,	PUNCT
ajis02-1563	242	15	vol	vol	NOUN
ajis02-1563	242	16	21	21	NUM
ajis02-1563	242	17	,	,	PUNCT
ajis02-1563	242	18	selected	select	VERB
ajis02-1563	242	19	papers	paper	NOUN
ajis02-1563	242	20	from	from	ADP
ajis02-1563	242	21	ausdm	ausdm	NOUN
ajis02-1563	242	22	spectral	spectral	ADJ
ajis02-1563	242	23	methods	method	NOUN
ajis02-1563	242	24	for	for	ADP
ajis02-1563	242	25	immunization	immunization	NOUN
ajis02-1563	242	26	of	of	ADP
ajis02-1563	242	27	large	large	ADJ
ajis02-1563	242	28	networks	network	NOUN
ajis02-1563	242	29	11	11	NUM
ajis02-1563	242	30	proof	proof	NOUN
ajis02-1563	242	31	.	.	PUNCT
ajis02-1563	243	1	by	by	ADP
ajis02-1563	243	2	lemma	lemma	PROPN
ajis02-1563	243	3	4	4	NUM
ajis02-1563	243	4	,	,	PUNCT
ajis02-1563	243	5	line	line	NOUN
ajis02-1563	243	6	2	2	NUM
ajis02-1563	243	7	takes	take	VERB
ajis02-1563	243	8	o(m	o(m	NOUN
ajis02-1563	243	9	)	)	PUNCT
ajis02-1563	243	10	time	time	NOUN
ajis02-1563	243	11	.	.	PUNCT
ajis02-1563	244	1	the	the	DET
ajis02-1563	244	2	scores	score	NOUN
ajis02-1563	244	3	for	for	ADP
ajis02-1563	244	4	all	all	DET
ajis02-1563	244	5	vertices	vertex	NOUN
ajis02-1563	244	6	can	can	AUX
ajis02-1563	244	7	be	be	AUX
ajis02-1563	244	8	stored	store	VERB
ajis02-1563	244	9	in	in	ADP
ajis02-1563	244	10	a	a	DET
ajis02-1563	244	11	maxheap	maxheap	NOUN
ajis02-1563	244	12	,	,	PUNCT
ajis02-1563	244	13	which	which	PRON
ajis02-1563	244	14	can	can	AUX
ajis02-1563	244	15	be	be	AUX
ajis02-1563	244	16	built	build	VERB
ajis02-1563	244	17	in	in	ADP
ajis02-1563	244	18	o(n	o(n	NUM
ajis02-1563	244	19	)	)	PUNCT
ajis02-1563	244	20	time	time	NOUN
ajis02-1563	244	21	while	while	SCONJ
ajis02-1563	244	22	each	each	DET
ajis02-1563	244	23	update	update	NOUN
ajis02-1563	244	24	-	-	PUNCT
ajis02-1563	244	25	key	key	NOUN
ajis02-1563	244	26	and	and	CCONJ
ajis02-1563	244	27	extract	extract	NOUN
ajis02-1563	244	28	-	-	PUNCT
ajis02-1563	244	29	max	max	NOUN
ajis02-1563	244	30	takes	take	VERB
ajis02-1563	244	31	𝑂(log	𝑂(log	NOUN
ajis02-1563	244	32	(	(	PUNCT
ajis02-1563	244	33	𝑛	𝑛	NOUN
ajis02-1563	244	34	)	)	PUNCT
ajis02-1563	244	35	)	)	PUNCT
ajis02-1563	244	36	time	time	NOUN
ajis02-1563	244	37	(	(	PUNCT
ajis02-1563	244	38	cormen	corman	NOUN
ajis02-1563	244	39	2009	2009	NUM
ajis02-1563	244	40	)	)	PUNCT
ajis02-1563	244	41	.	.	PUNCT
ajis02-1563	245	1	we	we	PRON
ajis02-1563	245	2	extract	extract	VERB
ajis02-1563	245	3	max	max	PROPN
ajis02-1563	245	4	from	from	ADP
ajis02-1563	245	5	the	the	DET
ajis02-1563	245	6	heap	heap	NOUN
ajis02-1563	245	7	k	k	PROPN
ajis02-1563	245	8	times	time	NOUN
ajis02-1563	245	9	,	,	PUNCT
ajis02-1563	245	10	hence	hence	ADV
ajis02-1563	245	11	its	its	PRON
ajis02-1563	245	12	total	total	ADJ
ajis02-1563	245	13	runtime	runtime	NOUN
ajis02-1563	245	14	is	be	AUX
ajis02-1563	245	15	𝑂(log	𝑂(log	NOUN
ajis02-1563	245	16	(	(	PUNCT
ajis02-1563	245	17	𝑛	𝑛	NOUN
ajis02-1563	245	18	)	)	PUNCT
ajis02-1563	245	19	)	)	PUNCT
ajis02-1563	245	20	.	.	PUNCT
ajis02-1563	246	1	as	as	SCONJ
ajis02-1563	246	2	argued	argue	VERB
ajis02-1563	246	3	by	by	ADP
ajis02-1563	246	4	lemma	lemma	PROPN
ajis02-1563	246	5	5	5	NUM
ajis02-1563	246	6	,	,	PUNCT
ajis02-1563	246	7	time	time	NOUN
ajis02-1563	246	8	consumed	consume	VERB
ajis02-1563	246	9	in	in	ADP
ajis02-1563	246	10	each	each	DET
ajis02-1563	246	11	call	call	NOUN
ajis02-1563	246	12	to	to	PART
ajis02-1563	246	13	update	update	VERB
ajis02-1563	246	14	-	-	PUNCT
ajis02-1563	246	15	score	score	NOUN
ajis02-1563	246	16	takes	take	VERB
ajis02-1563	246	17	o(m	o(m	NOUN
ajis02-1563	246	18	)	)	PUNCT
ajis02-1563	246	19	time	time	NOUN
ajis02-1563	246	20	,	,	PUNCT
ajis02-1563	246	21	we	we	PRON
ajis02-1563	246	22	get	get	VERB
ajis02-1563	246	23	that	that	DET
ajis02-1563	246	24	total	total	ADJ
ajis02-1563	246	25	time	time	NOUN
ajis02-1563	246	26	taken	take	VERB
ajis02-1563	246	27	by	by	ADP
ajis02-1563	246	28	the	the	DET
ajis02-1563	246	29	algorithm	algorithm	NOUN
ajis02-1563	246	30	is	be	AUX
ajis02-1563	246	31	𝑂(𝑛	𝑂(𝑛	AUX
ajis02-1563	246	32	+	+	NUM
ajis02-1563	246	33	𝑘𝑚	𝑘𝑚	NOUN
ajis02-1563	247	1	+	+	CCONJ
ajis02-1563	247	2	𝑘	𝑘	DET
ajis02-1563	247	3	𝑙𝑜𝑔	𝑙𝑜𝑔	NOUN
ajis02-1563	247	4	𝑛	𝑛	NOUN
ajis02-1563	247	5	)	)	PUNCT
ajis02-1563	247	6	.	.	PUNCT
ajis02-1563	248	1	for	for	ADP
ajis02-1563	248	2	the	the	DET
ajis02-1563	248	3	space	space	NOUN
ajis02-1563	248	4	complexity	complexity	NOUN
ajis02-1563	248	5	,	,	PUNCT
ajis02-1563	248	6	in	in	ADP
ajis02-1563	248	7	addition	addition	NOUN
ajis02-1563	248	8	to	to	ADP
ajis02-1563	248	9	storing	store	VERB
ajis02-1563	248	10	the	the	DET
ajis02-1563	248	11	graph	graph	NOUN
ajis02-1563	248	12	that	that	PRON
ajis02-1563	248	13	takes	take	VERB
ajis02-1563	248	14	o(n+m	o(n+m	PROPN
ajis02-1563	248	15	)	)	PUNCT
ajis02-1563	248	16	space	space	NOUN
ajis02-1563	248	17	,	,	PUNCT
ajis02-1563	248	18	we	we	PRON
ajis02-1563	248	19	need	need	VERB
ajis02-1563	248	20	o(n	o(n	NOUN
ajis02-1563	248	21	)	)	PUNCT
ajis02-1563	248	22	space	space	NOUN
ajis02-1563	248	23	to	to	PART
ajis02-1563	248	24	store	store	VERB
ajis02-1563	248	25	the	the	DET
ajis02-1563	248	26	three	three	NUM
ajis02-1563	248	27	additional	additional	ADJ
ajis02-1563	248	28	arrays	array	NOUN
ajis02-1563	248	29	.	.	PUNCT
ajis02-1563	249	1	5	5	NUM
ajis02-1563	249	2	experimental	experimental	ADJ
ajis02-1563	249	3	section	section	NOUN
ajis02-1563	249	4	we	we	PRON
ajis02-1563	249	5	present	present	VERB
ajis02-1563	249	6	results	result	NOUN
ajis02-1563	249	7	of	of	ADP
ajis02-1563	249	8	our	our	PRON
ajis02-1563	249	9	approximation	approximation	NOUN
ajis02-1563	249	10	algorithm	algorithm	NOUN
ajis02-1563	249	11	in	in	ADP
ajis02-1563	249	12	this	this	DET
ajis02-1563	249	13	section	section	NOUN
ajis02-1563	249	14	.	.	PUNCT
ajis02-1563	250	1	we	we	PRON
ajis02-1563	250	2	evaluate	evaluate	VERB
ajis02-1563	250	3	the	the	DET
ajis02-1563	250	4	goodness	goodness	NOUN
ajis02-1563	250	5	of	of	ADP
ajis02-1563	250	6	our	our	PRON
ajis02-1563	250	7	algorithm	algorithm	NOUN
ajis02-1563	250	8	on	on	ADP
ajis02-1563	250	9	real	real	ADJ
ajis02-1563	250	10	world	world	NOUN
ajis02-1563	250	11	graphs	graph	NOUN
ajis02-1563	250	12	to	to	PART
ajis02-1563	250	13	quantify	quantify	VERB
ajis02-1563	250	14	the	the	DET
ajis02-1563	250	15	scalability	scalability	NOUN
ajis02-1563	250	16	and	and	CCONJ
ajis02-1563	250	17	effectiveness	effectiveness	NOUN
ajis02-1563	250	18	on	on	ADP
ajis02-1563	250	19	large	large	ADJ
ajis02-1563	250	20	graphs	graph	NOUN
ajis02-1563	250	21	.	.	PUNCT
ajis02-1563	251	1	throughout	throughout	ADP
ajis02-1563	251	2	this	this	DET
ajis02-1563	251	3	paper	paper	NOUN
ajis02-1563	251	4	we	we	PRON
ajis02-1563	251	5	have	have	AUX
ajis02-1563	251	6	used	use	VERB
ajis02-1563	251	7	susceptible−infected−susceptible	susceptible−infected−susceptible	ADJ
ajis02-1563	251	8	(	(	PUNCT
ajis02-1563	251	9	sis	sis	NOUN
ajis02-1563	251	10	)	)	PUNCT
ajis02-1563	251	11	model	model	NOUN
ajis02-1563	251	12	for	for	ADP
ajis02-1563	251	13	virus	virus	NOUN
ajis02-1563	251	14	propagation	propagation	NOUN
ajis02-1563	251	15	in	in	ADP
ajis02-1563	251	16	graphs	graph	NOUN
ajis02-1563	251	17	.	.	PUNCT
ajis02-1563	252	1	for	for	ADP
ajis02-1563	252	2	benchmark	benchmark	ADJ
ajis02-1563	252	3	comparison	comparison	NOUN
ajis02-1563	252	4	we	we	PRON
ajis02-1563	252	5	also	also	ADV
ajis02-1563	252	6	implemented	implement	VERB
ajis02-1563	252	7	maxdegree	maxdegree	ADJ
ajis02-1563	252	8	and	and	CCONJ
ajis02-1563	252	9	updated	update	VERB
ajis02-1563	252	10	-	-	PUNCT
ajis02-1563	252	11	max	max	NOUN
ajis02-1563	252	12	-	-	PUNCT
ajis02-1563	252	13	degree	degree	NOUN
ajis02-1563	252	14	.	.	PUNCT
ajis02-1563	253	1	max	max	PROPN
ajis02-1563	253	2	-	-	PUNCT
ajis02-1563	253	3	degree	degree	NOUN
ajis02-1563	253	4	picks	pick	VERB
ajis02-1563	253	5	the	the	DET
ajis02-1563	253	6	top	top	ADJ
ajis02-1563	253	7	k	k	PROPN
ajis02-1563	253	8	maximum	maximum	ADJ
ajis02-1563	253	9	degree	degree	NOUN
ajis02-1563	253	10	vertices	vertex	NOUN
ajis02-1563	253	11	for	for	ADP
ajis02-1563	253	12	immunization	immunization	NOUN
ajis02-1563	253	13	while	while	SCONJ
ajis02-1563	253	14	updated	update	VERB
ajis02-1563	253	15	-	-	PUNCT
ajis02-1563	253	16	max	max	NOUN
ajis02-1563	253	17	-	-	PUNCT
ajis02-1563	253	18	degree	degree	NOUN
ajis02-1563	253	19	selects	select	VERB
ajis02-1563	253	20	the	the	DET
ajis02-1563	253	21	vertex	vertex	NOUN
ajis02-1563	253	22	with	with	ADP
ajis02-1563	253	23	the	the	DET
ajis02-1563	253	24	maximum	maximum	ADJ
ajis02-1563	253	25	degree	degree	NOUN
ajis02-1563	253	26	and	and	CCONJ
ajis02-1563	253	27	deletes	delete	VERB
ajis02-1563	253	28	that	that	DET
ajis02-1563	253	29	vertex	vertex	NOUN
ajis02-1563	253	30	and	and	CCONJ
ajis02-1563	253	31	repeats	repeat	VERB
ajis02-1563	253	32	k	k	PROPN
ajis02-1563	253	33	times	time	NOUN
ajis02-1563	253	34	.	.	PUNCT
ajis02-1563	254	1	we	we	PRON
ajis02-1563	254	2	use	use	VERB
ajis02-1563	254	3	the	the	DET
ajis02-1563	254	4	net	net	ADJ
ajis02-1563	254	5	-	-	PUNCT
ajis02-1563	254	6	shield	shield	NOUN
ajis02-1563	254	7	implementation	implementation	NOUN
ajis02-1563	254	8	which	which	PRON
ajis02-1563	254	9	is	be	AUX
ajis02-1563	254	10	available	available	ADJ
ajis02-1563	254	11	online1	online1	PROPN
ajis02-1563	254	12	.	.	PUNCT
ajis02-1563	255	1	we	we	PRON
ajis02-1563	255	2	implemented	implement	VERB
ajis02-1563	255	3	our	our	PRON
ajis02-1563	255	4	proposed	propose	VERB
ajis02-1563	255	5	algorithm	algorithm	NOUN
ajis02-1563	255	6	in	in	ADP
ajis02-1563	255	7	matlab	matlab	PROPN
ajis02-1563	255	8	and	and	CCONJ
ajis02-1563	255	9	our	our	PRON
ajis02-1563	255	10	implementation	implementation	NOUN
ajis02-1563	255	11	along	along	ADP
ajis02-1563	255	12	with	with	ADP
ajis02-1563	255	13	source	source	NOUN
ajis02-1563	255	14	code	code	NOUN
ajis02-1563	255	15	and	and	CCONJ
ajis02-1563	255	16	documentation	documentation	NOUN
ajis02-1563	255	17	is	be	AUX
ajis02-1563	255	18	available	available	ADJ
ajis02-1563	255	19	online	online	ADV
ajis02-1563	255	20	on	on	ADP
ajis02-1563	255	21	the	the	DET
ajis02-1563	255	22	given	give	VERB
ajis02-1563	255	23	link2	link2	PROPN
ajis02-1563	255	24	.	.	PUNCT
ajis02-1563	256	1	name	name	PROPN
ajis02-1563	256	2	node	node	ADJ
ajis02-1563	256	3	count	count	NOUN
ajis02-1563	256	4	edge	edge	NOUN
ajis02-1563	256	5	count	count	NOUN
ajis02-1563	256	6	karate	karate	NOUN
ajis02-1563	256	7	34	34	NUM
ajis02-1563	256	8	78	78	NUM
ajis02-1563	256	9	oregon	oregon	PROPN
ajis02-1563	256	10	10,670	10,670	NUM
ajis02-1563	256	11	22,002	22,002	NUM
ajis02-1563	256	12	aa	aa	NOUN
ajis02-1563	256	13	418,236	418,236	NUM
ajis02-1563	256	14	2,753,798	2,753,798	NUM
ajis02-1563	256	15	table	table	NOUN
ajis02-1563	256	16	1	1	NUM
ajis02-1563	256	17	summary	summary	NOUN
ajis02-1563	256	18	of	of	ADP
ajis02-1563	256	19	datasets	dataset	NOUN
ajis02-1563	256	20	the	the	DET
ajis02-1563	256	21	data	data	NOUN
ajis02-1563	256	22	sets	set	NOUN
ajis02-1563	256	23	used	use	VERB
ajis02-1563	256	24	in	in	ADP
ajis02-1563	256	25	experimentation	experimentation	NOUN
ajis02-1563	256	26	are	be	AUX
ajis02-1563	256	27	described	describe	VERB
ajis02-1563	256	28	in	in	ADP
ajis02-1563	256	29	table	table	NOUN
ajis02-1563	256	30	1	1	NUM
ajis02-1563	256	31	.	.	PUNCT
ajis02-1563	257	1	all	all	DET
ajis02-1563	257	2	the	the	DET
ajis02-1563	257	3	real	real	ADJ
ajis02-1563	257	4	graphs	graph	NOUN
ajis02-1563	257	5	used	use	VERB
ajis02-1563	257	6	for	for	ADP
ajis02-1563	257	7	experimentation	experimentation	NOUN
ajis02-1563	257	8	obey	obey	NOUN
ajis02-1563	257	9	power	power	NOUN
ajis02-1563	257	10	law	law	NOUN
ajis02-1563	257	11	distribution	distribution	NOUN
ajis02-1563	257	12	of	of	ADP
ajis02-1563	257	13	degrees	degree	NOUN
ajis02-1563	257	14	.	.	PUNCT
ajis02-1563	258	1	the	the	DET
ajis02-1563	258	2	first	first	ADJ
ajis02-1563	258	3	data	datum	NOUN
ajis02-1563	258	4	set	set	VERB
ajis02-1563	258	5	is	be	AUX
ajis02-1563	258	6	of	of	ADP
ajis02-1563	258	7	a	a	DET
ajis02-1563	258	8	local	local	ADJ
ajis02-1563	258	9	karate	karate	NOUN
ajis02-1563	258	10	club	club	NOUN
ajis02-1563	258	11	and	and	CCONJ
ajis02-1563	258	12	is	be	AUX
ajis02-1563	258	13	named	name	VERB
ajis02-1563	258	14	as	as	ADP
ajis02-1563	258	15	karate	karate	ADJ
ajis02-1563	258	16	graph3	graph3	NOUN
ajis02-1563	258	17	.	.	PUNCT
ajis02-1563	259	1	nodes	node	NOUN
ajis02-1563	259	2	of	of	ADP
ajis02-1563	259	3	the	the	DET
ajis02-1563	259	4	graph	graph	NOUN
ajis02-1563	259	5	represent	represent	VERB
ajis02-1563	259	6	members	member	NOUN
ajis02-1563	259	7	of	of	ADP
ajis02-1563	259	8	the	the	DET
ajis02-1563	259	9	club	club	NOUN
ajis02-1563	259	10	and	and	CCONJ
ajis02-1563	259	11	an	an	DET
ajis02-1563	259	12	edge	edge	NOUN
ajis02-1563	259	13	between	between	ADP
ajis02-1563	259	14	nodes	node	NOUN
ajis02-1563	259	15	show	show	VERB
ajis02-1563	259	16	that	that	SCONJ
ajis02-1563	259	17	corresponding	correspond	VERB
ajis02-1563	259	18	members	member	NOUN
ajis02-1563	259	19	are	be	AUX
ajis02-1563	259	20	friends	friend	NOUN
ajis02-1563	259	21	with	with	ADP
ajis02-1563	259	22	each	each	DET
ajis02-1563	259	23	other	other	ADJ
ajis02-1563	259	24	.	.	PUNCT
ajis02-1563	260	1	graph	graph	NOUN
ajis02-1563	260	2	consists	consist	VERB
ajis02-1563	260	3	of	of	ADP
ajis02-1563	260	4	34	34	NUM
ajis02-1563	260	5	nodes	node	NOUN
ajis02-1563	260	6	and	and	CCONJ
ajis02-1563	260	7	78	78	NUM
ajis02-1563	260	8	edges	edge	NOUN
ajis02-1563	260	9	.	.	PUNCT
ajis02-1563	261	1	the	the	DET
ajis02-1563	261	2	graph	graph	NOUN
ajis02-1563	261	3	is	be	AUX
ajis02-1563	261	4	undirected	undirected	ADJ
ajis02-1563	261	5	and	and	CCONJ
ajis02-1563	261	6	unweighted	unweighted	ADJ
ajis02-1563	261	7	.	.	PUNCT
ajis02-1563	262	1	the	the	DET
ajis02-1563	262	2	second	second	ADJ
ajis02-1563	262	3	data	datum	NOUN
ajis02-1563	262	4	set	set	VERB
ajis02-1563	262	5	is	be	AUX
ajis02-1563	262	6	from	from	ADP
ajis02-1563	262	7	oregon	oregon	PROPN
ajis02-1563	262	8	as	as	ADP
ajis02-1563	262	9	(	(	PUNCT
ajis02-1563	262	10	autonomous	autonomous	ADJ
ajis02-1563	262	11	system)4	system)4	PROPN
ajis02-1563	262	12	router	router	NOUN
ajis02-1563	262	13	graphs	graph	NOUN
ajis02-1563	262	14	,	,	PUNCT
ajis02-1563	262	15	which	which	PRON
ajis02-1563	262	16	are	be	AUX
ajis02-1563	262	17	as	as	ADP
ajis02-1563	262	18	level	level	NOUN
ajis02-1563	262	19	connectivity	connectivity	NOUN
ajis02-1563	262	20	networks	network	NOUN
ajis02-1563	262	21	inferred	infer	VERB
ajis02-1563	262	22	from	from	ADP
ajis02-1563	262	23	oregon	oregon	PROPN
ajis02-1563	262	24	route	route	NOUN
ajis02-1563	262	25	views	view	NOUN
ajis02-1563	262	26	.	.	PUNCT
ajis02-1563	263	1	there	there	PRON
ajis02-1563	263	2	are	be	VERB
ajis02-1563	263	3	a	a	DET
ajis02-1563	263	4	number	number	NOUN
ajis02-1563	263	5	of	of	ADP
ajis02-1563	263	6	oregon	oregon	PROPN
ajis02-1563	263	7	as	as	ADP
ajis02-1563	263	8	graphs	graph	NOUN
ajis02-1563	263	9	available	available	ADJ
ajis02-1563	263	10	and	and	CCONJ
ajis02-1563	263	11	each	each	DET
ajis02-1563	263	12	node	node	NOUN
ajis02-1563	263	13	represents	represent	VERB
ajis02-1563	263	14	a	a	DET
ajis02-1563	263	15	router	router	NOUN
ajis02-1563	263	16	and	and	CCONJ
ajis02-1563	263	17	an	an	DET
ajis02-1563	263	18	edge	edge	NOUN
ajis02-1563	263	19	between	between	ADP
ajis02-1563	263	20	two	two	NUM
ajis02-1563	263	21	routers	router	NOUN
ajis02-1563	263	22	represents	represent	VERB
ajis02-1563	263	23	a	a	DET
ajis02-1563	263	24	direct	direct	ADJ
ajis02-1563	263	25	peering	peering	ADJ
ajis02-1563	263	26	relationship	relationship	NOUN
ajis02-1563	263	27	between	between	ADP
ajis02-1563	263	28	two	two	NUM
ajis02-1563	263	29	routers	router	NOUN
ajis02-1563	263	30	.	.	PUNCT
ajis02-1563	264	1	we	we	PRON
ajis02-1563	264	2	have	have	AUX
ajis02-1563	264	3	selected	select	VERB
ajis02-1563	264	4	one	one	NUM
ajis02-1563	264	5	set	set	VERB
ajis02-1563	264	6	from	from	ADP
ajis02-1563	264	7	oregon	oregon	PROPN
ajis02-1563	264	8	router	router	NOUN
ajis02-1563	264	9	graphs	graph	NOUN
ajis02-1563	264	10	having	have	VERB
ajis02-1563	264	11	10,670	10,670	NUM
ajis02-1563	264	12	nodes	node	NOUN
ajis02-1563	264	13	and	and	CCONJ
ajis02-1563	264	14	22,002	22,002	NUM
ajis02-1563	264	15	edges	edge	NOUN
ajis02-1563	264	16	.	.	PUNCT
ajis02-1563	265	1	the	the	DET
ajis02-1563	265	2	graph	graph	NOUN
ajis02-1563	265	3	is	be	AUX
ajis02-1563	265	4	undirected	undirected	ADJ
ajis02-1563	265	5	and	and	CCONJ
ajis02-1563	265	6	unweighted	unweighted	ADJ
ajis02-1563	265	7	.	.	PUNCT
ajis02-1563	266	1	nodes	node	NOUN
ajis02-1563	266	2	selected	select	VERB
ajis02-1563	266	3	by	by	ADP
ajis02-1563	266	4	greedy	greedy	ADJ
ajis02-1563	266	5	algorithm	algorithm	NOUN
ajis02-1563	266	6	are	be	AUX
ajis02-1563	266	7	those	those	DET
ajis02-1563	266	8	routers	router	NOUN
ajis02-1563	266	9	whose	whose	DET
ajis02-1563	266	10	immunization	immunization	NOUN
ajis02-1563	266	11	will	will	AUX
ajis02-1563	266	12	maximally	maximally	ADV
ajis02-1563	266	13	reduce	reduce	VERB
ajis02-1563	266	14	the	the	DET
ajis02-1563	266	15	spread	spread	NOUN
ajis02-1563	266	16	of	of	ADP
ajis02-1563	266	17	virus	virus	NOUN
ajis02-1563	266	18	.	.	PUNCT
ajis02-1563	267	1	the	the	DET
ajis02-1563	267	2	third	third	ADJ
ajis02-1563	267	3	data	datum	NOUN
ajis02-1563	267	4	set	set	NOUN
ajis02-1563	267	5	(	(	PUNCT
ajis02-1563	267	6	aa	aa	NOUN
ajis02-1563	267	7	)	)	PUNCT
ajis02-1563	267	8	is	be	AUX
ajis02-1563	267	9	from	from	ADP
ajis02-1563	267	10	dblp5	dblp5	PROPN
ajis02-1563	267	11	dataset	dataset	NOUN
ajis02-1563	267	12	.	.	PUNCT
ajis02-1563	268	1	in	in	ADP
ajis02-1563	268	2	graph	graph	NOUN
ajis02-1563	268	3	a	a	DET
ajis02-1563	268	4	node	node	NOUN
ajis02-1563	268	5	represents	represent	VERB
ajis02-1563	268	6	an	an	DET
ajis02-1563	268	7	author	author	NOUN
ajis02-1563	268	8	and	and	CCONJ
ajis02-1563	268	9	presence	presence	NOUN
ajis02-1563	268	10	of	of	ADP
ajis02-1563	268	11	an	an	DET
ajis02-1563	268	12	edge	edge	NOUN
ajis02-1563	268	13	between	between	ADP
ajis02-1563	268	14	two	two	NUM
ajis02-1563	268	15	nodes	node	NOUN
ajis02-1563	268	16	shows	show	VERB
ajis02-1563	268	17	that	that	SCONJ
ajis02-1563	268	18	two	two	NUM
ajis02-1563	268	19	authors	author	NOUN
ajis02-1563	268	20	have	have	VERB
ajis02-1563	268	21	a	a	DET
ajis02-1563	268	22	co	co	NOUN
ajis02-1563	268	23	-	-	NOUN
ajis02-1563	268	24	authorship	authorship	NOUN
ajis02-1563	268	25	.	.	PUNCT
ajis02-1563	269	1	in	in	ADP
ajis02-1563	269	2	dblp	dblp	NOUN
ajis02-1563	269	3	there	there	PRON
ajis02-1563	269	4	is	be	VERB
ajis02-1563	269	5	total	total	ADJ
ajis02-1563	269	6	node	node	ADJ
ajis02-1563	269	7	count	count	NOUN
ajis02-1563	269	8	of	of	ADP
ajis02-1563	269	9	418,236	418,236	NUM
ajis02-1563	269	10	and	and	CCONJ
ajis02-1563	269	11	the	the	DET
ajis02-1563	269	12	number	number	NOUN
ajis02-1563	269	13	of	of	ADP
ajis02-1563	269	14	edges	edge	NOUN
ajis02-1563	269	15	among	among	ADP
ajis02-1563	269	16	nodes	node	NOUN
ajis02-1563	269	17	is	be	AUX
ajis02-1563	269	18	2,753,798	2,753,798	NUM
ajis02-1563	269	19	.	.	PUNCT
ajis02-1563	270	1	we	we	PRON
ajis02-1563	270	2	extracted	extract	VERB
ajis02-1563	270	3	smaller	small	ADJ
ajis02-1563	270	4	graphs	graph	NOUN
ajis02-1563	270	5	by	by	ADP
ajis02-1563	270	6	selecting	select	VERB
ajis02-1563	270	7	co	co	NOUN
ajis02-1563	270	8	-	-	NOUN
ajis02-1563	270	9	authorship	authorship	ADJ
ajis02-1563	270	10	graph	graph	NOUN
ajis02-1563	270	11	of	of	ADP
ajis02-1563	270	12	only	only	ADV
ajis02-1563	270	13	one	one	NUM
ajis02-1563	270	14	journal	journal	NOUN
ajis02-1563	270	15	(	(	PUNCT
ajis02-1563	270	16	e.g	e.g	NOUN
ajis02-1563	270	17	displays	display	NOUN
ajis02-1563	270	18	,	,	PUNCT
ajis02-1563	270	19	international	international	ADJ
ajis02-1563	270	20	journal	journal	NOUN
ajis02-1563	270	21	of	of	ADP
ajis02-1563	270	22	computational	computational	ADJ
ajis02-1563	270	23	intelligence	intelligence	NOUN
ajis02-1563	270	24	and	and	CCONJ
ajis02-1563	270	25	applications	application	NOUN
ajis02-1563	270	26	,	,	PUNCT
ajis02-1563	270	27	international	international	ADJ
ajis02-1563	270	28	journal	journal	NOUN
ajis02-1563	270	29	of	of	ADP
ajis02-1563	270	30	internet	internet	NOUN
ajis02-1563	270	31	and	and	CCONJ
ajis02-1563	270	32	enterprise	enterprise	NOUN
ajis02-1563	270	33	management	management	NOUN
ajis02-1563	270	34	,	,	PUNCT
ajis02-1563	270	35	etc	etc	X
ajis02-1563	270	36	.	.	X
ajis02-1563	270	37	)	)	PUNCT
ajis02-1563	270	38	.	.	PUNCT
ajis02-1563	271	1	we	we	PRON
ajis02-1563	271	2	ran	run	VERB
ajis02-1563	271	3	our	our	PRON
ajis02-1563	271	4	experiments	experiment	NOUN
ajis02-1563	271	5	on	on	ADP
ajis02-1563	271	6	20	20	NUM
ajis02-1563	271	7	different	different	ADJ
ajis02-1563	271	8	smaller	small	ADJ
ajis02-1563	271	9	co	co	NOUN
ajis02-1563	271	10	-	-	NOUN
ajis02-1563	271	11	authorship	authorship	ADJ
ajis02-1563	271	12	networks	network	NOUN
ajis02-1563	271	13	based	base	VERB
ajis02-1563	271	14	on	on	ADP
ajis02-1563	271	15	co	co	ADJ
ajis02-1563	271	16	-	-	NOUN
ajis02-1563	271	17	authorship	authorship	ADJ
ajis02-1563	271	18	graphs	graph	NOUN
ajis02-1563	271	19	of	of	ADP
ajis02-1563	271	20	20	20	NUM
ajis02-1563	271	21	different	different	ADJ
ajis02-1563	271	22	journals	journal	NOUN
ajis02-1563	271	23	.	.	PUNCT
ajis02-1563	272	1	for	for	ADP
ajis02-1563	272	2	the	the	DET
ajis02-1563	272	3	smaller	small	ADJ
ajis02-1563	272	4	sub	sub	NOUN
ajis02-1563	272	5	graphs	graph	NOUN
ajis02-1563	272	6	that	that	SCONJ
ajis02-1563	272	7	we	we	PRON
ajis02-1563	272	8	have	have	AUX
ajis02-1563	272	9	extracted	extract	VERB
ajis02-1563	272	10	from	from	ADP
ajis02-1563	272	11	dblp	dblp	NOUN
ajis02-1563	272	12	dataset	dataset	PROPN
ajis02-1563	272	13	,	,	PUNCT
ajis02-1563	272	14	node	node	ADJ
ajis02-1563	272	15	count	count	NOUN
ajis02-1563	272	16	goes	go	VERB
ajis02-1563	272	17	up	up	ADP
ajis02-1563	272	18	to	to	ADP
ajis02-1563	272	19	few	few	ADJ
ajis02-1563	272	20	1	1	NUM
ajis02-1563	272	21	https	https	NOUN
ajis02-1563	272	22	:	:	PUNCT
ajis02-1563	272	23	//www.dropbox.com	//www.dropbox.com	PUNCT
ajis02-1563	272	24	/	/	SYM
ajis02-1563	273	1	s	s	X
ajis02-1563	273	2	/	/	SYM
ajis02-1563	273	3	aaq5ly4mcxhijmg	aaq5ly4mcxhijmg	ADJ
ajis02-1563	273	4	/	/	SYM
ajis02-1563	273	5	netshieldplus.tar	netshieldplus.tar	SYM
ajis02-1563	273	6	2	2	NUM
ajis02-1563	273	7	www.dropbox.com	www.dropbox.com	NOUN
ajis02-1563	273	8	3	3	NUM
ajis02-1563	273	9	http://konect.uni-koblenz.de/networks/ucidata-zachary	http://konect.uni-koblenz.de/networks/ucidata-zachary	ADJ
ajis02-1563	273	10	4	4	NUM
ajis02-1563	273	11	http://snap.stanford.edu/data/oregon1.html	http://snap.stanford.edu/data/oregon1.html	NOUN
ajis02-1563	273	12	5	5	NUM
ajis02-1563	273	13	http://dblp.uni-trier.de/xml/	http://dblp.uni-trier.de/xml/	NOUN
ajis02-1563	273	14	australasian	australasian	ADJ
ajis02-1563	273	15	journal	journal	NOUN
ajis02-1563	273	16	of	of	ADP
ajis02-1563	273	17	information	information	NOUN
ajis02-1563	273	18	systems	system	NOUN
ajis02-1563	273	19	ahmad	ahmad	PROPN
ajis02-1563	273	20	,	,	PUNCT
ajis02-1563	273	21	traiq	traiq	NOUN
ajis02-1563	273	22	,	,	PUNCT
ajis02-1563	273	23	shabbir	shabbir	PROPN
ajis02-1563	273	24	&	&	CCONJ
ajis02-1563	273	25	khan	khan	PROPN
ajis02-1563	273	26	2017	2017	NUM
ajis02-1563	273	27	,	,	PUNCT
ajis02-1563	273	28	vol	vol	NOUN
ajis02-1563	273	29	21	21	NUM
ajis02-1563	273	30	,	,	PUNCT
ajis02-1563	273	31	selected	select	VERB
ajis02-1563	273	32	papers	paper	NOUN
ajis02-1563	273	33	from	from	ADP
ajis02-1563	273	34	ausdm	ausdm	NOUN
ajis02-1563	273	35	spectral	spectral	ADJ
ajis02-1563	273	36	methods	method	NOUN
ajis02-1563	273	37	for	for	ADP
ajis02-1563	273	38	immunization	immunization	NOUN
ajis02-1563	273	39	of	of	ADP
ajis02-1563	273	40	large	large	ADJ
ajis02-1563	273	41	networks	network	NOUN
ajis02-1563	273	42	12	12	NUM
ajis02-1563	273	43	thousands	thousand	NOUN
ajis02-1563	273	44	and	and	CCONJ
ajis02-1563	273	45	edge	edge	NOUN
ajis02-1563	273	46	count	count	NOUN
ajis02-1563	273	47	goes	go	VERB
ajis02-1563	273	48	up	up	ADP
ajis02-1563	273	49	to	to	ADP
ajis02-1563	273	50	few	few	ADJ
ajis02-1563	273	51	ten	ten	NUM
ajis02-1563	273	52	thousands	thousand	NOUN
ajis02-1563	273	53	.	.	PUNCT
ajis02-1563	274	1	co	co	VERB
ajis02-1563	274	2	-	-	NOUN
ajis02-1563	274	3	authorship	authorship	ADJ
ajis02-1563	274	4	graph	graph	NOUN
ajis02-1563	274	5	of	of	ADP
ajis02-1563	274	6	actainf	actainf	NOUN
ajis02-1563	274	7	contains	contain	VERB
ajis02-1563	274	8	1,791	1,791	NUM
ajis02-1563	274	9	nodes	node	NOUN
ajis02-1563	274	10	and	and	CCONJ
ajis02-1563	274	11	1,659	1,659	NUM
ajis02-1563	274	12	edges	edge	NOUN
ajis02-1563	274	13	,	,	PUNCT
ajis02-1563	274	14	graph	graph	NOUN
ajis02-1563	274	15	of	of	ADP
ajis02-1563	274	16	ai	ai	PROPN
ajis02-1563	274	17	communication	communication	NOUN
ajis02-1563	274	18	journal	journal	NOUN
ajis02-1563	274	19	has	have	VERB
ajis02-1563	274	20	node	node	ADJ
ajis02-1563	274	21	count	count	NOUN
ajis02-1563	274	22	of	of	ADP
ajis02-1563	274	23	1,203	1,203	NUM
ajis02-1563	274	24	and	and	CCONJ
ajis02-1563	274	25	edge	edge	NOUN
ajis02-1563	274	26	count	count	NOUN
ajis02-1563	274	27	of	of	ADP
ajis02-1563	274	28	2,204	2,204	NUM
ajis02-1563	274	29	,	,	PUNCT
ajis02-1563	274	30	sub	sub	NOUN
ajis02-1563	274	31	graph	graph	NOUN
ajis02-1563	274	32	of	of	ADP
ajis02-1563	274	33	asia	asia	PROPN
ajis02-1563	274	34	-	-	PUNCT
ajis02-1563	274	35	pacific	pacific	PROPN
ajis02-1563	274	36	journal	journal	NOUN
ajis02-1563	274	37	of	of	ADP
ajis02-1563	274	38	operational	operational	ADJ
ajis02-1563	274	39	research	research	NOUN
ajis02-1563	274	40	(	(	PUNCT
ajis02-1563	274	41	apjor	apjor	PROPN
ajis02-1563	274	42	)	)	PUNCT
ajis02-1563	274	43	has	have	VERB
ajis02-1563	274	44	1,132	1,132	NUM
ajis02-1563	274	45	nodes	node	NOUN
ajis02-1563	274	46	and	and	CCONJ
ajis02-1563	274	47	1,145	1,145	NUM
ajis02-1563	274	48	edges	edge	NOUN
ajis02-1563	274	49	,	,	PUNCT
ajis02-1563	274	50	computer	computer	NOUN
ajis02-1563	274	51	in	in	ADP
ajis02-1563	274	52	industry	industry	NOUN
ajis02-1563	274	53	journal	journal	NOUN
ajis02-1563	274	54	contains	contain	VERB
ajis02-1563	274	55	2,844	2,844	NUM
ajis02-1563	274	56	nodes	node	NOUN
ajis02-1563	274	57	and	and	CCONJ
ajis02-1563	274	58	4,466	4,466	NUM
ajis02-1563	274	59	edges	edge	NOUN
ajis02-1563	274	60	among	among	ADP
ajis02-1563	274	61	nodes	node	NOUN
ajis02-1563	274	62	,	,	PUNCT
ajis02-1563	274	63	journal	journal	NOUN
ajis02-1563	274	64	of	of	ADP
ajis02-1563	274	65	ieee	ieee	PROPN
ajis02-1563	274	66	wireless	wireless	NOUN
ajis02-1563	274	67	has	have	VERB
ajis02-1563	274	68	total	total	NOUN
ajis02-1563	274	69	of	of	ADP
ajis02-1563	274	70	7,882	7,882	NUM
ajis02-1563	274	71	authors	author	NOUN
ajis02-1563	274	72	and	and	CCONJ
ajis02-1563	274	73	16,557	16,557	NUM
ajis02-1563	274	74	co	co	ADJ
ajis02-1563	274	75	-	-	NOUN
ajis02-1563	274	76	authorship	authorship	ADJ
ajis02-1563	274	77	links	link	NOUN
ajis02-1563	274	78	among	among	ADP
ajis02-1563	274	79	authors	author	NOUN
ajis02-1563	274	80	.	.	PUNCT
ajis02-1563	275	1	detail	detail	NOUN
ajis02-1563	275	2	of	of	ADP
ajis02-1563	275	3	sub	sub	NOUN
ajis02-1563	275	4	graphs	graph	NOUN
ajis02-1563	275	5	of	of	ADP
ajis02-1563	275	6	dblp	dblp	NOUN
ajis02-1563	275	7	data	datum	NOUN
ajis02-1563	275	8	set	set	VERB
ajis02-1563	275	9	is	be	AUX
ajis02-1563	275	10	also	also	ADV
ajis02-1563	275	11	given	give	VERB
ajis02-1563	275	12	in	in	ADP
ajis02-1563	275	13	table	table	NOUN
ajis02-1563	275	14	2	2	NUM
ajis02-1563	275	15	.	.	PUNCT
ajis02-1563	276	1	these	these	DET
ajis02-1563	276	2	sub	sub	NOUN
ajis02-1563	276	3	graphs	graph	NOUN
ajis02-1563	276	4	are	be	AUX
ajis02-1563	276	5	also	also	ADV
ajis02-1563	276	6	undirected	undirected	ADJ
ajis02-1563	276	7	and	and	CCONJ
ajis02-1563	276	8	unweighted	unweighted	ADJ
ajis02-1563	276	9	.	.	PUNCT
ajis02-1563	277	1	name	name	NOUN
ajis02-1563	277	2	node	node	ADJ
ajis02-1563	277	3	count	count	NOUN
ajis02-1563	277	4	edge	edge	NOUN
ajis02-1563	277	5	count	count	NOUN
ajis02-1563	277	6	actainf	actainf	VERB
ajis02-1563	277	7	1,791	1,791	NUM
ajis02-1563	277	8	1,659	1,659	NUM
ajis02-1563	277	9	ai	ai	NOUN
ajis02-1563	277	10	communication	communication	NOUN
ajis02-1563	277	11	1,203	1,203	NUM
ajis02-1563	277	12	2,204	2,204	NUM
ajis02-1563	277	13	apjor	apjor	VERB
ajis02-1563	277	14	1,132	1,132	NUM
ajis02-1563	277	15	1,145	1,145	NUM
ajis02-1563	277	16	computer	computer	NOUN
ajis02-1563	277	17	in	in	ADP
ajis02-1563	277	18	industry	industry	NOUN
ajis02-1563	277	19	2,844	2,844	NUM
ajis02-1563	277	20	4,466	4,466	NUM
ajis02-1563	277	21	computing	computing	NOUN
ajis02-1563	277	22	and	and	CCONJ
ajis02-1563	277	23	informatics	informatic	NOUN
ajis02-1563	277	24	1,598	1,598	NUM
ajis02-1563	277	25	2,324	2,324	NUM
ajis02-1563	277	26	ecological	ecological	ADJ
ajis02-1563	277	27	informatics	informatic	NOUN
ajis02-1563	277	28	1,990	1,990	NUM
ajis02-1563	277	29	4,913	4,913	NUM
ajis02-1563	277	30	ieee	ieee	NOUN
ajis02-1563	277	31	wireless	wireless	NOUN
ajis02-1563	277	32	7,882	7,882	NUM
ajis02-1563	277	33	16,577	16,577	NUM
ajis02-1563	277	34	ijcia	ijcia	NOUN
ajis02-1563	277	35	848	848	NUM
ajis02-1563	277	36	975	975	NUM
ajis02-1563	277	37	ijiem	ijiem	NOUN
ajis02-1563	277	38	373	373	NUM
ajis02-1563	277	39	357	357	NUM
ajis02-1563	277	40	table	table	NOUN
ajis02-1563	277	41	2	2	NUM
ajis02-1563	277	42	summary	summary	NOUN
ajis02-1563	277	43	of	of	ADP
ajis02-1563	277	44	dblp	dblp	NOUN
ajis02-1563	277	45	subgraphs	subgraph	NOUN
ajis02-1563	277	46	we	we	PRON
ajis02-1563	277	47	did	do	VERB
ajis02-1563	277	48	extensive	extensive	ADJ
ajis02-1563	277	49	experimentation	experimentation	NOUN
ajis02-1563	277	50	with	with	ADP
ajis02-1563	277	51	varying	vary	VERB
ajis02-1563	277	52	count	count	NOUN
ajis02-1563	277	53	of	of	ADP
ajis02-1563	277	54	nodes	node	NOUN
ajis02-1563	277	55	to	to	PART
ajis02-1563	277	56	be	be	AUX
ajis02-1563	277	57	immunized	immunize	VERB
ajis02-1563	277	58	.	.	PUNCT
ajis02-1563	278	1	in	in	ADP
ajis02-1563	278	2	the	the	DET
ajis02-1563	278	3	results	result	NOUN
ajis02-1563	278	4	shown	show	VERB
ajis02-1563	278	5	,	,	PUNCT
ajis02-1563	278	6	x	x	ADJ
ajis02-1563	278	7	-	-	ADJ
ajis02-1563	278	8	axis	axis	NOUN
ajis02-1563	278	9	shows	show	VERB
ajis02-1563	278	10	the	the	DET
ajis02-1563	278	11	value	value	NOUN
ajis02-1563	278	12	of	of	ADP
ajis02-1563	278	13	k	k	PROPN
ajis02-1563	278	14	which	which	PRON
ajis02-1563	278	15	is	be	AUX
ajis02-1563	278	16	count	count	NOUN
ajis02-1563	278	17	of	of	ADP
ajis02-1563	278	18	immunized	immunize	VERB
ajis02-1563	278	19	nodes	node	NOUN
ajis02-1563	278	20	and	and	CCONJ
ajis02-1563	278	21	y	y	NOUN
ajis02-1563	278	22	-	-	PUNCT
ajis02-1563	278	23	axis	axis	NOUN
ajis02-1563	278	24	shows	show	VERB
ajis02-1563	278	25	the	the	DET
ajis02-1563	278	26	percentage	percentage	NOUN
ajis02-1563	278	27	of	of	ADP
ajis02-1563	278	28	eigendrop	eigendrop	NOUN
ajis02-1563	278	29	which	which	PRON
ajis02-1563	278	30	is	be	AUX
ajis02-1563	278	31	the	the	DET
ajis02-1563	278	32	achieved	achieve	VERB
ajis02-1563	278	33	benefit	benefit	NOUN
ajis02-1563	278	34	after	after	ADP
ajis02-1563	278	35	deleting	delete	VERB
ajis02-1563	278	36	k	k	PROPN
ajis02-1563	278	37	nodes	node	NOUN
ajis02-1563	278	38	from	from	ADP
ajis02-1563	278	39	graph	graph	NOUN
ajis02-1563	278	40	.	.	PUNCT
ajis02-1563	279	1	results	result	NOUN
ajis02-1563	279	2	are	be	AUX
ajis02-1563	279	3	evaluated	evaluate	VERB
ajis02-1563	279	4	on	on	ADP
ajis02-1563	279	5	the	the	DET
ajis02-1563	279	6	basis	basis	NOUN
ajis02-1563	279	7	of	of	ADP
ajis02-1563	279	8	percentage	percentage	NOUN
ajis02-1563	279	9	of	of	ADP
ajis02-1563	279	10	eigendrop	eigendrop	PROPN
ajis02-1563	279	11	.	.	PUNCT
ajis02-1563	280	1	eigendrop	eigendrop	PROPN
ajis02-1563	280	2	is	be	AUX
ajis02-1563	280	3	difference	difference	NOUN
ajis02-1563	280	4	of	of	ADP
ajis02-1563	280	5	largest	large	ADJ
ajis02-1563	280	6	eigenvalues	eigenvalue	NOUN
ajis02-1563	280	7	of	of	ADP
ajis02-1563	280	8	original	original	ADJ
ajis02-1563	280	9	graph	graph	NOUN
ajis02-1563	280	10	and	and	CCONJ
ajis02-1563	280	11	perturbed	perturb	VERB
ajis02-1563	280	12	version	version	NOUN
ajis02-1563	280	13	of	of	ADP
ajis02-1563	280	14	graph	graph	NOUN
ajis02-1563	280	15	after	after	ADP
ajis02-1563	280	16	immunization	immunization	NOUN
ajis02-1563	280	17	of	of	ADP
ajis02-1563	280	18	k	k	PROPN
ajis02-1563	280	19	nodes	node	NOUN
ajis02-1563	280	20	.	.	PUNCT
ajis02-1563	281	1	δ𝜆	δ𝜆	PRON
ajis02-1563	281	2	=	=	SYM
ajis02-1563	282	1	𝜆	𝜆	DET
ajis02-1563	282	2	−	−	PROPN
ajis02-1563	282	3	𝜆(𝑆	𝜆(𝑆	NUM
ajis02-1563	282	4	)	)	PUNCT
ajis02-1563	282	5	(	(	PUNCT
ajis02-1563	282	6	7	7	X
ajis02-1563	282	7	)	)	PUNCT
ajis02-1563	282	8	where	where	SCONJ
ajis02-1563	282	9	s	s	NOUN
ajis02-1563	282	10	is	be	AUX
ajis02-1563	282	11	the	the	DET
ajis02-1563	282	12	set	set	NOUN
ajis02-1563	282	13	containing	contain	VERB
ajis02-1563	282	14	nodes	node	NOUN
ajis02-1563	282	15	to	to	PART
ajis02-1563	282	16	be	be	AUX
ajis02-1563	282	17	immunized	immunize	VERB
ajis02-1563	282	18	having	have	VERB
ajis02-1563	282	19	cardinality	cardinality	PROPN
ajis02-1563	282	20	k.	k.	PROPN
ajis02-1563	283	1	it	it	PRON
ajis02-1563	283	2	is	be	AUX
ajis02-1563	283	3	clear	clear	ADJ
ajis02-1563	283	4	from	from	ADP
ajis02-1563	283	5	the	the	DET
ajis02-1563	283	6	results	result	NOUN
ajis02-1563	283	7	that	that	PRON
ajis02-1563	283	8	our	our	PRON
ajis02-1563	283	9	greedy	greedy	ADJ
ajis02-1563	283	10	algorithm	algorithm	NOUN
ajis02-1563	283	11	outperforms	outperform	NOUN
ajis02-1563	283	12	netsheild	netsheild	ADJ
ajis02-1563	283	13	approach	approach	NOUN
ajis02-1563	283	14	and	and	CCONJ
ajis02-1563	283	15	other	other	ADJ
ajis02-1563	283	16	approaches	approach	NOUN
ajis02-1563	283	17	like	like	ADP
ajis02-1563	283	18	top	top	ADJ
ajis02-1563	283	19	k	k	PROPN
ajis02-1563	283	20	degree	degree	NOUN
ajis02-1563	283	21	and	and	CCONJ
ajis02-1563	283	22	updated	update	VERB
ajis02-1563	283	23	maximum	maximum	ADJ
ajis02-1563	283	24	degree	degree	NOUN
ajis02-1563	283	25	approach	approach	NOUN
ajis02-1563	283	26	.	.	PUNCT
ajis02-1563	284	1	our	our	PRON
ajis02-1563	284	2	greedy	greedy	ADJ
ajis02-1563	284	3	algorithm	algorithm	NOUN
ajis02-1563	284	4	is	be	AUX
ajis02-1563	284	5	scalable	scalable	ADJ
ajis02-1563	284	6	for	for	ADP
ajis02-1563	284	7	larger	large	ADJ
ajis02-1563	284	8	values	value	NOUN
ajis02-1563	284	9	of	of	ADP
ajis02-1563	284	10	k	k	PROPN
ajis02-1563	284	11	as	as	ADV
ajis02-1563	284	12	well	well	ADV
ajis02-1563	284	13	as	as	ADP
ajis02-1563	284	14	for	for	ADP
ajis02-1563	284	15	larger	large	ADJ
ajis02-1563	284	16	graphs	graph	NOUN
ajis02-1563	284	17	as	as	SCONJ
ajis02-1563	284	18	our	our	PRON
ajis02-1563	284	19	algorithm	algorithm	NOUN
ajis02-1563	284	20	has	have	VERB
ajis02-1563	284	21	less	less	ADJ
ajis02-1563	284	22	running	running	NOUN
ajis02-1563	284	23	time	time	NOUN
ajis02-1563	284	24	complexity	complexity	NOUN
ajis02-1563	284	25	than	than	ADP
ajis02-1563	284	26	netsheild	netsheild	NOUN
ajis02-1563	284	27	,	,	PUNCT
ajis02-1563	284	28	top	top	ADJ
ajis02-1563	284	29	k	k	PROPN
ajis02-1563	284	30	degree	degree	NOUN
ajis02-1563	284	31	and	and	CCONJ
ajis02-1563	284	32	updated	update	VERB
ajis02-1563	284	33	maximum	maximum	ADJ
ajis02-1563	284	34	degree	degree	NOUN
ajis02-1563	284	35	.	.	PUNCT
ajis02-1563	285	1	figure	figure	NOUN
ajis02-1563	285	2	1	1	NUM
ajis02-1563	285	3	eigendrop	eigendrop	NOUN
ajis02-1563	285	4	of	of	ADP
ajis02-1563	285	5	actainf	actainf	ADJ
ajis02-1563	285	6	graph	graph	NOUN
ajis02-1563	285	7	australasian	australasian	ADJ
ajis02-1563	285	8	journal	journal	NOUN
ajis02-1563	285	9	of	of	ADP
ajis02-1563	285	10	information	information	NOUN
ajis02-1563	285	11	systems	system	NOUN
ajis02-1563	285	12	ahmad	ahmad	PROPN
ajis02-1563	285	13	,	,	PUNCT
ajis02-1563	285	14	traiq	traiq	NOUN
ajis02-1563	285	15	,	,	PUNCT
ajis02-1563	285	16	shabbir	shabbir	PROPN
ajis02-1563	285	17	&	&	CCONJ
ajis02-1563	285	18	khan	khan	PROPN
ajis02-1563	285	19	2017	2017	NUM
ajis02-1563	285	20	,	,	PUNCT
ajis02-1563	285	21	vol	vol	NOUN
ajis02-1563	285	22	21	21	NUM
ajis02-1563	285	23	,	,	PUNCT
ajis02-1563	285	24	selected	select	VERB
ajis02-1563	285	25	papers	paper	NOUN
ajis02-1563	285	26	from	from	ADP
ajis02-1563	285	27	ausdm	ausdm	NOUN
ajis02-1563	285	28	spectral	spectral	ADJ
ajis02-1563	285	29	methods	method	NOUN
ajis02-1563	285	30	for	for	ADP
ajis02-1563	285	31	immunization	immunization	NOUN
ajis02-1563	285	32	of	of	ADP
ajis02-1563	285	33	large	large	ADJ
ajis02-1563	285	34	networks	network	NOUN
ajis02-1563	285	35	13	13	NUM
ajis02-1563	285	36	figure	figure	NOUN
ajis02-1563	285	37	2	2	NUM
ajis02-1563	285	38	eigendrop	eigendrop	NOUN
ajis02-1563	285	39	of	of	ADP
ajis02-1563	285	40	aicommunication	aicommunication	NOUN
ajis02-1563	285	41	graph	graph	NOUN
ajis02-1563	285	42	figure	figure	NOUN
ajis02-1563	285	43	3	3	NUM
ajis02-1563	285	44	eigendrop	eigendrop	NOUN
ajis02-1563	285	45	of	of	ADP
ajis02-1563	285	46	apjor	apjor	ADJ
ajis02-1563	285	47	graph	graph	NOUN
ajis02-1563	285	48	figure	figure	NOUN
ajis02-1563	285	49	4	4	NUM
ajis02-1563	285	50	eigendrop	eigendrop	NOUN
ajis02-1563	285	51	of	of	ADP
ajis02-1563	285	52	computer	computer	NOUN
ajis02-1563	285	53	in	in	ADP
ajis02-1563	285	54	industry	industry	NOUN
ajis02-1563	285	55	graph	graph	NOUN
ajis02-1563	285	56	australasian	australasian	ADJ
ajis02-1563	285	57	journal	journal	NOUN
ajis02-1563	285	58	of	of	ADP
ajis02-1563	285	59	information	information	NOUN
ajis02-1563	285	60	systems	system	NOUN
ajis02-1563	285	61	ahmad	ahmad	PROPN
ajis02-1563	285	62	,	,	PUNCT
ajis02-1563	285	63	traiq	traiq	NOUN
ajis02-1563	285	64	,	,	PUNCT
ajis02-1563	285	65	shabbir	shabbir	PROPN
ajis02-1563	285	66	&	&	CCONJ
ajis02-1563	285	67	khan	khan	PROPN
ajis02-1563	285	68	2017	2017	NUM
ajis02-1563	285	69	,	,	PUNCT
ajis02-1563	285	70	vol	vol	NOUN
ajis02-1563	285	71	21	21	NUM
ajis02-1563	285	72	,	,	PUNCT
ajis02-1563	285	73	selected	select	VERB
ajis02-1563	285	74	papers	paper	NOUN
ajis02-1563	285	75	from	from	ADP
ajis02-1563	285	76	ausdm	ausdm	NOUN
ajis02-1563	285	77	spectral	spectral	ADJ
ajis02-1563	285	78	methods	method	NOUN
ajis02-1563	285	79	for	for	ADP
ajis02-1563	285	80	immunization	immunization	NOUN
ajis02-1563	285	81	of	of	ADP
ajis02-1563	285	82	large	large	ADJ
ajis02-1563	285	83	networks	network	NOUN
ajis02-1563	285	84	14	14	NUM
ajis02-1563	285	85	figure	figure	NOUN
ajis02-1563	285	86	5	5	NUM
ajis02-1563	285	87	eigendrop	eigendrop	NOUN
ajis02-1563	285	88	of	of	ADP
ajis02-1563	285	89	computing	computing	NOUN
ajis02-1563	285	90	and	and	CCONJ
ajis02-1563	285	91	informatics	informatics	PROPN
ajis02-1563	285	92	graph	graph	NOUN
ajis02-1563	285	93	figure	figure	NOUN
ajis02-1563	285	94	6	6	NUM
ajis02-1563	285	95	eigendrop	eigendrop	NOUN
ajis02-1563	285	96	of	of	ADP
ajis02-1563	285	97	ecological	ecological	ADJ
ajis02-1563	285	98	informatics	informatic	NOUN
ajis02-1563	285	99	graph	graph	NOUN
ajis02-1563	285	100	figure	figure	VERB
ajis02-1563	285	101	7	7	NUM
ajis02-1563	285	102	eigendrop	eigendrop	NOUN
ajis02-1563	285	103	of	of	ADP
ajis02-1563	285	104	ieee	ieee	NOUN
ajis02-1563	285	105	wireless	wireless	NOUN
ajis02-1563	285	106	graph	graph	NOUN
ajis02-1563	285	107	australasian	australasian	ADJ
ajis02-1563	285	108	journal	journal	NOUN
ajis02-1563	285	109	of	of	ADP
ajis02-1563	285	110	information	information	NOUN
ajis02-1563	285	111	systems	system	NOUN
ajis02-1563	285	112	ahmad	ahmad	PROPN
ajis02-1563	285	113	,	,	PUNCT
ajis02-1563	285	114	traiq	traiq	NOUN
ajis02-1563	285	115	,	,	PUNCT
ajis02-1563	285	116	shabbir	shabbir	PROPN
ajis02-1563	285	117	&	&	CCONJ
ajis02-1563	285	118	khan	khan	PROPN
ajis02-1563	285	119	2017	2017	NUM
ajis02-1563	285	120	,	,	PUNCT
ajis02-1563	285	121	vol	vol	NOUN
ajis02-1563	285	122	21	21	NUM
ajis02-1563	285	123	,	,	PUNCT
ajis02-1563	285	124	selected	select	VERB
ajis02-1563	285	125	papers	paper	NOUN
ajis02-1563	285	126	from	from	ADP
ajis02-1563	285	127	ausdm	ausdm	NOUN
ajis02-1563	285	128	spectral	spectral	ADJ
ajis02-1563	285	129	methods	method	NOUN
ajis02-1563	285	130	for	for	ADP
ajis02-1563	285	131	immunization	immunization	NOUN
ajis02-1563	285	132	of	of	ADP
ajis02-1563	285	133	large	large	ADJ
ajis02-1563	285	134	networks	network	NOUN
ajis02-1563	285	135	15	15	NUM
ajis02-1563	285	136	figure	figure	NOUN
ajis02-1563	285	137	8	8	NUM
ajis02-1563	285	138	eigendrop	eigendrop	NOUN
ajis02-1563	285	139	of	of	ADP
ajis02-1563	285	140	ijcia	ijcia	NOUN
ajis02-1563	285	141	graph	graph	NOUN
ajis02-1563	285	142	figure	figure	NOUN
ajis02-1563	285	143	9	9	NUM
ajis02-1563	285	144	eigendrop	eigendrop	NOUN
ajis02-1563	285	145	of	of	ADP
ajis02-1563	285	146	ijiem	ijiem	NOUN
ajis02-1563	285	147	graph	graph	NOUN
ajis02-1563	285	148	figure	figure	NOUN
ajis02-1563	285	149	10	10	NUM
ajis02-1563	285	150	eigendrop	eigendrop	NOUN
ajis02-1563	285	151	of	of	ADP
ajis02-1563	285	152	oregon	oregon	PROPN
ajis02-1563	285	153	graph	graph	NOUN
ajis02-1563	285	154	6	6	NUM
ajis02-1563	285	155	conclusion	conclusion	NOUN
ajis02-1563	285	156	in	in	ADP
ajis02-1563	285	157	this	this	DET
ajis02-1563	285	158	work	work	NOUN
ajis02-1563	285	159	,	,	PUNCT
ajis02-1563	285	160	we	we	PRON
ajis02-1563	285	161	explored	explore	VERB
ajis02-1563	285	162	some	some	DET
ajis02-1563	285	163	links	link	NOUN
ajis02-1563	285	164	between	between	ADP
ajis02-1563	285	165	established	establish	VERB
ajis02-1563	285	166	graph	graph	NOUN
ajis02-1563	285	167	vulnerability	vulnerability	NOUN
ajis02-1563	285	168	measure	measure	NOUN
ajis02-1563	285	169	and	and	CCONJ
ajis02-1563	285	170	other	other	ADJ
ajis02-1563	285	171	spectral	spectral	ADJ
ajis02-1563	285	172	properties	property	NOUN
ajis02-1563	285	173	of	of	ADP
ajis02-1563	285	174	even	even	ADJ
ajis02-1563	285	175	powers	power	NOUN
ajis02-1563	285	176	of	of	ADP
ajis02-1563	285	177	adjacency	adjacency	NOUN
ajis02-1563	285	178	matrix	matrix	NOUN
ajis02-1563	285	179	of	of	ADP
ajis02-1563	285	180	the	the	DET
ajis02-1563	285	181	graph	graph	NOUN
ajis02-1563	285	182	.	.	PUNCT
ajis02-1563	286	1	we	we	PRON
ajis02-1563	286	2	define	define	VERB
ajis02-1563	286	3	shield	shield	NOUN
ajis02-1563	286	4	value	value	NOUN
ajis02-1563	286	5	in	in	ADP
ajis02-1563	286	6	terms	term	NOUN
ajis02-1563	286	7	of	of	ADP
ajis02-1563	286	8	trace	trace	NOUN
ajis02-1563	286	9	of	of	ADP
ajis02-1563	286	10	the	the	DET
ajis02-1563	286	11	adjacency	adjacency	NOUN
ajis02-1563	286	12	matrix	matrix	NOUN
ajis02-1563	286	13	of	of	ADP
ajis02-1563	286	14	the	the	DET
ajis02-1563	286	15	graph	graph	NOUN
ajis02-1563	286	16	.	.	PUNCT
ajis02-1563	287	1	based	base	VERB
ajis02-1563	287	2	on	on	ADP
ajis02-1563	287	3	these	these	DET
ajis02-1563	287	4	insights	insight	NOUN
ajis02-1563	287	5	we	we	PRON
ajis02-1563	287	6	present	present	VERB
ajis02-1563	287	7	a	a	DET
ajis02-1563	287	8	greedy	greedy	ADJ
ajis02-1563	287	9	algorithm	algorithm	NOUN
ajis02-1563	287	10	that	that	PRON
ajis02-1563	287	11	iteratively	iteratively	ADV
ajis02-1563	287	12	selects	select	VERB
ajis02-1563	287	13	k	k	PROPN
ajis02-1563	287	14	nodes	nod	VERB
ajis02-1563	287	15	such	such	ADJ
ajis02-1563	287	16	that	that	SCONJ
ajis02-1563	287	17	the	the	DET
ajis02-1563	287	18	impact	impact	NOUN
ajis02-1563	287	19	of	of	ADP
ajis02-1563	287	20	each	each	DET
ajis02-1563	287	21	node	node	NOUN
ajis02-1563	287	22	is	be	AUX
ajis02-1563	287	23	maximum	maximum	ADJ
ajis02-1563	287	24	in	in	ADP
ajis02-1563	287	25	the	the	DET
ajis02-1563	287	26	graph	graph	NOUN
ajis02-1563	287	27	,	,	PUNCT
ajis02-1563	287	28	in	in	ADP
ajis02-1563	287	29	the	the	DET
ajis02-1563	287	30	respective	respective	ADJ
ajis02-1563	287	31	iteration	iteration	NOUN
ajis02-1563	287	32	,	,	PUNCT
ajis02-1563	287	33	and	and	CCONJ
ajis02-1563	287	34	thus	thus	ADV
ajis02-1563	287	35	we	we	PRON
ajis02-1563	287	36	maximally	maximally	ADV
ajis02-1563	287	37	reduce	reduce	VERB
ajis02-1563	287	38	the	the	DET
ajis02-1563	287	39	spread	spread	NOUN
ajis02-1563	287	40	of	of	ADP
ajis02-1563	287	41	a	a	DET
ajis02-1563	287	42	potential	potential	ADJ
ajis02-1563	287	43	infection	infection	NOUN
ajis02-1563	287	44	in	in	ADP
ajis02-1563	287	45	the	the	DET
ajis02-1563	287	46	graph	graph	NOUN
ajis02-1563	287	47	by	by	ADP
ajis02-1563	287	48	removing	remove	VERB
ajis02-1563	287	49	those	those	DET
ajis02-1563	287	50	vertices	vertex	NOUN
ajis02-1563	287	51	.	.	PUNCT
ajis02-1563	288	1	our	our	PRON
ajis02-1563	288	2	algorithm	algorithm	NOUN
ajis02-1563	288	3	is	be	AUX
ajis02-1563	288	4	scalable	scalable	ADJ
ajis02-1563	288	5	to	to	ADP
ajis02-1563	288	6	large	large	ADJ
ajis02-1563	288	7	graphs	graph	NOUN
ajis02-1563	288	8	since	since	SCONJ
ajis02-1563	288	9	it	it	PRON
ajis02-1563	288	10	has	have	AUX
ajis02-1563	288	11	linear	linear	ADJ
ajis02-1563	288	12	running	running	NOUN
ajis02-1563	288	13	time	time	NOUN
ajis02-1563	288	14	in	in	ADP
ajis02-1563	288	15	the	the	DET
ajis02-1563	288	16	size	size	NOUN
ajis02-1563	288	17	of	of	ADP
ajis02-1563	288	18	the	the	DET
ajis02-1563	288	19	graph	graph	NOUN
ajis02-1563	288	20	.	.	PUNCT
ajis02-1563	289	1	we	we	PRON
ajis02-1563	289	2	have	have	AUX
ajis02-1563	289	3	conducted	conduct	VERB
ajis02-1563	289	4	australasian	australasian	ADJ
ajis02-1563	289	5	journal	journal	NOUN
ajis02-1563	289	6	of	of	ADP
ajis02-1563	289	7	information	information	NOUN
ajis02-1563	289	8	systems	system	NOUN
ajis02-1563	289	9	ahmad	ahmad	PROPN
ajis02-1563	289	10	,	,	PUNCT
ajis02-1563	289	11	traiq	traiq	NOUN
ajis02-1563	289	12	,	,	PUNCT
ajis02-1563	289	13	shabbir	shabbir	PROPN
ajis02-1563	289	14	&	&	CCONJ
ajis02-1563	289	15	khan	khan	PROPN
ajis02-1563	289	16	2017	2017	NUM
ajis02-1563	289	17	,	,	PUNCT
ajis02-1563	289	18	vol	vol	NOUN
ajis02-1563	289	19	21	21	NUM
ajis02-1563	289	20	,	,	PUNCT
ajis02-1563	289	21	selected	select	VERB
ajis02-1563	289	22	papers	paper	NOUN
ajis02-1563	289	23	from	from	ADP
ajis02-1563	289	24	ausdm	ausdm	NOUN
ajis02-1563	289	25	spectral	spectral	ADJ
ajis02-1563	289	26	methods	method	NOUN
ajis02-1563	289	27	for	for	ADP
ajis02-1563	289	28	immunization	immunization	NOUN
ajis02-1563	289	29	of	of	ADP
ajis02-1563	289	30	large	large	ADJ
ajis02-1563	289	31	networks	network	NOUN
ajis02-1563	289	32	16	16	NUM
ajis02-1563	289	33	experiments	experiment	NOUN
ajis02-1563	289	34	on	on	ADP
ajis02-1563	289	35	different	different	ADJ
ajis02-1563	289	36	real	real	ADJ
ajis02-1563	289	37	world	world	NOUN
ajis02-1563	289	38	communication	communication	NOUN
ajis02-1563	289	39	graphs	graph	NOUN
ajis02-1563	289	40	to	to	PART
ajis02-1563	289	41	confirm	confirm	VERB
ajis02-1563	289	42	the	the	DET
ajis02-1563	289	43	accuracy	accuracy	NOUN
ajis02-1563	289	44	and	and	CCONJ
ajis02-1563	289	45	efficiency	efficiency	NOUN
ajis02-1563	289	46	of	of	ADP
ajis02-1563	289	47	our	our	PRON
ajis02-1563	289	48	algorithm	algorithm	NOUN
ajis02-1563	289	49	.	.	PUNCT
ajis02-1563	290	1	our	our	PRON
ajis02-1563	290	2	algorithm	algorithm	NOUN
ajis02-1563	290	3	outperforms	outperform	VERB
ajis02-1563	290	4	the	the	DET
ajis02-1563	290	5	state	state	NOUN
ajis02-1563	290	6	of	of	ADP
ajis02-1563	290	7	the	the	DET
ajis02-1563	290	8	art	art	NOUN
ajis02-1563	290	9	algorithm	algorithm	NOUN
ajis02-1563	290	10	in	in	ADP
ajis02-1563	290	11	performance	performance	NOUN
ajis02-1563	290	12	as	as	ADV
ajis02-1563	290	13	well	well	ADV
ajis02-1563	290	14	as	as	ADP
ajis02-1563	290	15	in	in	ADP
ajis02-1563	290	16	quality	quality	NOUN
ajis02-1563	290	17	.	.	PUNCT
ajis02-1563	291	1	the	the	DET
ajis02-1563	291	2	main	main	ADJ
ajis02-1563	291	3	limitation	limitation	NOUN
ajis02-1563	291	4	of	of	ADP
ajis02-1563	291	5	this	this	DET
ajis02-1563	291	6	work	work	NOUN
ajis02-1563	291	7	is	be	AUX
ajis02-1563	291	8	that	that	SCONJ
ajis02-1563	291	9	we	we	PRON
ajis02-1563	291	10	used	use	VERB
ajis02-1563	291	11	only	only	ADV
ajis02-1563	291	12	p=4	p=4	ADV
ajis02-1563	291	13	,	,	PUNCT
ajis02-1563	291	14	but	but	CCONJ
ajis02-1563	291	15	it	it	PRON
ajis02-1563	291	16	is	be	AUX
ajis02-1563	291	17	theoretically	theoretically	ADV
ajis02-1563	291	18	clear	clear	ADJ
ajis02-1563	291	19	that	that	SCONJ
ajis02-1563	291	20	using	use	VERB
ajis02-1563	291	21	large	large	ADJ
ajis02-1563	291	22	values	value	NOUN
ajis02-1563	291	23	of	of	ADP
ajis02-1563	291	24	p	p	NOUN
ajis02-1563	291	25	would	would	AUX
ajis02-1563	291	26	yield	yield	VERB
ajis02-1563	291	27	better	well	ADJ
ajis02-1563	291	28	immunization	immunization	NOUN
ajis02-1563	291	29	performance	performance	NOUN
ajis02-1563	291	30	.	.	PUNCT
ajis02-1563	292	1	for	for	ADP
ajis02-1563	292	2	the	the	DET
ajis02-1563	292	3	future	future	ADJ
ajis02-1563	292	4	work	work	NOUN
ajis02-1563	292	5	,	,	PUNCT
ajis02-1563	292	6	we	we	PRON
ajis02-1563	292	7	will	will	AUX
ajis02-1563	292	8	consider	consider	VERB
ajis02-1563	292	9	the	the	DET
ajis02-1563	292	10	large	large	ADJ
ajis02-1563	292	11	values	value	NOUN
ajis02-1563	292	12	of	of	ADP
ajis02-1563	292	13	the	the	DET
ajis02-1563	292	14	parameter	parameter	NOUN
ajis02-1563	292	15	p	p	NOUN
ajis02-1563	292	16	,	,	PUNCT
ajis02-1563	292	17	used	use	VERB
ajis02-1563	292	18	in	in	ADP
ajis02-1563	292	19	the	the	DET
ajis02-1563	292	20	definition	definition	NOUN
ajis02-1563	292	21	of	of	ADP
ajis02-1563	292	22	our	our	PRON
ajis02-1563	292	23	shield	shield	NOUN
ajis02-1563	292	24	value	value	NOUN
ajis02-1563	292	25	.	.	PUNCT
ajis02-1563	293	1	references	reference	NOUN
ajis02-1563	293	2	abbas	abbas	PROPN
ajis02-1563	293	3	,	,	PUNCT
ajis02-1563	293	4	s.	s.	PROPN
ajis02-1563	293	5	,	,	PUNCT
ajis02-1563	293	6	tariq	tariq	PROPN
ajis02-1563	293	7	,	,	PUNCT
ajis02-1563	293	8	j.	j.	PROPN
ajis02-1563	293	9	,	,	PUNCT
ajis02-1563	293	10	zaman	zaman	PROPN
ajis02-1563	293	11	,	,	PUNCT
ajis02-1563	293	12	a.	a.	PROPN
ajis02-1563	293	13	,	,	PUNCT
ajis02-1563	293	14	&	&	CCONJ
ajis02-1563	293	15	khan	khan	PROPN
ajis02-1563	293	16	,	,	PUNCT
ajis02-1563	293	17	i.	i.	PROPN
ajis02-1563	293	18	(	(	PUNCT
ajis02-1563	293	19	2017	2017	NUM
ajis02-1563	293	20	)	)	PUNCT
ajis02-1563	293	21	.	.	PUNCT
ajis02-1563	294	1	sampling	sample	VERB
ajis02-1563	294	2	based	base	VERB
ajis02-1563	294	3	efficient	efficient	ADJ
ajis02-1563	294	4	algorithm	algorithm	NOUN
ajis02-1563	294	5	to	to	PART
ajis02-1563	294	6	estimate	estimate	VERB
ajis02-1563	294	7	the	the	DET
ajis02-1563	294	8	spectral	spectral	ADJ
ajis02-1563	294	9	radius	radius	NOUN
ajis02-1563	294	10	of	of	ADP
ajis02-1563	294	11	large	large	ADJ
ajis02-1563	294	12	graphs	graph	NOUN
ajis02-1563	294	13	.	.	PUNCT
ajis02-1563	295	1	in	in	ADP
ajis02-1563	295	2	37th	37th	ADJ
ajis02-1563	295	3	ieee	ieee	NOUN
ajis02-1563	295	4	international	international	ADJ
ajis02-1563	295	5	conference	conference	NOUN
ajis02-1563	295	6	on	on	ADP
ajis02-1563	295	7	distributed	distribute	VERB
ajis02-1563	295	8	computing	computing	NOUN
ajis02-1563	295	9	systems	system	NOUN
ajis02-1563	295	10	workshops	workshop	NOUN
ajis02-1563	295	11	,	,	PUNCT
ajis02-1563	295	12	icdcs	icdc	VERB
ajis02-1563	295	13	workshops	workshop	NOUN
ajis02-1563	295	14	(	(	PUNCT
ajis02-1563	295	15	pp	pp	ADJ
ajis02-1563	295	16	.	.	PUNCT
ajis02-1563	295	17	175	175	NUM
ajis02-1563	295	18	-	-	SYM
ajis02-1563	295	19	180	180	NUM
ajis02-1563	295	20	)	)	PUNCT
ajis02-1563	295	21	.	.	PUNCT
ajis02-1563	296	1	ieee	ieee	PROPN
ajis02-1563	296	2	.	.	PUNCT
ajis02-1563	297	1	doi	doi	PROPN
ajis02-1563	297	2	:	:	PUNCT
ajis02-1563	297	3	10.1109	10.1109	NUM
ajis02-1563	297	4	/	/	SYM
ajis02-1563	297	5	icdcsw.2017.71	icdcsw.2017.71	NOUN
ajis02-1563	297	6	ahmad	ahmad	PROPN
ajis02-1563	297	7	,	,	PUNCT
ajis02-1563	297	8	m.	m.	NOUN
ajis02-1563	297	9	,	,	PUNCT
ajis02-1563	297	10	tariq	tariq	PROPN
ajis02-1563	297	11	,	,	PUNCT
ajis02-1563	297	12	j.	j.	PROPN
ajis02-1563	297	13	,	,	PUNCT
ajis02-1563	297	14	farhan	farhan	PROPN
ajis02-1563	297	15	,	,	PUNCT
ajis02-1563	297	16	m.	m.	NOUN
ajis02-1563	297	17	,	,	PUNCT
ajis02-1563	297	18	shabbir	shabbir	PROPN
ajis02-1563	297	19	,	,	PUNCT
ajis02-1563	297	20	m.	m.	NOUN
ajis02-1563	297	21	,	,	PUNCT
ajis02-1563	297	22	&	&	CCONJ
ajis02-1563	297	23	khan	khan	PROPN
ajis02-1563	297	24	,	,	PUNCT
ajis02-1563	297	25	i.	i.	PROPN
ajis02-1563	297	26	(	(	PUNCT
ajis02-1563	297	27	2016	2016	NUM
ajis02-1563	297	28	)	)	PUNCT
ajis02-1563	297	29	.	.	PUNCT
ajis02-1563	298	1	who	who	PRON
ajis02-1563	298	2	should	should	AUX
ajis02-1563	298	3	receive	receive	VERB
ajis02-1563	298	4	the	the	DET
ajis02-1563	298	5	vaccine	vaccine	NOUN
ajis02-1563	298	6	?	?	PUNCT
ajis02-1563	299	1	in	in	ADP
ajis02-1563	299	2	14th	14th	ADJ
ajis02-1563	299	3	australasian	australasian	ADJ
ajis02-1563	299	4	data	data	NOUN
ajis02-1563	299	5	mining	mining	NOUN
ajis02-1563	299	6	conference	conference	NOUN
ajis02-1563	299	7	,	,	PUNCT
ajis02-1563	299	8	australian	australian	ADJ
ajis02-1563	299	9	computer	computer	NOUN
ajis02-1563	299	10	society	society	NOUN
ajis02-1563	299	11	.	.	PUNCT
ajis02-1563	300	1	bienstock	bienstock	PROPN
ajis02-1563	300	2	,	,	PUNCT
ajis02-1563	300	3	d.	d.	PROPN
ajis02-1563	300	4	,	,	PUNCT
ajis02-1563	300	5	&	&	CCONJ
ajis02-1563	300	6	seymour	seymour	PROPN
ajis02-1563	300	7	,	,	PUNCT
ajis02-1563	300	8	p.	p.	NOUN
ajis02-1563	300	9	(	(	PUNCT
ajis02-1563	300	10	1991	1991	NUM
ajis02-1563	300	11	)	)	PUNCT
ajis02-1563	300	12	.	.	PUNCT
ajis02-1563	301	1	monotonicity	monotonicity	NOUN
ajis02-1563	301	2	in	in	ADP
ajis02-1563	301	3	graph	graph	NOUN
ajis02-1563	301	4	searching	search	VERB
ajis02-1563	301	5	.	.	PUNCT
ajis02-1563	302	1	journal	journal	NOUN
ajis02-1563	302	2	of	of	ADP
ajis02-1563	302	3	algorithms	algorithm	NOUN
ajis02-1563	302	4	,	,	PUNCT
ajis02-1563	302	5	12(2	12(2	NUM
ajis02-1563	302	6	)	)	PUNCT
ajis02-1563	302	7	,	,	PUNCT
ajis02-1563	302	8	239	239	NUM
ajis02-1563	302	9	-	-	SYM
ajis02-1563	302	10	245	245	NUM
ajis02-1563	302	11	.	.	PUNCT
ajis02-1563	303	1	doi	doi	NOUN
ajis02-1563	303	2	:	:	PUNCT
ajis02-1563	303	3	10.1016/01966774(91)90003	10.1016/01966774(91)90003	NUM
ajis02-1563	303	4	-	-	PROPN
ajis02-1563	303	5	h	h	NOUN
ajis02-1563	303	6	bondy	bondy	PROPN
ajis02-1563	303	7	,	,	PUNCT
ajis02-1563	303	8	j.	j.	PROPN
ajis02-1563	303	9	a.	a.	PROPN
ajis02-1563	303	10	,	,	PUNCT
ajis02-1563	303	11	&	&	CCONJ
ajis02-1563	303	12	murty	murty	PROPN
ajis02-1563	303	13	,	,	PUNCT
ajis02-1563	303	14	u.	u.	PROPN
ajis02-1563	303	15	s.	s.	PROPN
ajis02-1563	303	16	r.	r.	PROPN
ajis02-1563	303	17	(	(	PUNCT
ajis02-1563	303	18	1976	1976	NUM
ajis02-1563	303	19	)	)	PUNCT
ajis02-1563	303	20	.	.	PUNCT
ajis02-1563	304	1	graph	graph	NOUN
ajis02-1563	304	2	theory	theory	NOUN
ajis02-1563	304	3	with	with	ADP
ajis02-1563	304	4	applications	application	NOUN
ajis02-1563	304	5	(	(	PUNCT
ajis02-1563	304	6	vol	vol	NOUN
ajis02-1563	304	7	.	.	NOUN
ajis02-1563	304	8	290	290	NUM
ajis02-1563	304	9	)	)	PUNCT
ajis02-1563	304	10	.	.	PUNCT
ajis02-1563	305	1	london	london	PROPN
ajis02-1563	305	2	:	:	PUNCT
ajis02-1563	305	3	macmillan	macmillan	PROPN
ajis02-1563	305	4	.	.	PUNCT
ajis02-1563	305	5	briesemeister	briesemeister	PROPN
ajis02-1563	305	6	,	,	PUNCT
ajis02-1563	305	7	l.	l.	PROPN
ajis02-1563	305	8	,	,	PUNCT
ajis02-1563	305	9	lincoln	lincoln	PROPN
ajis02-1563	305	10	,	,	PUNCT
ajis02-1563	305	11	p.	p.	PROPN
ajis02-1563	305	12	,	,	PUNCT
ajis02-1563	305	13	&	&	CCONJ
ajis02-1563	305	14	porras	porras	PROPN
ajis02-1563	305	15	,	,	PUNCT
ajis02-1563	305	16	p.	p.	NOUN
ajis02-1563	305	17	(	(	PUNCT
ajis02-1563	305	18	2003	2003	NUM
ajis02-1563	305	19	)	)	PUNCT
ajis02-1563	305	20	.	.	PUNCT
ajis02-1563	306	1	epidemic	epidemic	NOUN
ajis02-1563	306	2	profiles	profile	NOUN
ajis02-1563	306	3	and	and	CCONJ
ajis02-1563	306	4	defense	defense	NOUN
ajis02-1563	306	5	of	of	ADP
ajis02-1563	306	6	scale	scale	NOUN
ajis02-1563	306	7	-	-	PUNCT
ajis02-1563	306	8	free	free	ADJ
ajis02-1563	306	9	networks	network	NOUN
ajis02-1563	306	10	.	.	PUNCT
ajis02-1563	307	1	in	in	ADP
ajis02-1563	307	2	proceedings	proceeding	NOUN
ajis02-1563	307	3	of	of	ADP
ajis02-1563	307	4	the	the	DET
ajis02-1563	307	5	2003	2003	NUM
ajis02-1563	307	6	acm	acm	NOUN
ajis02-1563	307	7	workshop	workshop	NOUN
ajis02-1563	307	8	on	on	ADP
ajis02-1563	307	9	rapid	rapid	ADJ
ajis02-1563	307	10	malcode	malcode	NOUN
ajis02-1563	307	11	,	,	PUNCT
ajis02-1563	307	12	worm	worm	NOUN
ajis02-1563	307	13	,	,	PUNCT
ajis02-1563	307	14	(	(	PUNCT
ajis02-1563	307	15	pp	pp	ADV
ajis02-1563	307	16	.	.	PUNCT
ajis02-1563	308	1	67	67	NUM
ajis02-1563	308	2	-	-	SYM
ajis02-1563	308	3	75	75	NUM
ajis02-1563	308	4	)	)	PUNCT
ajis02-1563	308	5	.	.	PUNCT
ajis02-1563	309	1	acm	acm	PROPN
ajis02-1563	309	2	.	.	PUNCT
ajis02-1563	310	1	doi	doi	PROPN
ajis02-1563	310	2	:	:	PUNCT
ajis02-1563	310	3	10.1145/948187.948200	10.1145/948187.948200	NUM
ajis02-1563	310	4	chakrabarti	chakrabarti	NOUN
ajis02-1563	310	5	,	,	PUNCT
ajis02-1563	310	6	d.	d.	PROPN
ajis02-1563	310	7	,	,	PUNCT
ajis02-1563	310	8	wang	wang	PROPN
ajis02-1563	310	9	,	,	PUNCT
ajis02-1563	310	10	y.	y.	PROPN
ajis02-1563	310	11	,	,	PUNCT
ajis02-1563	310	12	wang	wang	PROPN
ajis02-1563	310	13	,	,	PUNCT
ajis02-1563	310	14	c.	c.	PROPN
ajis02-1563	310	15	,	,	PUNCT
ajis02-1563	310	16	leskovec	leskovec	PROPN
ajis02-1563	310	17	,	,	PUNCT
ajis02-1563	310	18	j.	j.	PROPN
ajis02-1563	310	19	,	,	PUNCT
ajis02-1563	310	20	&	&	CCONJ
ajis02-1563	310	21	faloutsos	faloutsos	PROPN
ajis02-1563	310	22	,	,	PUNCT
ajis02-1563	310	23	c.	c.	NOUN
ajis02-1563	310	24	(	(	PUNCT
ajis02-1563	310	25	2008	2008	NUM
ajis02-1563	310	26	)	)	PUNCT
ajis02-1563	310	27	.	.	PUNCT
ajis02-1563	311	1	epidemic	epidemic	NOUN
ajis02-1563	311	2	thresholds	threshold	NOUN
ajis02-1563	311	3	in	in	ADP
ajis02-1563	311	4	real	real	ADJ
ajis02-1563	311	5	networks	network	NOUN
ajis02-1563	311	6	.	.	PUNCT
ajis02-1563	312	1	acm	acm	NOUN
ajis02-1563	312	2	transactions	transaction	NOUN
ajis02-1563	312	3	on	on	ADP
ajis02-1563	312	4	information	information	NOUN
ajis02-1563	312	5	and	and	CCONJ
ajis02-1563	312	6	system	system	NOUN
ajis02-1563	312	7	security	security	NOUN
ajis02-1563	312	8	(	(	PUNCT
ajis02-1563	312	9	tissec	tissec	PROPN
ajis02-1563	312	10	)	)	PUNCT
ajis02-1563	312	11	,	,	PUNCT
ajis02-1563	312	12	10(4	10(4	NUM
ajis02-1563	312	13	)	)	PUNCT
ajis02-1563	312	14	,	,	PUNCT
ajis02-1563	312	15	.	.	PUNCT
ajis02-1563	313	1	doi	doi	NOUN
ajis02-1563	313	2	:	:	PUNCT
ajis02-1563	313	3	10.1145/1284680.1284681	10.1145/1284680.1284681	NUM
ajis02-1563	313	4	chen	chen	PROPN
ajis02-1563	313	5	,	,	PUNCT
ajis02-1563	313	6	c.	c.	PROPN
ajis02-1563	313	7	,	,	PUNCT
ajis02-1563	313	8	tong	tong	PROPN
ajis02-1563	313	9	,	,	PUNCT
ajis02-1563	313	10	h.	h.	PROPN
ajis02-1563	313	11	,	,	PUNCT
ajis02-1563	313	12	prakash	prakash	PROPN
ajis02-1563	313	13	,	,	PUNCT
ajis02-1563	313	14	b.	b.	PROPN
ajis02-1563	313	15	a.	a.	PROPN
ajis02-1563	313	16	,	,	PUNCT
ajis02-1563	313	17	tsourakakis	tsourakaki	NOUN
ajis02-1563	313	18	,	,	PUNCT
ajis02-1563	313	19	c.	c.	PROPN
ajis02-1563	313	20	e.	e.	PROPN
ajis02-1563	313	21	,	,	PUNCT
ajis02-1563	313	22	eliassi	eliassi	PROPN
ajis02-1563	313	23	-	-	PUNCT
ajis02-1563	313	24	rad	rad	PROPN
ajis02-1563	313	25	,	,	PUNCT
ajis02-1563	313	26	t.	t.	PROPN
ajis02-1563	313	27	,	,	PUNCT
ajis02-1563	313	28	faloutsos	faloutsos	PROPN
ajis02-1563	313	29	,	,	PUNCT
ajis02-1563	313	30	c.	c.	PROPN
ajis02-1563	313	31	,	,	PUNCT
ajis02-1563	313	32	&	&	CCONJ
ajis02-1563	313	33	chau	chau	PROPN
ajis02-1563	313	34	,	,	PUNCT
ajis02-1563	313	35	d.	d.	PROPN
ajis02-1563	313	36	h.	h.	PROPN
ajis02-1563	313	37	(	(	PUNCT
ajis02-1563	313	38	2016	2016	NUM
ajis02-1563	313	39	)	)	PUNCT
ajis02-1563	313	40	.	.	PUNCT
ajis02-1563	314	1	node	node	ADJ
ajis02-1563	314	2	immunization	immunization	NOUN
ajis02-1563	314	3	on	on	ADP
ajis02-1563	314	4	large	large	ADJ
ajis02-1563	314	5	graphs	graph	NOUN
ajis02-1563	314	6	:	:	PUNCT
ajis02-1563	314	7	theory	theory	NOUN
ajis02-1563	314	8	and	and	CCONJ
ajis02-1563	314	9	algorithms	algorithm	NOUN
ajis02-1563	314	10	.	.	PUNCT
ajis02-1563	315	1	ieee	ieee	NOUN
ajis02-1563	315	2	transactions	transaction	NOUN
ajis02-1563	315	3	on	on	ADP
ajis02-1563	315	4	knowledge	knowledge	NOUN
ajis02-1563	315	5	and	and	CCONJ
ajis02-1563	315	6	data	datum	NOUN
ajis02-1563	315	7	engineering	engineering	NOUN
ajis02-1563	315	8	,	,	PUNCT
ajis02-1563	315	9	28(1	28(1	NOUN
ajis02-1563	315	10	)	)	PUNCT
ajis02-1563	315	11	,	,	PUNCT
ajis02-1563	315	12	113	113	NUM
ajis02-1563	315	13	-	-	SYM
ajis02-1563	315	14	126	126	NUM
ajis02-1563	315	15	.	.	PUNCT
ajis02-1563	316	1	doi	doi	NOUN
ajis02-1563	316	2	:	:	PUNCT
ajis02-1563	316	3	10.1109	10.1109	NUM
ajis02-1563	316	4	/	/	SYM
ajis02-1563	316	5	tkde.2015.2465378	tkde.2015.2465378	NUM
ajis02-1563	316	6	chung	chung	PROPN
ajis02-1563	316	7	,	,	PUNCT
ajis02-1563	316	8	f.	f.	PROPN
ajis02-1563	316	9	r.	r.	PROPN
ajis02-1563	316	10	(	(	PUNCT
ajis02-1563	316	11	1997	1997	NUM
ajis02-1563	316	12	)	)	PUNCT
ajis02-1563	316	13	.	.	PUNCT
ajis02-1563	317	1	spectral	spectral	ADJ
ajis02-1563	317	2	graph	graph	NOUN
ajis02-1563	317	3	theory	theory	NOUN
ajis02-1563	317	4	(	(	PUNCT
ajis02-1563	317	5	no	no	INTJ
ajis02-1563	317	6	.	.	NOUN
ajis02-1563	317	7	92	92	NUM
ajis02-1563	317	8	)	)	PUNCT
ajis02-1563	317	9	.	.	PUNCT
ajis02-1563	318	1	american	american	PROPN
ajis02-1563	318	2	mathematical	mathematical	PROPN
ajis02-1563	318	3	soc	soc	PROPN
ajis02-1563	318	4	.	.	PUNCT
ajis02-1563	319	1	cormen	corman	NOUN
ajis02-1563	319	2	,	,	PUNCT
ajis02-1563	319	3	t.	t.	PROPN
ajis02-1563	319	4	h.	h.	PROPN
ajis02-1563	319	5	,	,	PUNCT
ajis02-1563	319	6	stein	stein	PROPN
ajis02-1563	319	7	,	,	PUNCT
ajis02-1563	319	8	c.	c.	PROPN
ajis02-1563	319	9	,	,	PUNCT
ajis02-1563	319	10	rivest	riv	ADJ
ajis02-1563	319	11	,	,	PUNCT
ajis02-1563	319	12	r.	r.	PROPN
ajis02-1563	319	13	l.	l.	PROPN
ajis02-1563	319	14	,	,	PUNCT
ajis02-1563	319	15	&	&	CCONJ
ajis02-1563	319	16	leiserson	leiserson	PROPN
ajis02-1563	319	17	,	,	PUNCT
ajis02-1563	319	18	c.	c.	PROPN
ajis02-1563	319	19	e.	e.	PROPN
ajis02-1563	319	20	(	(	PUNCT
ajis02-1563	319	21	2001	2001	NUM
ajis02-1563	319	22	)	)	PUNCT
ajis02-1563	319	23	.	.	PUNCT
ajis02-1563	320	1	introduction	introduction	NOUN
ajis02-1563	320	2	to	to	ADP
ajis02-1563	320	3	algorithms	algorithms	PROPN
ajis02-1563	320	4	(	(	PUNCT
ajis02-1563	320	5	2nd	2nd	ADJ
ajis02-1563	320	6	ed	ed	NOUN
ajis02-1563	320	7	.	.	PUNCT
ajis02-1563	320	8	)	)	PUNCT
ajis02-1563	320	9	.	.	PUNCT
ajis02-1563	321	1	mcgraw	mcgraw	PROPN
ajis02-1563	321	2	-	-	PUNCT
ajis02-1563	321	3	hill	hill	NOUN
ajis02-1563	321	4	higher	high	ADJ
ajis02-1563	321	5	education	education	NOUN
ajis02-1563	321	6	.	.	PUNCT
ajis02-1563	322	1	daadaa	daadaa	NOUN
ajis02-1563	322	2	,	,	PUNCT
ajis02-1563	322	3	y.	y.	PROPN
ajis02-1563	322	4	,	,	PUNCT
ajis02-1563	322	5	jamshed	jamshe	VERB
ajis02-1563	322	6	,	,	PUNCT
ajis02-1563	322	7	a.	a.	PROPN
ajis02-1563	322	8	,	,	PUNCT
ajis02-1563	322	9	&	&	CCONJ
ajis02-1563	322	10	shabbir	shabbir	PROPN
ajis02-1563	322	11	,	,	PUNCT
ajis02-1563	322	12	m.	m.	NOUN
ajis02-1563	322	13	(	(	PUNCT
ajis02-1563	322	14	2016	2016	NUM
ajis02-1563	322	15	)	)	PUNCT
ajis02-1563	322	16	.	.	PUNCT
ajis02-1563	323	1	network	network	NOUN
ajis02-1563	323	2	decontamination	decontamination	NOUN
ajis02-1563	323	3	with	with	ADP
ajis02-1563	323	4	a	a	DET
ajis02-1563	323	5	single	single	ADJ
ajis02-1563	323	6	agent	agent	NOUN
ajis02-1563	323	7	.	.	PUNCT
ajis02-1563	324	1	graphs	graph	NOUN
ajis02-1563	324	2	and	and	CCONJ
ajis02-1563	324	3	combinatorics	combinatoric	NOUN
ajis02-1563	324	4	,	,	PUNCT
ajis02-1563	324	5	32(2	32(2	NUM
ajis02-1563	324	6	)	)	PUNCT
ajis02-1563	324	7	,	,	PUNCT
ajis02-1563	324	8	559	559	NUM
ajis02-1563	324	9	-	-	SYM
ajis02-1563	324	10	581	581	NUM
ajis02-1563	324	11	.	.	PUNCT
ajis02-1563	325	1	doi	doi	NOUN
ajis02-1563	325	2	:	:	PUNCT
ajis02-1563	325	3	10.1007	10.1007	NUM
ajis02-1563	325	4	/	/	SYM
ajis02-1563	325	5	s00373015	s00373015	NUM
ajis02-1563	325	6	-	-	PUNCT
ajis02-1563	325	7	1579	1579	NUM
ajis02-1563	325	8	-	-	SYM
ajis02-1563	325	9	5	5	NUM
ajis02-1563	325	10	erdös	erdös	ADJ
ajis02-1563	325	11	,	,	PUNCT
ajis02-1563	325	12	d.	d.	PROPN
ajis02-1563	325	13	,	,	PUNCT
ajis02-1563	325	14	ishakian	ishakian	ADJ
ajis02-1563	325	15	,	,	PUNCT
ajis02-1563	325	16	v.	v.	PROPN
ajis02-1563	325	17	,	,	PUNCT
ajis02-1563	325	18	lapets	lapet	NOUN
ajis02-1563	325	19	,	,	PUNCT
ajis02-1563	325	20	a.	a.	NOUN
ajis02-1563	325	21	,	,	PUNCT
ajis02-1563	325	22	terzi	terzi	NOUN
ajis02-1563	325	23	,	,	PUNCT
ajis02-1563	325	24	e.	e.	PROPN
ajis02-1563	325	25	,	,	PUNCT
ajis02-1563	325	26	&	&	CCONJ
ajis02-1563	325	27	bestavros	bestavros	PROPN
ajis02-1563	325	28	,	,	PUNCT
ajis02-1563	325	29	a.	a.	NOUN
ajis02-1563	325	30	(	(	PUNCT
ajis02-1563	325	31	2012	2012	NUM
ajis02-1563	325	32	)	)	PUNCT
ajis02-1563	325	33	.	.	PUNCT
ajis02-1563	326	1	the	the	DET
ajis02-1563	326	2	filter	filter	NOUN
ajis02-1563	326	3	-	-	PUNCT
ajis02-1563	326	4	placement	placement	NOUN
ajis02-1563	326	5	problem	problem	NOUN
ajis02-1563	326	6	and	and	CCONJ
ajis02-1563	326	7	its	its	PRON
ajis02-1563	326	8	application	application	NOUN
ajis02-1563	326	9	to	to	ADP
ajis02-1563	326	10	minimizing	minimize	VERB
ajis02-1563	326	11	information	information	NOUN
ajis02-1563	326	12	multiplicity	multiplicity	NOUN
ajis02-1563	326	13	.	.	PUNCT
ajis02-1563	327	1	proceedings	proceeding	NOUN
ajis02-1563	327	2	of	of	ADP
ajis02-1563	327	3	the	the	DET
ajis02-1563	327	4	vldb	vldb	NOUN
ajis02-1563	327	5	endowment	endowment	NOUN
ajis02-1563	327	6	,	,	PUNCT
ajis02-1563	327	7	5(5	5(5	NUM
ajis02-1563	327	8	)	)	PUNCT
ajis02-1563	327	9	,	,	PUNCT
ajis02-1563	327	10	418	418	NUM
ajis02-1563	327	11	-	-	SYM
ajis02-1563	327	12	429	429	NUM
ajis02-1563	327	13	.	.	PUNCT
ajis02-1563	327	14	flocchini	flocchini	NOUN
ajis02-1563	327	15	,	,	PUNCT
ajis02-1563	327	16	p.	p.	PROPN
ajis02-1563	327	17	,	,	PUNCT
ajis02-1563	327	18	huang	huang	PROPN
ajis02-1563	327	19	,	,	PUNCT
ajis02-1563	327	20	m.	m.	PROPN
ajis02-1563	327	21	j.	j.	PROPN
ajis02-1563	327	22	,	,	PUNCT
ajis02-1563	327	23	&	&	CCONJ
ajis02-1563	327	24	luccio	luccio	PROPN
ajis02-1563	327	25	,	,	PUNCT
ajis02-1563	327	26	f.	f.	PROPN
ajis02-1563	327	27	l.	l.	PROPN
ajis02-1563	327	28	(	(	PUNCT
ajis02-1563	327	29	2007	2007	NUM
ajis02-1563	327	30	)	)	PUNCT
ajis02-1563	327	31	.	.	PUNCT
ajis02-1563	328	1	decontaminating	decontaminate	VERB
ajis02-1563	328	2	chordal	chordal	ADJ
ajis02-1563	328	3	rings	ring	NOUN
ajis02-1563	328	4	and	and	CCONJ
ajis02-1563	328	5	tori	tori	NOUN
ajis02-1563	328	6	using	use	VERB
ajis02-1563	328	7	mobile	mobile	ADJ
ajis02-1563	328	8	agents	agent	NOUN
ajis02-1563	328	9	.	.	PUNCT
ajis02-1563	329	1	international	international	ADJ
ajis02-1563	329	2	journal	journal	NOUN
ajis02-1563	329	3	of	of	ADP
ajis02-1563	329	4	foundations	foundation	NOUN
ajis02-1563	329	5	of	of	ADP
ajis02-1563	329	6	computer	computer	NOUN
ajis02-1563	329	7	science	science	NOUN
ajis02-1563	329	8	,	,	PUNCT
ajis02-1563	329	9	18(03	18(03	NUM
ajis02-1563	329	10	)	)	PUNCT
ajis02-1563	329	11	,	,	PUNCT
ajis02-1563	329	12	547	547	NUM
ajis02-1563	329	13	-	-	SYM
ajis02-1563	329	14	563	563	NUM
ajis02-1563	329	15	.	.	PUNCT
ajis02-1563	330	1	doi	doi	NOUN
ajis02-1563	330	2	:	:	PUNCT
ajis02-1563	330	3	10.1142	10.1142	NUM
ajis02-1563	330	4	/	/	SYM
ajis02-1563	330	5	s0129054107004838	s0129054107004838	NOUN
ajis02-1563	330	6	flocchini	flocchini	ADJ
ajis02-1563	330	7	,	,	PUNCT
ajis02-1563	330	8	p.	p.	PROPN
ajis02-1563	330	9	,	,	PUNCT
ajis02-1563	330	10	huang	huang	PROPN
ajis02-1563	330	11	,	,	PUNCT
ajis02-1563	330	12	m.	m.	PROPN
ajis02-1563	330	13	j.	j.	PROPN
ajis02-1563	330	14	,	,	PUNCT
ajis02-1563	330	15	&	&	CCONJ
ajis02-1563	330	16	luccio	luccio	PROPN
ajis02-1563	330	17	,	,	PUNCT
ajis02-1563	330	18	f.	f.	PROPN
ajis02-1563	330	19	l.	l.	PROPN
ajis02-1563	330	20	(	(	PUNCT
ajis02-1563	330	21	2008	2008	NUM
ajis02-1563	330	22	)	)	PUNCT
ajis02-1563	330	23	.	.	PUNCT
ajis02-1563	331	1	decontamination	decontamination	NOUN
ajis02-1563	331	2	of	of	ADP
ajis02-1563	331	3	hypercubes	hypercube	NOUN
ajis02-1563	331	4	by	by	ADP
ajis02-1563	331	5	mobile	mobile	ADJ
ajis02-1563	331	6	agents	agent	NOUN
ajis02-1563	331	7	.	.	PUNCT
ajis02-1563	332	1	networks	network	NOUN
ajis02-1563	332	2	,	,	PUNCT
ajis02-1563	332	3	52(3	52(3	NOUN
ajis02-1563	332	4	)	)	PUNCT
ajis02-1563	332	5	,	,	PUNCT
ajis02-1563	332	6	167	167	NUM
ajis02-1563	332	7	-	-	SYM
ajis02-1563	332	8	178	178	NUM
ajis02-1563	332	9	.	.	PUNCT
ajis02-1563	333	1	doi	doi	NOUN
ajis02-1563	333	2	:	:	PUNCT
ajis02-1563	333	3	10.1002	10.1002	NUM
ajis02-1563	333	4	/	/	SYM
ajis02-1563	333	5	net.20240	net.20240	NUM
ajis02-1563	333	6	fraigniaud	fraigniaud	NOUN
ajis02-1563	333	7	,	,	PUNCT
ajis02-1563	333	8	p.	p.	NOUN
ajis02-1563	333	9	,	,	PUNCT
ajis02-1563	333	10	&	&	CCONJ
ajis02-1563	333	11	nisse	nisse	PROPN
ajis02-1563	333	12	,	,	PUNCT
ajis02-1563	333	13	n.	n.	PROPN
ajis02-1563	333	14	(	(	PUNCT
ajis02-1563	333	15	2008	2008	NUM
ajis02-1563	333	16	)	)	PUNCT
ajis02-1563	333	17	.	.	PUNCT
ajis02-1563	334	1	monotony	monotony	NOUN
ajis02-1563	334	2	properties	property	NOUN
ajis02-1563	334	3	of	of	ADP
ajis02-1563	334	4	connected	connected	ADJ
ajis02-1563	334	5	visible	visible	ADJ
ajis02-1563	334	6	graph	graph	NOUN
ajis02-1563	334	7	searching	searching	NOUN
ajis02-1563	334	8	.	.	PUNCT
ajis02-1563	335	1	information	information	NOUN
ajis02-1563	335	2	and	and	CCONJ
ajis02-1563	335	3	computation	computation	NOUN
ajis02-1563	335	4	,	,	PUNCT
ajis02-1563	335	5	206(12	206(12	NUM
ajis02-1563	335	6	)	)	PUNCT
ajis02-1563	335	7	,	,	PUNCT
ajis02-1563	335	8	1383	1383	NUM
ajis02-1563	335	9	-	-	SYM
ajis02-1563	335	10	1393	1393	NUM
ajis02-1563	335	11	.	.	PUNCT
ajis02-1563	336	1	doi	doi	NOUN
ajis02-1563	336	2	:	:	PUNCT
ajis02-1563	336	3	10.1016	10.1016	NUM
ajis02-1563	336	4	/	/	SYM
ajis02-1563	336	5	j.ic.2008.09.002	j.ic.2008.09.002	PROPN
ajis02-1563	336	6	ganesh	ganesh	PROPN
ajis02-1563	336	7	,	,	PUNCT
ajis02-1563	336	8	a.	a.	PROPN
ajis02-1563	336	9	,	,	PUNCT
ajis02-1563	336	10	massoulié	massoulié	PROPN
ajis02-1563	336	11	,	,	PUNCT
ajis02-1563	336	12	l.	l.	PROPN
ajis02-1563	336	13	,	,	PUNCT
ajis02-1563	336	14	&	&	CCONJ
ajis02-1563	336	15	towsley	towsley	PROPN
ajis02-1563	336	16	,	,	PUNCT
ajis02-1563	336	17	d.	d.	PROPN
ajis02-1563	336	18	(	(	PUNCT
ajis02-1563	336	19	2005	2005	NUM
ajis02-1563	336	20	)	)	PUNCT
ajis02-1563	336	21	.	.	PUNCT
ajis02-1563	337	1	the	the	DET
ajis02-1563	337	2	effect	effect	NOUN
ajis02-1563	337	3	of	of	ADP
ajis02-1563	337	4	network	network	NOUN
ajis02-1563	337	5	topology	topology	NOUN
ajis02-1563	337	6	on	on	ADP
ajis02-1563	337	7	the	the	DET
ajis02-1563	337	8	spread	spread	NOUN
ajis02-1563	337	9	of	of	ADP
ajis02-1563	337	10	epidemics	epidemic	NOUN
ajis02-1563	337	11	.	.	PUNCT
ajis02-1563	338	1	in	in	ADP
ajis02-1563	338	2	infocom	infocom	PROPN
ajis02-1563	338	3	2005	2005	NUM
ajis02-1563	338	4	.	.	PUNCT
ajis02-1563	339	1	24th	24th	ADJ
ajis02-1563	339	2	annual	annual	ADJ
ajis02-1563	339	3	joint	joint	ADJ
ajis02-1563	339	4	conference	conference	NOUN
ajis02-1563	339	5	of	of	ADP
ajis02-1563	339	6	the	the	DET
ajis02-1563	339	7	ieee	ieee	NOUN
ajis02-1563	339	8	computer	computer	NOUN
ajis02-1563	339	9	and	and	CCONJ
ajis02-1563	339	10	communications	communication	NOUN
ajis02-1563	339	11	societies	society	NOUN
ajis02-1563	339	12	.	.	PUNCT
ajis02-1563	340	1	proceedings	proceeding	NOUN
ajis02-1563	340	2	ieee	ieee	NOUN
ajis02-1563	340	3	(	(	PUNCT
ajis02-1563	340	4	vol	vol	NOUN
ajis02-1563	340	5	.	.	PROPN
ajis02-1563	340	6	2	2	NUM
ajis02-1563	340	7	,	,	PUNCT
ajis02-1563	340	8	pp	pp	ADJ
ajis02-1563	340	9	.	.	PUNCT
ajis02-1563	341	1	1455	1455	NUM
ajis02-1563	341	2	-	-	SYM
ajis02-1563	341	3	1466	1466	NUM
ajis02-1563	341	4	)	)	PUNCT
ajis02-1563	341	5	.	.	PUNCT
ajis02-1563	342	1	ieee	ieee	PROPN
ajis02-1563	342	2	.	.	PUNCT
ajis02-1563	343	1	doi	doi	PROPN
ajis02-1563	343	2	:	:	PUNCT
ajis02-1563	343	3	10.1109	10.1109	NUM
ajis02-1563	343	4	/	/	SYM
ajis02-1563	343	5	infcom.2005.1498374	infcom.2005.1498374	ADJ
ajis02-1563	343	6	australasian	australasian	ADJ
ajis02-1563	343	7	journal	journal	NOUN
ajis02-1563	343	8	of	of	ADP
ajis02-1563	343	9	information	information	NOUN
ajis02-1563	343	10	systems	system	NOUN
ajis02-1563	343	11	ahmad	ahmad	PROPN
ajis02-1563	343	12	,	,	PUNCT
ajis02-1563	343	13	traiq	traiq	NOUN
ajis02-1563	343	14	,	,	PUNCT
ajis02-1563	343	15	shabbir	shabbir	PROPN
ajis02-1563	343	16	&	&	CCONJ
ajis02-1563	343	17	khan	khan	PROPN
ajis02-1563	343	18	2017	2017	NUM
ajis02-1563	343	19	,	,	PUNCT
ajis02-1563	343	20	vol	vol	NOUN
ajis02-1563	343	21	21	21	NUM
ajis02-1563	343	22	,	,	PUNCT
ajis02-1563	343	23	selected	select	VERB
ajis02-1563	343	24	papers	paper	NOUN
ajis02-1563	343	25	from	from	ADP
ajis02-1563	343	26	ausdm	ausdm	NOUN
ajis02-1563	343	27	spectral	spectral	ADJ
ajis02-1563	343	28	methods	method	NOUN
ajis02-1563	343	29	for	for	ADP
ajis02-1563	343	30	immunization	immunization	NOUN
ajis02-1563	343	31	of	of	ADP
ajis02-1563	343	32	large	large	ADJ
ajis02-1563	343	33	networks	network	NOUN
ajis02-1563	343	34	17	17	NUM
ajis02-1563	343	35	kempe	kempe	ADJ
ajis02-1563	343	36	,	,	PUNCT
ajis02-1563	343	37	d.	d.	PROPN
ajis02-1563	343	38	,	,	PUNCT
ajis02-1563	343	39	kleinberg	kleinberg	PROPN
ajis02-1563	343	40	,	,	PUNCT
ajis02-1563	343	41	j.	j.	PROPN
ajis02-1563	343	42	,	,	PUNCT
ajis02-1563	343	43	&	&	CCONJ
ajis02-1563	343	44	tardos	tardo	NOUN
ajis02-1563	343	45	,	,	PUNCT
ajis02-1563	343	46	é	é	X
ajis02-1563	343	47	.	.	PUNCT
ajis02-1563	344	1	(	(	PUNCT
ajis02-1563	344	2	2003	2003	NUM
ajis02-1563	344	3	)	)	PUNCT
ajis02-1563	344	4	.	.	PUNCT
ajis02-1563	345	1	maximizing	maximize	VERB
ajis02-1563	345	2	the	the	DET
ajis02-1563	345	3	spread	spread	NOUN
ajis02-1563	345	4	of	of	ADP
ajis02-1563	345	5	influence	influence	NOUN
ajis02-1563	345	6	through	through	ADP
ajis02-1563	345	7	a	a	DET
ajis02-1563	345	8	social	social	ADJ
ajis02-1563	345	9	network	network	NOUN
ajis02-1563	345	10	.	.	PUNCT
ajis02-1563	346	1	in	in	ADP
ajis02-1563	346	2	proceedings	proceeding	NOUN
ajis02-1563	346	3	of	of	ADP
ajis02-1563	346	4	the	the	DET
ajis02-1563	346	5	ninth	ninth	ADJ
ajis02-1563	346	6	acm	acm	PROPN
ajis02-1563	346	7	sigkdd	sigkdd	PROPN
ajis02-1563	346	8	international	international	ADJ
ajis02-1563	346	9	conference	conference	NOUN
ajis02-1563	346	10	on	on	ADP
ajis02-1563	346	11	knowledge	knowledge	NOUN
ajis02-1563	346	12	discovery	discovery	PROPN
ajis02-1563	346	13	and	and	CCONJ
ajis02-1563	346	14	data	datum	NOUN
ajis02-1563	346	15	mining	mining	NOUN
ajis02-1563	346	16	(	(	PUNCT
ajis02-1563	346	17	pp	pp	ADJ
ajis02-1563	346	18	.	.	PUNCT
ajis02-1563	347	1	137	137	NUM
ajis02-1563	347	2	-	-	SYM
ajis02-1563	347	3	146	146	NUM
ajis02-1563	347	4	)	)	PUNCT
ajis02-1563	347	5	.	.	PUNCT
ajis02-1563	348	1	acm	acm	PROPN
ajis02-1563	348	2	.	.	PUNCT
ajis02-1563	349	1	doi	doi	PROPN
ajis02-1563	349	2	:	:	PUNCT
ajis02-1563	349	3	10.1145/956750.956769	10.1145/956750.956769	NUM
ajis02-1563	349	4	kreyszig	kreyszig	PROPN
ajis02-1563	349	5	,	,	PUNCT
ajis02-1563	349	6	e.	e.	PROPN
ajis02-1563	349	7	(	(	PUNCT
ajis02-1563	349	8	1989	1989	NUM
ajis02-1563	349	9	)	)	PUNCT
ajis02-1563	349	10	.	.	PUNCT
ajis02-1563	350	1	introductory	introductory	ADJ
ajis02-1563	350	2	functional	functional	ADJ
ajis02-1563	350	3	analysis	analysis	NOUN
ajis02-1563	350	4	with	with	ADP
ajis02-1563	350	5	applications	application	NOUN
ajis02-1563	350	6	(	(	PUNCT
ajis02-1563	350	7	vol	vol	NOUN
ajis02-1563	350	8	.	.	NOUN
ajis02-1563	350	9	1	1	NUM
ajis02-1563	350	10	)	)	PUNCT
ajis02-1563	350	11	.	.	PUNCT
ajis02-1563	351	1	new	new	PROPN
ajis02-1563	351	2	york	york	PROPN
ajis02-1563	351	3	:	:	PUNCT
ajis02-1563	351	4	wiley	wiley	PROPN
ajis02-1563	351	5	.	.	PUNCT
ajis02-1563	352	1	kuhlman	kuhlman	PROPN
ajis02-1563	352	2	,	,	PUNCT
ajis02-1563	352	3	c.	c.	PROPN
ajis02-1563	352	4	j.	j.	PROPN
ajis02-1563	352	5	,	,	PUNCT
ajis02-1563	352	6	tuli	tuli	PROPN
ajis02-1563	352	7	,	,	PUNCT
ajis02-1563	352	8	g.	g.	PROPN
ajis02-1563	352	9	,	,	PUNCT
ajis02-1563	352	10	swarup	swarup	PROPN
ajis02-1563	352	11	,	,	PUNCT
ajis02-1563	352	12	s.	s.	PROPN
ajis02-1563	352	13	,	,	PUNCT
ajis02-1563	352	14	marathe	marathe	PROPN
ajis02-1563	352	15	,	,	PUNCT
ajis02-1563	352	16	m.	m.	NOUN
ajis02-1563	352	17	v.	v.	PROPN
ajis02-1563	352	18	,	,	PUNCT
ajis02-1563	352	19	&	&	CCONJ
ajis02-1563	352	20	ravi	ravi	PROPN
ajis02-1563	352	21	,	,	PUNCT
ajis02-1563	352	22	s.	s.	PROPN
ajis02-1563	352	23	s.	s.	PROPN
ajis02-1563	352	24	(	(	PUNCT
ajis02-1563	352	25	2013	2013	NUM
ajis02-1563	352	26	)	)	PUNCT
ajis02-1563	352	27	.	.	PUNCT
ajis02-1563	353	1	blocking	block	VERB
ajis02-1563	353	2	simple	simple	ADJ
ajis02-1563	353	3	and	and	CCONJ
ajis02-1563	353	4	complex	complex	ADJ
ajis02-1563	353	5	contagion	contagion	NOUN
ajis02-1563	353	6	by	by	ADP
ajis02-1563	353	7	edge	edge	NOUN
ajis02-1563	353	8	removal	removal	NOUN
ajis02-1563	353	9	.	.	PUNCT
ajis02-1563	354	1	in	in	ADP
ajis02-1563	354	2	ieee	ieee	PROPN
ajis02-1563	354	3	13th	13th	PROPN
ajis02-1563	354	4	international	international	ADJ
ajis02-1563	354	5	conference	conference	NOUN
ajis02-1563	354	6	data	datum	NOUN
ajis02-1563	354	7	mining	mining	NOUN
ajis02-1563	354	8	(	(	PUNCT
ajis02-1563	354	9	icdm	icdm	NOUN
ajis02-1563	354	10	)	)	PUNCT
ajis02-1563	354	11	,	,	PUNCT
ajis02-1563	354	12	(	(	PUNCT
ajis02-1563	354	13	pp	pp	ADV
ajis02-1563	354	14	.	.	PUNCT
ajis02-1563	355	1	399	399	NUM
ajis02-1563	355	2	-	-	SYM
ajis02-1563	355	3	408	408	NUM
ajis02-1563	355	4	)	)	PUNCT
ajis02-1563	355	5	.	.	PUNCT
ajis02-1563	356	1	ieee	ieee	PROPN
ajis02-1563	356	2	.	.	PUNCT
ajis02-1563	357	1	doi	doi	PROPN
ajis02-1563	357	2	:	:	PUNCT
ajis02-1563	357	3	10.1109	10.1109	NUM
ajis02-1563	357	4	/	/	SYM
ajis02-1563	357	5	icdm.2013.47	icdm.2013.47	PROPN
ajis02-1563	357	6	nemhauser	nemhauser	NOUN
ajis02-1563	357	7	,	,	PUNCT
ajis02-1563	357	8	g.	g.	PROPN
ajis02-1563	357	9	l.	l.	PROPN
ajis02-1563	357	10	,	,	PUNCT
ajis02-1563	357	11	wolsey	wolsey	NOUN
ajis02-1563	357	12	,	,	PUNCT
ajis02-1563	357	13	l.	l.	PROPN
ajis02-1563	357	14	a.	a.	PROPN
ajis02-1563	357	15	,	,	PUNCT
ajis02-1563	357	16	&	&	CCONJ
ajis02-1563	357	17	fisher	fisher	PROPN
ajis02-1563	357	18	,	,	PUNCT
ajis02-1563	357	19	m.	m.	NOUN
ajis02-1563	357	20	l.	l.	PROPN
ajis02-1563	357	21	(	(	PUNCT
ajis02-1563	357	22	1978	1978	NUM
ajis02-1563	357	23	)	)	PUNCT
ajis02-1563	357	24	.	.	PUNCT
ajis02-1563	358	1	an	an	DET
ajis02-1563	358	2	analysis	analysis	NOUN
ajis02-1563	358	3	of	of	ADP
ajis02-1563	358	4	approximations	approximation	NOUN
ajis02-1563	358	5	for	for	ADP
ajis02-1563	358	6	maximizing	maximize	VERB
ajis02-1563	358	7	submodular	submodular	ADJ
ajis02-1563	358	8	set	set	NOUN
ajis02-1563	358	9	functions	function	NOUN
ajis02-1563	358	10	—	—	PUNCT
ajis02-1563	358	11	i.	i.	PROPN
ajis02-1563	358	12	mathematical	mathematical	PROPN
ajis02-1563	358	13	programming	programming	NOUN
ajis02-1563	358	14	,	,	PUNCT
ajis02-1563	358	15	14(1	14(1	NUM
ajis02-1563	358	16	)	)	PUNCT
ajis02-1563	358	17	,	,	PUNCT
ajis02-1563	358	18	265	265	NUM
ajis02-1563	358	19	-	-	SYM
ajis02-1563	358	20	294	294	NUM
ajis02-1563	358	21	.	.	PUNCT
ajis02-1563	359	1	doi	doi	NOUN
ajis02-1563	359	2	:	:	PUNCT
ajis02-1563	359	3	10.1007	10.1007	NUM
ajis02-1563	359	4	/	/	SYM
ajis02-1563	359	5	bf01588971	bf01588971	NOUN
ajis02-1563	359	6	prakash	prakash	PROPN
ajis02-1563	359	7	,	,	PUNCT
ajis02-1563	359	8	b.	b.	PROPN
ajis02-1563	359	9	a.	a.	PROPN
ajis02-1563	359	10	,	,	PUNCT
ajis02-1563	359	11	vreeken	vreeken	VERB
ajis02-1563	359	12	,	,	PUNCT
ajis02-1563	359	13	j.	j.	PROPN
ajis02-1563	359	14	,	,	PUNCT
ajis02-1563	359	15	&	&	CCONJ
ajis02-1563	359	16	faloutsos	faloutsos	PROPN
ajis02-1563	359	17	,	,	PUNCT
ajis02-1563	359	18	c.	c.	PROPN
ajis02-1563	359	19	(	(	PUNCT
ajis02-1563	359	20	2012	2012	NUM
ajis02-1563	359	21	)	)	PUNCT
ajis02-1563	359	22	.	.	PUNCT
ajis02-1563	360	1	spotting	spot	VERB
ajis02-1563	360	2	culprits	culprit	NOUN
ajis02-1563	360	3	in	in	ADP
ajis02-1563	360	4	epidemics	epidemic	NOUN
ajis02-1563	360	5	:	:	PUNCT
ajis02-1563	360	6	how	how	SCONJ
ajis02-1563	360	7	many	many	ADJ
ajis02-1563	360	8	and	and	CCONJ
ajis02-1563	360	9	which	which	PRON
ajis02-1563	360	10	ones	one	NOUN
ajis02-1563	360	11	?	?	PUNCT
ajis02-1563	360	12	.	.	PUNCT
ajis02-1563	361	1	in	in	ADP
ajis02-1563	361	2	ieee	ieee	PROPN
ajis02-1563	361	3	12th	12th	PROPN
ajis02-1563	361	4	international	international	ADJ
ajis02-1563	361	5	conference	conference	NOUN
ajis02-1563	361	6	on	on	ADP
ajis02-1563	361	7	data	datum	NOUN
ajis02-1563	361	8	mining	mining	NOUN
ajis02-1563	361	9	(	(	PUNCT
ajis02-1563	361	10	icdm	icdm	NOUN
ajis02-1563	361	11	)	)	PUNCT
ajis02-1563	361	12	,	,	PUNCT
ajis02-1563	361	13	(	(	PUNCT
ajis02-1563	361	14	pp	pp	X
ajis02-1563	361	15	.	.	PUNCT
ajis02-1563	362	1	11	11	NUM
ajis02-1563	362	2	-	-	SYM
ajis02-1563	362	3	20	20	NUM
ajis02-1563	362	4	)	)	PUNCT
ajis02-1563	362	5	.	.	PUNCT
ajis02-1563	363	1	ieee	ieee	PROPN
ajis02-1563	363	2	.	.	PUNCT
ajis02-1563	364	1	doi	doi	PROPN
ajis02-1563	364	2	:	:	PUNCT
ajis02-1563	364	3	10.1109	10.1109	NUM
ajis02-1563	364	4	/	/	SYM
ajis02-1563	364	5	icdm.2012.136	icdm.2012.136	PROPN
ajis02-1563	364	6	seeman	seeman	PROPN
ajis02-1563	364	7	,	,	PUNCT
ajis02-1563	364	8	l.	l.	PROPN
ajis02-1563	364	9	,	,	PUNCT
ajis02-1563	364	10	&	&	CCONJ
ajis02-1563	364	11	singer	singer	NOUN
ajis02-1563	364	12	,	,	PUNCT
ajis02-1563	364	13	y.	y.	PROPN
ajis02-1563	364	14	(	(	PUNCT
ajis02-1563	364	15	2013	2013	NUM
ajis02-1563	364	16	)	)	PUNCT
ajis02-1563	364	17	.	.	PUNCT
ajis02-1563	365	1	adaptive	adaptive	ADJ
ajis02-1563	365	2	seeding	seed	VERB
ajis02-1563	365	3	in	in	ADP
ajis02-1563	365	4	social	social	ADJ
ajis02-1563	365	5	networks	network	NOUN
ajis02-1563	365	6	.	.	PUNCT
ajis02-1563	366	1	in	in	ADP
ajis02-1563	366	2	ieee	ieee	PROPN
ajis02-1563	366	3	54th	54th	ADJ
ajis02-1563	366	4	annual	annual	ADJ
ajis02-1563	366	5	symposium	symposium	NOUN
ajis02-1563	366	6	on	on	ADP
ajis02-1563	366	7	foundations	foundation	NOUN
ajis02-1563	366	8	of	of	ADP
ajis02-1563	366	9	computer	computer	NOUN
ajis02-1563	366	10	science	science	NOUN
ajis02-1563	366	11	(	(	PUNCT
ajis02-1563	366	12	focs	focs	PROPN
ajis02-1563	366	13	)	)	PUNCT
ajis02-1563	366	14	,	,	PUNCT
ajis02-1563	366	15	(	(	PUNCT
ajis02-1563	366	16	pp	pp	ADV
ajis02-1563	366	17	.	.	PUNCT
ajis02-1563	367	1	459	459	NUM
ajis02-1563	367	2	-	-	SYM
ajis02-1563	367	3	468	468	NUM
ajis02-1563	367	4	)	)	PUNCT
ajis02-1563	367	5	.	.	PUNCT
ajis02-1563	368	1	ieee	ieee	PROPN
ajis02-1563	368	2	.	.	PUNCT
ajis02-1563	369	1	doi	doi	PROPN
ajis02-1563	369	2	:	:	PUNCT
ajis02-1563	369	3	10.1109	10.1109	NUM
ajis02-1563	369	4	/	/	SYM
ajis02-1563	369	5	focs.2013.56	focs.2013.56	ADJ
ajis02-1563	369	6	serre	serre	X
ajis02-1563	369	7	,	,	PUNCT
ajis02-1563	369	8	d.	d.	PROPN
ajis02-1563	369	9	(	(	PUNCT
ajis02-1563	369	10	2002	2002	NUM
ajis02-1563	369	11	)	)	PUNCT
ajis02-1563	369	12	.	.	PUNCT
ajis02-1563	370	1	matrices	matrix	NOUN
ajis02-1563	370	2	,	,	PUNCT
ajis02-1563	370	3	volume	volume	NOUN
ajis02-1563	370	4	216	216	NUM
ajis02-1563	370	5	of	of	ADP
ajis02-1563	370	6	graduate	graduate	ADJ
ajis02-1563	370	7	texts	text	NOUN
ajis02-1563	370	8	in	in	ADP
ajis02-1563	370	9	mathematics	mathematic	NOUN
ajis02-1563	370	10	.	.	PUNCT
ajis02-1563	371	1	song	song	PROPN
ajis02-1563	371	2	,	,	PUNCT
ajis02-1563	371	3	c.	c.	PROPN
ajis02-1563	371	4	,	,	PUNCT
ajis02-1563	371	5	hsu	hsu	PROPN
ajis02-1563	371	6	,	,	PUNCT
ajis02-1563	371	7	w.	w.	PROPN
ajis02-1563	371	8	,	,	PUNCT
ajis02-1563	371	9	&	&	CCONJ
ajis02-1563	371	10	lee	lee	PROPN
ajis02-1563	371	11	,	,	PUNCT
ajis02-1563	371	12	m.	m.	PROPN
ajis02-1563	371	13	l.	l.	PROPN
ajis02-1563	371	14	(	(	PUNCT
ajis02-1563	371	15	2015	2015	NUM
ajis02-1563	371	16	)	)	PUNCT
ajis02-1563	371	17	.	.	PUNCT
ajis02-1563	372	1	node	node	ADJ
ajis02-1563	372	2	immunization	immunization	NOUN
ajis02-1563	372	3	over	over	ADP
ajis02-1563	372	4	infectious	infectious	ADJ
ajis02-1563	372	5	period	period	NOUN
ajis02-1563	372	6	.	.	PUNCT
ajis02-1563	373	1	in	in	ADP
ajis02-1563	373	2	proceedings	proceeding	NOUN
ajis02-1563	373	3	of	of	ADP
ajis02-1563	373	4	the	the	DET
ajis02-1563	373	5	24th	24th	PROPN
ajis02-1563	373	6	acm	acm	PROPN
ajis02-1563	373	7	international	international	ADJ
ajis02-1563	373	8	conference	conference	NOUN
ajis02-1563	373	9	on	on	ADP
ajis02-1563	373	10	information	information	NOUN
ajis02-1563	373	11	and	and	CCONJ
ajis02-1563	373	12	knowledge	knowledge	NOUN
ajis02-1563	373	13	management	management	NOUN
ajis02-1563	373	14	(	(	PUNCT
ajis02-1563	373	15	pp	pp	PROPN
ajis02-1563	373	16	.	.	PUNCT
ajis02-1563	373	17	831	831	NUM
ajis02-1563	373	18	-	-	SYM
ajis02-1563	373	19	840	840	NUM
ajis02-1563	373	20	)	)	PUNCT
ajis02-1563	373	21	.	.	PUNCT
ajis02-1563	374	1	acm	acm	PROPN
ajis02-1563	374	2	.	.	PUNCT
ajis02-1563	375	1	doi	doi	PROPN
ajis02-1563	375	2	:	:	PUNCT
ajis02-1563	375	3	10.1145/2806416.2806522	10.1145/2806416.2806522	NUM
ajis02-1563	375	4	strang	strang	PROPN
ajis02-1563	375	5	,	,	PUNCT
ajis02-1563	375	6	g.	g.	PROPN
ajis02-1563	375	7	(	(	PUNCT
ajis02-1563	375	8	2006	2006	NUM
ajis02-1563	375	9	)	)	PUNCT
ajis02-1563	375	10	.	.	PUNCT
ajis02-1563	376	1	linear	linear	PROPN
ajis02-1563	376	2	algebra	algebra	NOUN
ajis02-1563	376	3	and	and	CCONJ
ajis02-1563	376	4	its	its	PRON
ajis02-1563	376	5	applications	application	NOUN
ajis02-1563	376	6	.	.	PUNCT
ajis02-1563	377	1	belmont	belmont	PROPN
ajis02-1563	377	2	,	,	PUNCT
ajis02-1563	377	3	ca	ca	PROPN
ajis02-1563	377	4	:	:	PUNCT
ajis02-1563	377	5	thomson	thomson	PROPN
ajis02-1563	377	6	,	,	PUNCT
ajis02-1563	377	7	brooks	brooks	PROPN
ajis02-1563	377	8	/	/	SYM
ajis02-1563	377	9	cole	cole	PROPN
ajis02-1563	377	10	.	.	PUNCT
ajis02-1563	378	1	tariq	tariq	PROPN
ajis02-1563	378	2	,	,	PUNCT
ajis02-1563	378	3	j.	j.	PROPN
ajis02-1563	378	4	,	,	PUNCT
ajis02-1563	378	5	ahmad	ahmad	PROPN
ajis02-1563	378	6	,	,	PUNCT
ajis02-1563	378	7	m.	m.	NOUN
ajis02-1563	378	8	,	,	PUNCT
ajis02-1563	378	9	khan	khan	PROPN
ajis02-1563	378	10	,	,	PUNCT
ajis02-1563	378	11	i.	i.	PROPN
ajis02-1563	378	12	,	,	PUNCT
ajis02-1563	378	13	&	&	CCONJ
ajis02-1563	378	14	shabbir	shabbir	PROPN
ajis02-1563	378	15	,	,	PUNCT
ajis02-1563	378	16	m.	m.	NOUN
ajis02-1563	378	17	(	(	PUNCT
ajis02-1563	378	18	2017	2017	NUM
ajis02-1563	378	19	)	)	PUNCT
ajis02-1563	378	20	.	.	PUNCT
ajis02-1563	379	1	scalable	scalable	ADJ
ajis02-1563	379	2	approximation	approximation	NOUN
ajis02-1563	379	3	algorithm	algorithm	NOUN
ajis02-1563	379	4	for	for	ADP
ajis02-1563	379	5	network	network	NOUN
ajis02-1563	379	6	immunization	immunization	NOUN
ajis02-1563	379	7	.	.	PUNCT
ajis02-1563	380	1	in	in	ADP
ajis02-1563	380	2	21st	21st	ADJ
ajis02-1563	380	3	pasific	pasific	PROPN
ajis02-1563	380	4	asia	asia	PROPN
ajis02-1563	380	5	conference	conference	PROPN
ajis02-1563	380	6	on	on	ADP
ajis02-1563	380	7	information	information	NOUN
ajis02-1563	380	8	systems	system	NOUN
ajis02-1563	380	9	,	,	PUNCT
ajis02-1563	380	10	pacis	pacis	ADV
ajis02-1563	380	11	.	.	PUNCT
ajis02-1563	381	1	tong	tong	PROPN
ajis02-1563	381	2	,	,	PUNCT
ajis02-1563	381	3	h.	h.	PROPN
ajis02-1563	381	4	,	,	PUNCT
ajis02-1563	381	5	prakash	prakash	PROPN
ajis02-1563	381	6	,	,	PUNCT
ajis02-1563	381	7	b.	b.	PROPN
ajis02-1563	381	8	a.	a.	PROPN
ajis02-1563	381	9	,	,	PUNCT
ajis02-1563	381	10	eliassi	eliassi	NOUN
ajis02-1563	381	11	-	-	PUNCT
ajis02-1563	381	12	rad	rad	PROPN
ajis02-1563	381	13	,	,	PUNCT
ajis02-1563	381	14	t.	t.	PROPN
ajis02-1563	381	15	,	,	PUNCT
ajis02-1563	381	16	faloutsos	faloutsos	PROPN
ajis02-1563	381	17	,	,	PUNCT
ajis02-1563	381	18	m.	m.	NOUN
ajis02-1563	381	19	,	,	PUNCT
ajis02-1563	381	20	&	&	CCONJ
ajis02-1563	381	21	faloutsos	faloutsos	PROPN
ajis02-1563	381	22	,	,	PUNCT
ajis02-1563	381	23	c.	c.	PROPN
ajis02-1563	381	24	(	(	PUNCT
ajis02-1563	381	25	2012	2012	NUM
ajis02-1563	381	26	)	)	PUNCT
ajis02-1563	381	27	.	.	PUNCT
ajis02-1563	382	1	gelling	gelling	NOUN
ajis02-1563	382	2	,	,	PUNCT
ajis02-1563	382	3	and	and	CCONJ
ajis02-1563	382	4	melting	melting	NOUN
ajis02-1563	382	5	,	,	PUNCT
ajis02-1563	382	6	large	large	ADJ
ajis02-1563	382	7	graphs	graph	NOUN
ajis02-1563	382	8	by	by	ADP
ajis02-1563	382	9	edge	edge	NOUN
ajis02-1563	382	10	manipulation	manipulation	NOUN
ajis02-1563	382	11	.	.	PUNCT
ajis02-1563	383	1	in	in	ADP
ajis02-1563	383	2	proceedings	proceeding	NOUN
ajis02-1563	383	3	of	of	ADP
ajis02-1563	383	4	the	the	DET
ajis02-1563	383	5	21st	21st	PROPN
ajis02-1563	383	6	acm	acm	PROPN
ajis02-1563	383	7	international	international	ADJ
ajis02-1563	383	8	conference	conference	NOUN
ajis02-1563	383	9	on	on	ADP
ajis02-1563	383	10	information	information	NOUN
ajis02-1563	383	11	and	and	CCONJ
ajis02-1563	383	12	knowledge	knowledge	NOUN
ajis02-1563	383	13	management	management	NOUN
ajis02-1563	383	14	(	(	PUNCT
ajis02-1563	383	15	pp	pp	ADJ
ajis02-1563	383	16	.	.	PUNCT
ajis02-1563	384	1	245	245	NUM
ajis02-1563	384	2	-	-	SYM
ajis02-1563	384	3	254	254	NUM
ajis02-1563	384	4	)	)	PUNCT
ajis02-1563	384	5	.	.	PUNCT
ajis02-1563	385	1	acm	acm	PROPN
ajis02-1563	385	2	.	.	PUNCT
ajis02-1563	386	1	doi	doi	PROPN
ajis02-1563	386	2	:	:	PUNCT
ajis02-1563	386	3	10.1145/2396761.2396795	10.1145/2396761.2396795	NUM
ajis02-1563	386	4	west	west	PROPN
ajis02-1563	386	5	,	,	PUNCT
ajis02-1563	386	6	d.	d.	PROPN
ajis02-1563	386	7	b.	b.	PROPN
ajis02-1563	386	8	(	(	PUNCT
ajis02-1563	386	9	2001	2001	NUM
ajis02-1563	386	10	)	)	PUNCT
ajis02-1563	386	11	.	.	PUNCT
ajis02-1563	387	1	introduction	introduction	NOUN
ajis02-1563	387	2	to	to	ADP
ajis02-1563	387	3	graph	graph	NOUN
ajis02-1563	387	4	theory	theory	NOUN
ajis02-1563	387	5	(	(	PUNCT
ajis02-1563	387	6	vol	vol	NOUN
ajis02-1563	387	7	.	.	NOUN
ajis02-1563	387	8	2	2	NUM
ajis02-1563	387	9	)	)	PUNCT
ajis02-1563	387	10	.	.	PUNCT
ajis02-1563	388	1	upper	upper	ADJ
ajis02-1563	388	2	saddle	saddle	PROPN
ajis02-1563	388	3	river	river	NOUN
ajis02-1563	388	4	:	:	PUNCT
ajis02-1563	388	5	prentice	prentice	PROPN
ajis02-1563	388	6	hall	hall	PROPN
ajis02-1563	388	7	.	.	PUNCT
ajis02-1563	389	1	zhang	zhang	PROPN
ajis02-1563	389	2	,	,	PUNCT
ajis02-1563	389	3	y.	y.	PROPN
ajis02-1563	389	4	,	,	PUNCT
ajis02-1563	389	5	&	&	CCONJ
ajis02-1563	389	6	prakash	prakash	PROPN
ajis02-1563	389	7	,	,	PUNCT
ajis02-1563	389	8	b.	b.	PROPN
ajis02-1563	389	9	a.	a.	PROPN
ajis02-1563	389	10	(	(	PUNCT
ajis02-1563	389	11	2014a	2014a	NUM
ajis02-1563	389	12	)	)	PUNCT
ajis02-1563	389	13	.	.	PUNCT
ajis02-1563	390	1	dava	dava	PROPN
ajis02-1563	390	2	:	:	PUNCT
ajis02-1563	390	3	distributing	distribute	VERB
ajis02-1563	390	4	vaccines	vaccine	NOUN
ajis02-1563	390	5	over	over	ADP
ajis02-1563	390	6	networks	network	NOUN
ajis02-1563	390	7	under	under	ADP
ajis02-1563	390	8	prior	prior	ADJ
ajis02-1563	390	9	information	information	NOUN
ajis02-1563	390	10	.	.	PUNCT
ajis02-1563	391	1	in	in	ADP
ajis02-1563	391	2	proceedings	proceeding	NOUN
ajis02-1563	391	3	of	of	ADP
ajis02-1563	391	4	the	the	DET
ajis02-1563	391	5	2014	2014	NUM
ajis02-1563	391	6	siam	siam	ADJ
ajis02-1563	391	7	international	international	ADJ
ajis02-1563	391	8	conference	conference	NOUN
ajis02-1563	391	9	on	on	ADP
ajis02-1563	391	10	data	datum	NOUN
ajis02-1563	391	11	mining	mining	NOUN
ajis02-1563	391	12	(	(	PUNCT
ajis02-1563	391	13	pp	pp	ADJ
ajis02-1563	391	14	.	.	PUNCT
ajis02-1563	392	1	46	46	NUM
ajis02-1563	392	2	-	-	SYM
ajis02-1563	392	3	54	54	NUM
ajis02-1563	392	4	)	)	PUNCT
ajis02-1563	392	5	.	.	PUNCT
ajis02-1563	393	1	siam	siam	PROPN
ajis02-1563	393	2	.	.	PUNCT
ajis02-1563	394	1	doi	doi	PROPN
ajis02-1563	394	2	:	:	PUNCT
ajis02-1563	394	3	10.1137/1.9781611973440.6	10.1137/1.9781611973440.6	PROPN
ajis02-1563	394	4	zhang	zhang	PROPN
ajis02-1563	394	5	,	,	PUNCT
ajis02-1563	394	6	y.	y.	PROPN
ajis02-1563	394	7	,	,	PUNCT
ajis02-1563	394	8	&	&	CCONJ
ajis02-1563	394	9	prakash	prakash	PROPN
ajis02-1563	394	10	,	,	PUNCT
ajis02-1563	394	11	b.	b.	PROPN
ajis02-1563	394	12	a.	a.	PROPN
ajis02-1563	394	13	(	(	PUNCT
ajis02-1563	394	14	2014b	2014b	NUM
ajis02-1563	394	15	)	)	PUNCT
ajis02-1563	394	16	.	.	PUNCT
ajis02-1563	395	1	scalable	scalable	ADJ
ajis02-1563	395	2	vaccine	vaccine	NOUN
ajis02-1563	395	3	distribution	distribution	NOUN
ajis02-1563	395	4	in	in	ADP
ajis02-1563	395	5	large	large	ADJ
ajis02-1563	395	6	graphs	graph	NOUN
ajis02-1563	395	7	given	give	VERB
ajis02-1563	395	8	uncertain	uncertain	ADJ
ajis02-1563	395	9	data	datum	NOUN
ajis02-1563	395	10	.	.	PUNCT
ajis02-1563	396	1	in	in	ADP
ajis02-1563	396	2	proceedings	proceeding	NOUN
ajis02-1563	396	3	of	of	ADP
ajis02-1563	396	4	the	the	DET
ajis02-1563	396	5	23rd	23rd	ADJ
ajis02-1563	396	6	acm	acm	PROPN
ajis02-1563	396	7	international	international	ADJ
ajis02-1563	396	8	conference	conference	NOUN
ajis02-1563	396	9	on	on	ADP
ajis02-1563	396	10	information	information	NOUN
ajis02-1563	396	11	and	and	CCONJ
ajis02-1563	396	12	knowledge	knowledge	NOUN
ajis02-1563	396	13	management	management	NOUN
ajis02-1563	396	14	(	(	PUNCT
ajis02-1563	396	15	pp	pp	ADJ
ajis02-1563	396	16	.	.	PUNCT
ajis02-1563	397	1	1719	1719	NUM
ajis02-1563	397	2	-	-	SYM
ajis02-1563	397	3	1728	1728	NUM
ajis02-1563	397	4	)	)	PUNCT
ajis02-1563	397	5	.	.	PUNCT
ajis02-1563	398	1	acm	acm	PROPN
ajis02-1563	398	2	.	.	PUNCT
ajis02-1563	399	1	doi	doi	PROPN
ajis02-1563	399	2	:	:	PUNCT
ajis02-1563	399	3	10.1145/2661829.2662088	10.1145/2661829.2662088	NUM
ajis02-1563	399	4	copyright	copyright	NOUN
ajis02-1563	399	5	:	:	PUNCT
ajis02-1563	399	6	©	©	PROPN
ajis02-1563	399	7	2017	2017	NUM
ajis02-1563	399	8	ahmad	ahmad	NOUN
ajis02-1563	399	9	,	,	PUNCT
ajis02-1563	399	10	traiq	traiq	NOUN
ajis02-1563	399	11	,	,	PUNCT
ajis02-1563	399	12	shabbir	shabbir	PROPN
ajis02-1563	399	13	&	&	CCONJ
ajis02-1563	399	14	khan	khan	PROPN
ajis02-1563	399	15	.	.	PUNCT
ajis02-1563	400	1	this	this	PRON
ajis02-1563	400	2	is	be	AUX
ajis02-1563	400	3	an	an	DET
ajis02-1563	400	4	open	open	ADJ
ajis02-1563	400	5	-	-	PUNCT
ajis02-1563	400	6	access	access	NOUN
ajis02-1563	400	7	article	article	NOUN
ajis02-1563	400	8	distributed	distribute	VERB
ajis02-1563	400	9	under	under	ADP
ajis02-1563	400	10	the	the	DET
ajis02-1563	400	11	terms	term	NOUN
ajis02-1563	400	12	of	of	ADP
ajis02-1563	400	13	the	the	DET
ajis02-1563	400	14	creative	creative	ADJ
ajis02-1563	400	15	commons	common	NOUN
ajis02-1563	400	16	attribution	attribution	NOUN
ajis02-1563	400	17	-	-	PUNCT
ajis02-1563	400	18	noncommercial	noncommercial	ADJ
ajis02-1563	400	19	3.0	3.0	NUM
ajis02-1563	400	20	australia	australia	NOUN
ajis02-1563	400	21	license	license	NOUN
ajis02-1563	400	22	,	,	PUNCT
ajis02-1563	400	23	which	which	PRON
ajis02-1563	400	24	permits	permit	VERB
ajis02-1563	400	25	non	non	ADJ
ajis02-1563	400	26	-	-	ADJ
ajis02-1563	400	27	commercial	commercial	ADJ
ajis02-1563	400	28	use	use	NOUN
ajis02-1563	400	29	,	,	PUNCT
ajis02-1563	400	30	distribution	distribution	NOUN
ajis02-1563	400	31	,	,	PUNCT
ajis02-1563	400	32	and	and	CCONJ
ajis02-1563	400	33	reproduction	reproduction	NOUN
ajis02-1563	400	34	in	in	ADP
ajis02-1563	400	35	any	any	DET
ajis02-1563	400	36	medium	medium	NOUN
ajis02-1563	400	37	,	,	PUNCT
ajis02-1563	400	38	provided	provide	VERB
ajis02-1563	400	39	the	the	DET
ajis02-1563	400	40	original	original	ADJ
ajis02-1563	400	41	author	author	NOUN
ajis02-1563	400	42	and	and	CCONJ
ajis02-1563	400	43	ajis	ajis	ADV
ajis02-1563	400	44	are	be	AUX
ajis02-1563	400	45	credited	credit	VERB
ajis02-1563	400	46	.	.	PUNCT
ajis02-1563	401	1	http://creativecommons.org/licenses/by-nc/3.0/au/	http://creativecommons.org/licenses/by-nc/3.0/au/	ADJ
ajis02-1563	401	2	australasian	australasian	ADJ
ajis02-1563	401	3	journal	journal	NOUN
ajis02-1563	401	4	of	of	ADP
ajis02-1563	401	5	information	information	NOUN
ajis02-1563	401	6	systems	system	NOUN
ajis02-1563	401	7	ahmad	ahmad	PROPN
ajis02-1563	401	8	,	,	PUNCT
ajis02-1563	401	9	traiq	traiq	NOUN
ajis02-1563	401	10	,	,	PUNCT
ajis02-1563	401	11	shabbir	shabbir	PROPN
ajis02-1563	401	12	&	&	CCONJ
ajis02-1563	401	13	khan	khan	PROPN
ajis02-1563	401	14	2017	2017	NUM
ajis02-1563	401	15	,	,	PUNCT
ajis02-1563	401	16	vol	vol	NOUN
ajis02-1563	401	17	21	21	NUM
ajis02-1563	401	18	,	,	PUNCT
ajis02-1563	401	19	selected	select	VERB
ajis02-1563	401	20	papers	paper	NOUN
ajis02-1563	401	21	from	from	ADP
ajis02-1563	401	22	ausdm	ausdm	NOUN
ajis02-1563	401	23	spectral	spectral	ADJ
ajis02-1563	401	24	methods	method	NOUN
ajis02-1563	401	25	for	for	ADP
ajis02-1563	401	26	immunization	immunization	NOUN
ajis02-1563	401	27	of	of	ADP
ajis02-1563	401	28	large	large	ADJ
ajis02-1563	401	29	networks	network	NOUN
ajis02-1563	401	30	18	18	NUM