id	sid	tid	token	lemma	pos
ijassa-1405	1	1	adv	adv	PROPN
ijassa-1405	1	2	syst	syst	PROPN
ijassa-1405	1	3	sci	sci	PROPN
ijassa-1405	1	4	appl	appl	PROPN
ijassa-1405	1	5	2023	2023	NUM
ijassa-1405	1	6	;	;	PUNCT
ijassa-1405	1	7	02:164–177	02:164–177	NUM
ijassa-1405	1	8	published	publish	VERB
ijassa-1405	1	9	online	online	ADV
ijassa-1405	1	10	at	at	ADP
ijassa-1405	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1405	1	12	.	.	PUNCT
ijassa-1405	2	1	pairwise	pairwise	NOUN
ijassa-1405	2	2	similarity	similarity	NOUN
ijassa-1405	2	3	estimation	estimation	NOUN
ijassa-1405	2	4	for	for	ADP
ijassa-1405	2	5	discrete	discrete	ADJ
ijassa-1405	2	6	optimization	optimization	NOUN
ijassa-1405	2	7	problems	problem	NOUN
ijassa-1405	2	8	darya	darya	VERB
ijassa-1405	2	9	lemtyuzhnikova1,2	lemtyuzhnikova1,2	PROPN
ijassa-1405	2	10	*	*	PROPN
ijassa-1405	2	11	,	,	PUNCT
ijassa-1405	2	12	pavel	pavel	PROPN
ijassa-1405	2	13	chebotarev3,4	chebotarev3,4	PROPN
ijassa-1405	2	14	,	,	PUNCT
ijassa-1405	2	15	mikhail	mikhail	PROPN
ijassa-1405	2	16	goubko5	goubko5	PROPN
ijassa-1405	2	17	,	,	PUNCT
ijassa-1405	2	18	nikita	nikita	PROPN
ijassa-1405	2	19	shushko1	shushko1	PROPN
ijassa-1405	2	20	,	,	PUNCT
ijassa-1405	2	21	mikhail	mikhail	PROPN
ijassa-1405	2	22	somov1	somov1	PROPN
ijassa-1405	2	23	1institute	1institute	NUM
ijassa-1405	2	24	of	of	ADP
ijassa-1405	2	25	control	control	PROPN
ijassa-1405	2	26	sciences	science	NOUN
ijassa-1405	2	27	of	of	ADP
ijassa-1405	2	28	ras	ras	PROPN
ijassa-1405	2	29	,	,	PUNCT
ijassa-1405	2	30	moscow	moscow	PROPN
ijassa-1405	2	31	,	,	PUNCT
ijassa-1405	2	32	russia	russia	PROPN
ijassa-1405	2	33	2moscow	2moscow	NUM
ijassa-1405	2	34	aviation	aviation	NOUN
ijassa-1405	2	35	institute	institute	NOUN
ijassa-1405	2	36	,	,	PUNCT
ijassa-1405	2	37	moscow	moscow	PROPN
ijassa-1405	2	38	,	,	PUNCT
ijassa-1405	2	39	russia	russia	PROPN
ijassa-1405	2	40	3technion	3technion	PROPN
ijassa-1405	2	41	–	–	PUNCT
ijassa-1405	2	42	israel	israel	PROPN
ijassa-1405	2	43	institute	institute	PROPN
ijassa-1405	2	44	of	of	ADP
ijassa-1405	2	45	technology	technology	PROPN
ijassa-1405	2	46	,	,	PUNCT
ijassa-1405	2	47	haifa	haifa	PROPN
ijassa-1405	2	48	,	,	PUNCT
ijassa-1405	2	49	israel	israel	PROPN
ijassa-1405	3	1	4kharkevich	4kharkevich	PROPN
ijassa-1405	3	2	institute	institute	VERB
ijassa-1405	3	3	for	for	ADP
ijassa-1405	3	4	information	information	NOUN
ijassa-1405	3	5	transmission	transmission	NOUN
ijassa-1405	3	6	problems	problem	NOUN
ijassa-1405	3	7	of	of	ADP
ijassa-1405	3	8	ras	ras	PROPN
ijassa-1405	3	9	,	,	PUNCT
ijassa-1405	3	10	moscow	moscow	PROPN
ijassa-1405	3	11	,	,	PUNCT
ijassa-1405	3	12	russia	russia	PROPN
ijassa-1405	3	13	5flöha	5flöha	NUM
ijassa-1405	3	14	,	,	PUNCT
ijassa-1405	3	15	altran	altran	VERB
ijassa-1405	3	16	deutschland	deutschland	PROPN
ijassa-1405	3	17	s.a.s	s.a.s	PROPN
ijassa-1405	3	18	.	.	PROPN
ijassa-1405	3	19	&	&	CCONJ
ijassa-1405	3	20	co.	co.	PROPN
ijassa-1405	3	21	kg	kg	PROPN
ijassa-1405	3	22	abstract	abstract	NOUN
ijassa-1405	3	23	:	:	PUNCT
ijassa-1405	3	24	in	in	ADP
ijassa-1405	3	25	this	this	DET
ijassa-1405	3	26	paper	paper	NOUN
ijassa-1405	3	27	,	,	PUNCT
ijassa-1405	3	28	we	we	PRON
ijassa-1405	3	29	propose	propose	VERB
ijassa-1405	3	30	a	a	DET
ijassa-1405	3	31	new	new	ADJ
ijassa-1405	3	32	method	method	NOUN
ijassa-1405	3	33	,	,	PUNCT
ijassa-1405	3	34	called	call	VERB
ijassa-1405	3	35	the	the	DET
ijassa-1405	3	36	pairwise	pairwise	NOUN
ijassa-1405	3	37	similarity	similarity	NOUN
ijassa-1405	3	38	method	method	NOUN
ijassa-1405	3	39	,	,	PUNCT
ijassa-1405	3	40	for	for	ADP
ijassa-1405	3	41	assessing	assess	VERB
ijassa-1405	3	42	the	the	DET
ijassa-1405	3	43	similarity	similarity	NOUN
ijassa-1405	3	44	of	of	ADP
ijassa-1405	3	45	instances	instance	NOUN
ijassa-1405	3	46	of	of	ADP
ijassa-1405	3	47	optimization	optimization	NOUN
ijassa-1405	3	48	problems	problem	NOUN
ijassa-1405	3	49	.	.	PUNCT
ijassa-1405	4	1	this	this	DET
ijassa-1405	4	2	method	method	NOUN
ijassa-1405	4	3	is	be	AUX
ijassa-1405	4	4	a	a	DET
ijassa-1405	4	5	generalization	generalization	NOUN
ijassa-1405	4	6	of	of	ADP
ijassa-1405	4	7	the	the	DET
ijassa-1405	4	8	metric	metric	ADJ
ijassa-1405	4	9	approach	approach	NOUN
ijassa-1405	4	10	proposed	propose	VERB
ijassa-1405	4	11	earlier	early	ADV
ijassa-1405	4	12	for	for	ADP
ijassa-1405	4	13	scheduling	scheduling	NOUN
ijassa-1405	4	14	problems	problem	NOUN
ijassa-1405	4	15	.	.	PUNCT
ijassa-1405	5	1	it	it	PRON
ijassa-1405	5	2	relaxes	relax	VERB
ijassa-1405	5	3	the	the	DET
ijassa-1405	5	4	requirements	requirement	NOUN
ijassa-1405	5	5	to	to	ADP
ijassa-1405	5	6	the	the	DET
ijassa-1405	5	7	structure	structure	NOUN
ijassa-1405	5	8	of	of	ADP
ijassa-1405	5	9	the	the	DET
ijassa-1405	5	10	problem	problem	NOUN
ijassa-1405	5	11	constraints	constraint	VERB
ijassa-1405	5	12	.	.	PUNCT
ijassa-1405	6	1	the	the	DET
ijassa-1405	6	2	method	method	NOUN
ijassa-1405	6	3	involves	involve	VERB
ijassa-1405	6	4	a	a	DET
ijassa-1405	6	5	dissimilarity	dissimilarity	NOUN
ijassa-1405	6	6	function	function	NOUN
ijassa-1405	6	7	for	for	ADP
ijassa-1405	6	8	the	the	DET
ijassa-1405	6	9	comparison	comparison	NOUN
ijassa-1405	6	10	of	of	ADP
ijassa-1405	6	11	instances	instance	NOUN
ijassa-1405	6	12	.	.	PUNCT
ijassa-1405	7	1	it	it	PRON
ijassa-1405	7	2	identifies	identify	VERB
ijassa-1405	7	3	“	"	PUNCT
ijassa-1405	7	4	simple	simple	ADJ
ijassa-1405	7	5	”	"	PUNCT
ijassa-1405	7	6	instances	instance	NOUN
ijassa-1405	7	7	that	that	PRON
ijassa-1405	7	8	can	can	AUX
ijassa-1405	7	9	be	be	AUX
ijassa-1405	7	10	solved	solve	VERB
ijassa-1405	7	11	in	in	ADP
ijassa-1405	7	12	polynomial	polynomial	ADJ
ijassa-1405	7	13	time	time	NOUN
ijassa-1405	7	14	and	and	CCONJ
ijassa-1405	7	15	uses	use	VERB
ijassa-1405	7	16	them	they	PRON
ijassa-1405	7	17	to	to	PART
ijassa-1405	7	18	get	get	VERB
ijassa-1405	7	19	good	good	ADJ
ijassa-1405	7	20	approximations	approximation	NOUN
ijassa-1405	7	21	for	for	ADP
ijassa-1405	7	22	other	other	ADJ
ijassa-1405	7	23	instances	instance	NOUN
ijassa-1405	7	24	.	.	PUNCT
ijassa-1405	8	1	we	we	PRON
ijassa-1405	8	2	apply	apply	VERB
ijassa-1405	8	3	the	the	DET
ijassa-1405	8	4	pairwise	pairwise	NOUN
ijassa-1405	8	5	similarity	similarity	NOUN
ijassa-1405	8	6	method	method	NOUN
ijassa-1405	8	7	to	to	ADP
ijassa-1405	8	8	two	two	NUM
ijassa-1405	8	9	discrete	discrete	ADJ
ijassa-1405	8	10	optimization	optimization	NOUN
ijassa-1405	8	11	problems	problem	NOUN
ijassa-1405	8	12	:	:	PUNCT
ijassa-1405	8	13	the	the	DET
ijassa-1405	8	14	majority	majority	NOUN
ijassa-1405	8	15	domination	domination	NOUN
ijassa-1405	8	16	problem	problem	NOUN
ijassa-1405	8	17	and	and	CCONJ
ijassa-1405	8	18	the	the	DET
ijassa-1405	8	19	maximum	maximum	ADJ
ijassa-1405	8	20	cut	cut	NOUN
ijassa-1405	8	21	problem	problem	NOUN
ijassa-1405	8	22	.	.	PUNCT
ijassa-1405	9	1	keywords	keyword	NOUN
ijassa-1405	9	2	:	:	PUNCT
ijassa-1405	9	3	pairwise	pairwise	NOUN
ijassa-1405	9	4	similarity	similarity	NOUN
ijassa-1405	9	5	method	method	NOUN
ijassa-1405	9	6	,	,	PUNCT
ijassa-1405	9	7	pairwise	pairwise	NOUN
ijassa-1405	9	8	dissimilarity	dissimilarity	NOUN
ijassa-1405	9	9	function	function	NOUN
ijassa-1405	9	10	,	,	PUNCT
ijassa-1405	9	11	discrete	discrete	ADJ
ijassa-1405	9	12	optimization	optimization	NOUN
ijassa-1405	9	13	,	,	PUNCT
ijassa-1405	9	14	np	np	NOUN
ijassa-1405	9	15	-	-	PUNCT
ijassa-1405	9	16	hard	hard	ADJ
ijassa-1405	9	17	problems	problem	NOUN
ijassa-1405	9	18	,	,	PUNCT
ijassa-1405	9	19	special	special	ADJ
ijassa-1405	9	20	case	case	NOUN
ijassa-1405	9	21	,	,	PUNCT
ijassa-1405	9	22	majority	majority	NOUN
ijassa-1405	9	23	domination	domination	NOUN
ijassa-1405	9	24	problem	problem	NOUN
ijassa-1405	9	25	,	,	PUNCT
ijassa-1405	9	26	maximum	maximum	ADJ
ijassa-1405	9	27	cut	cut	NOUN
ijassa-1405	9	28	problem	problem	NOUN
ijassa-1405	9	29	1	1	NUM
ijassa-1405	9	30	.	.	PUNCT
ijassa-1405	10	1	introduction	introduction	NOUN
ijassa-1405	10	2	the	the	DET
ijassa-1405	10	3	problem	problem	NOUN
ijassa-1405	10	4	of	of	ADP
ijassa-1405	10	5	np	np	NOUN
ijassa-1405	10	6	-	-	PUNCT
ijassa-1405	10	7	hardness	hardness	NOUN
ijassa-1405	10	8	is	be	AUX
ijassa-1405	10	9	related	relate	VERB
ijassa-1405	10	10	to	to	ADP
ijassa-1405	10	11	one	one	NUM
ijassa-1405	10	12	of	of	ADP
ijassa-1405	10	13	the	the	DET
ijassa-1405	10	14	key	key	ADJ
ijassa-1405	10	15	problems	problem	NOUN
ijassa-1405	10	16	of	of	ADP
ijassa-1405	10	17	theoretical	theoretical	ADJ
ijassa-1405	10	18	computer	computer	NOUN
ijassa-1405	10	19	science	science	NOUN
ijassa-1405	10	20	of	of	ADP
ijassa-1405	10	21	the	the	DET
ijassa-1405	10	22	relationship	relationship	NOUN
ijassa-1405	10	23	between	between	ADP
ijassa-1405	10	24	complexity	complexity	NOUN
ijassa-1405	10	25	classes	class	NOUN
ijassa-1405	10	26	p	p	NOUN
ijassa-1405	10	27	and	and	CCONJ
ijassa-1405	10	28	np	np	INTJ
ijassa-1405	10	29	.	.	PROPN
ijassa-1405	11	1	to	to	ADP
ijassa-1405	11	2	date	date	NOUN
ijassa-1405	11	3	,	,	PUNCT
ijassa-1405	11	4	there	there	PRON
ijassa-1405	11	5	is	be	VERB
ijassa-1405	11	6	no	no	DET
ijassa-1405	11	7	way	way	NOUN
ijassa-1405	11	8	to	to	PART
ijassa-1405	11	9	quantify	quantify	VERB
ijassa-1405	11	10	the	the	DET
ijassa-1405	11	11	complexity	complexity	NOUN
ijassa-1405	11	12	of	of	ADP
ijassa-1405	11	13	np	np	NOUN
ijassa-1405	11	14	-	-	PUNCT
ijassa-1405	11	15	hard	hard	ADJ
ijassa-1405	11	16	problems	problem	NOUN
ijassa-1405	11	17	.	.	PUNCT
ijassa-1405	12	1	analyzing	analyze	VERB
ijassa-1405	12	2	the	the	DET
ijassa-1405	12	3	behavior	behavior	NOUN
ijassa-1405	12	4	of	of	ADP
ijassa-1405	12	5	heuristic	heuristic	ADJ
ijassa-1405	12	6	algorithms	algorithm	NOUN
ijassa-1405	12	7	as	as	SCONJ
ijassa-1405	12	8	applied	apply	VERB
ijassa-1405	12	9	to	to	ADP
ijassa-1405	12	10	various	various	ADJ
ijassa-1405	12	11	problem	problem	NOUN
ijassa-1405	12	12	instances	instance	NOUN
ijassa-1405	12	13	leads	lead	VERB
ijassa-1405	12	14	to	to	ADP
ijassa-1405	12	15	the	the	DET
ijassa-1405	12	16	identification	identification	NOUN
ijassa-1405	12	17	of	of	ADP
ijassa-1405	12	18	patterns	pattern	NOUN
ijassa-1405	12	19	in	in	ADP
ijassa-1405	12	20	the	the	DET
ijassa-1405	12	21	data	datum	NOUN
ijassa-1405	12	22	.	.	PUNCT
ijassa-1405	13	1	studying	study	VERB
ijassa-1405	13	2	such	such	ADJ
ijassa-1405	13	3	patterns	pattern	NOUN
ijassa-1405	13	4	allows	allow	VERB
ijassa-1405	13	5	one	one	NUM
ijassa-1405	13	6	to	to	PART
ijassa-1405	13	7	gain	gain	VERB
ijassa-1405	13	8	insight	insight	NOUN
ijassa-1405	13	9	into	into	ADP
ijassa-1405	13	10	the	the	DET
ijassa-1405	13	11	complexity	complexity	NOUN
ijassa-1405	13	12	structure	structure	NOUN
ijassa-1405	13	13	of	of	ADP
ijassa-1405	13	14	np	np	NOUN
ijassa-1405	13	15	-	-	PUNCT
ijassa-1405	13	16	hard	hard	ADJ
ijassa-1405	13	17	problems	problem	NOUN
ijassa-1405	13	18	.	.	PUNCT
ijassa-1405	14	1	in	in	ADP
ijassa-1405	14	2	this	this	DET
ijassa-1405	14	3	paper	paper	NOUN
ijassa-1405	14	4	,	,	PUNCT
ijassa-1405	14	5	we	we	PRON
ijassa-1405	14	6	propose	propose	VERB
ijassa-1405	14	7	a	a	DET
ijassa-1405	14	8	general	general	ADJ
ijassa-1405	14	9	method	method	NOUN
ijassa-1405	14	10	for	for	ADP
ijassa-1405	14	11	estimating	estimate	VERB
ijassa-1405	14	12	the	the	DET
ijassa-1405	14	13	computational	computational	ADJ
ijassa-1405	14	14	complexity	complexity	NOUN
ijassa-1405	14	15	of	of	ADP
ijassa-1405	14	16	np	np	NOUN
ijassa-1405	14	17	-	-	PUNCT
ijassa-1405	14	18	hard	hard	ADJ
ijassa-1405	14	19	problems	problem	NOUN
ijassa-1405	14	20	based	base	VERB
ijassa-1405	14	21	on	on	ADP
ijassa-1405	14	22	comparing	compare	VERB
ijassa-1405	14	23	the	the	DET
ijassa-1405	14	24	problem	problem	NOUN
ijassa-1405	14	25	instances	instance	NOUN
ijassa-1405	14	26	using	use	VERB
ijassa-1405	14	27	a	a	DET
ijassa-1405	14	28	dissimilarity	dissimilarity	NOUN
ijassa-1405	14	29	function	function	NOUN
ijassa-1405	14	30	.	.	PUNCT
ijassa-1405	15	1	the	the	DET
ijassa-1405	15	2	proposed	propose	VERB
ijassa-1405	15	3	method	method	NOUN
ijassa-1405	15	4	is	be	AUX
ijassa-1405	15	5	based	base	VERB
ijassa-1405	15	6	on	on	ADP
ijassa-1405	15	7	the	the	DET
ijassa-1405	15	8	metric	metric	ADJ
ijassa-1405	15	9	approach	approach	NOUN
ijassa-1405	15	10	,	,	PUNCT
ijassa-1405	15	11	which	which	PRON
ijassa-1405	15	12	was	be	AUX
ijassa-1405	15	13	originally	originally	ADV
ijassa-1405	15	14	formulated	formulate	VERB
ijassa-1405	15	15	for	for	ADP
ijassa-1405	15	16	scheduling	scheduling	NOUN
ijassa-1405	15	17	problems	problem	NOUN
ijassa-1405	15	18	[	[	X
ijassa-1405	15	19	2	2	NUM
ijassa-1405	15	20	,	,	PUNCT
ijassa-1405	15	21	4	4	NUM
ijassa-1405	15	22	,	,	PUNCT
ijassa-1405	15	23	6	6	NUM
ijassa-1405	15	24	,	,	PUNCT
ijassa-1405	15	25	7	7	NUM
ijassa-1405	15	26	,	,	PUNCT
ijassa-1405	15	27	8	8	NUM
ijassa-1405	15	28	]	]	PUNCT
ijassa-1405	15	29	.	.	PUNCT
ijassa-1405	16	1	the	the	DET
ijassa-1405	16	2	metric	metric	ADJ
ijassa-1405	16	3	approach	approach	NOUN
ijassa-1405	16	4	was	be	AUX
ijassa-1405	16	5	tested	test	VERB
ijassa-1405	16	6	for	for	ADP
ijassa-1405	16	7	problem	problem	NOUN
ijassa-1405	16	8	instances	instance	NOUN
ijassa-1405	16	9	of	of	ADP
ijassa-1405	16	10	the	the	DET
ijassa-1405	16	11	same	same	ADJ
ijassa-1405	16	12	dimension	dimension	NOUN
ijassa-1405	16	13	without	without	ADP
ijassa-1405	16	14	taking	take	VERB
ijassa-1405	16	15	into	into	ADP
ijassa-1405	16	16	account	account	NOUN
ijassa-1405	16	17	the	the	DET
ijassa-1405	16	18	difference	difference	NOUN
ijassa-1405	16	19	in	in	ADP
ijassa-1405	16	20	the	the	DET
ijassa-1405	16	21	structure	structure	NOUN
ijassa-1405	16	22	of	of	ADP
ijassa-1405	16	23	the	the	DET
ijassa-1405	16	24	constraints	constraint	NOUN
ijassa-1405	16	25	.	.	PUNCT
ijassa-1405	17	1	first	first	ADV
ijassa-1405	17	2	,	,	PUNCT
ijassa-1405	17	3	instances	instance	NOUN
ijassa-1405	17	4	were	be	AUX
ijassa-1405	17	5	found	find	VERB
ijassa-1405	17	6	that	that	SCONJ
ijassa-1405	17	7	enables	enable	VERB
ijassa-1405	17	8	obtaining	obtain	VERB
ijassa-1405	17	9	an	an	DET
ijassa-1405	17	10	exact	exact	ADJ
ijassa-1405	17	11	solution	solution	NOUN
ijassa-1405	17	12	in	in	ADP
ijassa-1405	17	13	a	a	DET
ijassa-1405	17	14	reasonable	reasonable	ADJ
ijassa-1405	17	15	time	time	NOUN
ijassa-1405	17	16	.	.	PUNCT
ijassa-1405	18	1	to	to	PART
ijassa-1405	18	2	compare	compare	VERB
ijassa-1405	18	3	a	a	DET
ijassa-1405	18	4	general	general	ADJ
ijassa-1405	18	5	instance	instance	NOUN
ijassa-1405	18	6	with	with	ADP
ijassa-1405	18	7	such	such	DET
ijassa-1405	18	8	an	an	DET
ijassa-1405	18	9	instance	instance	NOUN
ijassa-1405	18	10	,	,	PUNCT
ijassa-1405	18	11	metrics	metric	NOUN
ijassa-1405	18	12	were	be	AUX
ijassa-1405	18	13	proposed	propose	VERB
ijassa-1405	18	14	that	that	PRON
ijassa-1405	18	15	evaluate	evaluate	VERB
ijassa-1405	18	16	the	the	DET
ijassa-1405	18	17	difference	difference	NOUN
ijassa-1405	18	18	between	between	ADP
ijassa-1405	18	19	the	the	DET
ijassa-1405	18	20	objective	objective	ADJ
ijassa-1405	18	21	functions	function	NOUN
ijassa-1405	18	22	of	of	ADP
ijassa-1405	18	23	those	those	DET
ijassa-1405	18	24	two	two	NUM
ijassa-1405	18	25	instances	instance	NOUN
ijassa-1405	18	26	.	.	PUNCT
ijassa-1405	19	1	an	an	DET
ijassa-1405	19	2	exact	exact	ADJ
ijassa-1405	19	3	solution	solution	NOUN
ijassa-1405	19	4	to	to	ADP
ijassa-1405	19	5	the	the	DET
ijassa-1405	19	6	first	first	ADJ
ijassa-1405	19	7	instance	instance	NOUN
ijassa-1405	19	8	induces	induce	VERB
ijassa-1405	19	9	an	an	DET
ijassa-1405	19	10	approximate	approximate	ADJ
ijassa-1405	19	11	solution	solution	NOUN
ijassa-1405	19	12	for	for	ADP
ijassa-1405	19	13	the	the	DET
ijassa-1405	19	14	second	second	ADJ
ijassa-1405	19	15	instance	instance	NOUN
ijassa-1405	19	16	and	and	CCONJ
ijassa-1405	19	17	the	the	DET
ijassa-1405	19	18	characteristics	characteristic	NOUN
ijassa-1405	19	19	of	of	ADP
ijassa-1405	19	20	the	the	DET
ijassa-1405	19	21	latter	latter	ADJ
ijassa-1405	19	22	solution	solution	NOUN
ijassa-1405	19	23	∗corresponding	∗corresponde	VERB
ijassa-1405	19	24	author	author	NOUN
ijassa-1405	19	25	:	:	PUNCT
ijassa-1405	19	26	darabbt@gmail.com	darabbt@gmail.com	X
ijassa-1405	19	27	pairwise	pairwise	NOUN
ijassa-1405	19	28	similarity	similarity	NOUN
ijassa-1405	19	29	estimation	estimation	NOUN
ijassa-1405	19	30	for	for	ADP
ijassa-1405	19	31	discrete	discrete	ADJ
ijassa-1405	19	32	optimization	optimization	NOUN
ijassa-1405	19	33	problems	problem	NOUN
ijassa-1405	19	34	165	165	NUM
ijassa-1405	19	35	have	have	AUX
ijassa-1405	19	36	been	be	AUX
ijassa-1405	19	37	assessed	assess	VERB
ijassa-1405	19	38	using	use	VERB
ijassa-1405	19	39	the	the	DET
ijassa-1405	19	40	above	above	ADJ
ijassa-1405	19	41	metrics	metric	NOUN
ijassa-1405	19	42	.	.	PUNCT
ijassa-1405	20	1	more	more	ADV
ijassa-1405	20	2	specifically	specifically	ADV
ijassa-1405	20	3	,	,	PUNCT
ijassa-1405	20	4	the	the	DET
ijassa-1405	20	5	metric	metric	NOUN
ijassa-1405	20	6	was	be	AUX
ijassa-1405	20	7	defined	define	VERB
ijassa-1405	20	8	as	as	ADP
ijassa-1405	20	9	the	the	DET
ijassa-1405	20	10	upper	upper	ADJ
ijassa-1405	20	11	bound	bind	VERB
ijassa-1405	20	12	for	for	ADP
ijassa-1405	20	13	the	the	DET
ijassa-1405	20	14	absolute	absolute	ADJ
ijassa-1405	20	15	error	error	NOUN
ijassa-1405	20	16	of	of	ADP
ijassa-1405	20	17	the	the	DET
ijassa-1405	20	18	approximate	approximate	ADJ
ijassa-1405	20	19	solution	solution	NOUN
ijassa-1405	20	20	.	.	PUNCT
ijassa-1405	21	1	computational	computational	ADJ
ijassa-1405	21	2	experiments	experiment	NOUN
ijassa-1405	21	3	for	for	ADP
ijassa-1405	21	4	solving	solve	VERB
ijassa-1405	21	5	some	some	DET
ijassa-1405	21	6	problems	problem	NOUN
ijassa-1405	21	7	of	of	ADP
ijassa-1405	21	8	scheduling	scheduling	NOUN
ijassa-1405	21	9	theory	theory	NOUN
ijassa-1405	21	10	by	by	ADP
ijassa-1405	21	11	approximate	approximate	ADJ
ijassa-1405	21	12	algorithms	algorithm	NOUN
ijassa-1405	21	13	in	in	ADP
ijassa-1405	21	14	polynomial	polynomial	ADJ
ijassa-1405	21	15	time	time	NOUN
ijassa-1405	21	16	have	have	AUX
ijassa-1405	21	17	shown	show	VERB
ijassa-1405	21	18	that	that	SCONJ
ijassa-1405	21	19	with	with	ADP
ijassa-1405	21	20	increasing	increase	VERB
ijassa-1405	21	21	dimension	dimension	NOUN
ijassa-1405	21	22	,	,	PUNCT
ijassa-1405	21	23	the	the	DET
ijassa-1405	21	24	upper	upper	ADJ
ijassa-1405	21	25	bound	bind	VERB
ijassa-1405	21	26	for	for	ADP
ijassa-1405	21	27	the	the	DET
ijassa-1405	21	28	relative	relative	ADJ
ijassa-1405	21	29	error	error	NOUN
ijassa-1405	21	30	of	of	ADP
ijassa-1405	21	31	the	the	DET
ijassa-1405	21	32	objective	objective	ADJ
ijassa-1405	21	33	function	function	NOUN
ijassa-1405	21	34	tends	tend	VERB
ijassa-1405	21	35	to	to	ADP
ijassa-1405	21	36	zero	zero	NUM
ijassa-1405	21	37	,	,	PUNCT
ijassa-1405	21	38	while	while	SCONJ
ijassa-1405	21	39	the	the	DET
ijassa-1405	21	40	proportion	proportion	NOUN
ijassa-1405	21	41	of	of	ADP
ijassa-1405	21	42	problems	problem	NOUN
ijassa-1405	21	43	that	that	PRON
ijassa-1405	21	44	can	can	AUX
ijassa-1405	21	45	be	be	AUX
ijassa-1405	21	46	solved	solve	VERB
ijassa-1405	21	47	exactly	exactly	ADV
ijassa-1405	21	48	in	in	ADP
ijassa-1405	21	49	polynomial	polynomial	ADJ
ijassa-1405	21	50	time	time	NOUN
ijassa-1405	21	51	tends	tend	VERB
ijassa-1405	21	52	to	to	PART
ijassa-1405	21	53	100	100	NUM
ijassa-1405	21	54	%	%	NOUN
ijassa-1405	21	55	.	.	PUNCT
ijassa-1405	22	1	this	this	PRON
ijassa-1405	22	2	means	mean	VERB
ijassa-1405	22	3	that	that	SCONJ
ijassa-1405	22	4	the	the	DET
ijassa-1405	22	5	proposed	propose	VERB
ijassa-1405	22	6	algorithms	algorithms	NOUN
ijassa-1405	22	7	can	can	AUX
ijassa-1405	22	8	be	be	AUX
ijassa-1405	22	9	effectively	effectively	ADV
ijassa-1405	22	10	used	use	VERB
ijassa-1405	22	11	for	for	ADP
ijassa-1405	22	12	most	most	ADJ
ijassa-1405	22	13	of	of	ADP
ijassa-1405	22	14	the	the	DET
ijassa-1405	22	15	instances	instance	NOUN
ijassa-1405	22	16	of	of	ADP
ijassa-1405	22	17	the	the	DET
ijassa-1405	22	18	problems	problem	NOUN
ijassa-1405	22	19	under	under	ADP
ijassa-1405	22	20	consideration	consideration	NOUN
ijassa-1405	22	21	.	.	PUNCT
ijassa-1405	23	1	this	this	PRON
ijassa-1405	23	2	made	make	VERB
ijassa-1405	23	3	it	it	PRON
ijassa-1405	23	4	possible	possible	ADJ
ijassa-1405	23	5	to	to	PART
ijassa-1405	23	6	obtain	obtain	VERB
ijassa-1405	23	7	exact	exact	ADJ
ijassa-1405	23	8	or	or	CCONJ
ijassa-1405	23	9	fairly	fairly	ADV
ijassa-1405	23	10	close	close	ADJ
ijassa-1405	23	11	to	to	ADP
ijassa-1405	23	12	exact	exact	ADJ
ijassa-1405	23	13	solutions	solution	NOUN
ijassa-1405	23	14	.	.	PUNCT
ijassa-1405	24	1	moreover	moreover	ADV
ijassa-1405	24	2	,	,	PUNCT
ijassa-1405	24	3	with	with	ADP
ijassa-1405	24	4	an	an	DET
ijassa-1405	24	5	increase	increase	NOUN
ijassa-1405	24	6	in	in	ADP
ijassa-1405	24	7	the	the	DET
ijassa-1405	24	8	dimension	dimension	NOUN
ijassa-1405	24	9	of	of	ADP
ijassa-1405	24	10	the	the	DET
ijassa-1405	24	11	problem	problem	NOUN
ijassa-1405	24	12	,	,	PUNCT
ijassa-1405	24	13	the	the	DET
ijassa-1405	24	14	proportion	proportion	NOUN
ijassa-1405	24	15	of	of	ADP
ijassa-1405	24	16	such	such	ADJ
ijassa-1405	24	17	instances	instance	NOUN
ijassa-1405	24	18	increases	increase	VERB
ijassa-1405	24	19	[	[	X
ijassa-1405	24	20	6	6	NUM
ijassa-1405	24	21	,	,	PUNCT
ijassa-1405	24	22	7	7	NUM
ijassa-1405	24	23	,	,	PUNCT
ijassa-1405	24	24	8	8	NUM
ijassa-1405	24	25	]	]	PUNCT
ijassa-1405	24	26	.	.	PUNCT
ijassa-1405	25	1	furthermore	furthermore	ADV
ijassa-1405	25	2	,	,	PUNCT
ijassa-1405	25	3	[	[	X
ijassa-1405	25	4	2	2	NUM
ijassa-1405	25	5	]	]	PUNCT
ijassa-1405	25	6	studied	study	VERB
ijassa-1405	25	7	the	the	DET
ijassa-1405	25	8	possibility	possibility	NOUN
ijassa-1405	25	9	of	of	ADP
ijassa-1405	25	10	finding	find	VERB
ijassa-1405	25	11	approximate	approximate	ADJ
ijassa-1405	25	12	schedules	schedule	NOUN
ijassa-1405	25	13	using	use	VERB
ijassa-1405	25	14	the	the	DET
ijassa-1405	25	15	metric	metric	ADJ
ijassa-1405	25	16	approach	approach	NOUN
ijassa-1405	25	17	for	for	ADP
ijassa-1405	25	18	an	an	DET
ijassa-1405	25	19	np	np	NOUN
ijassa-1405	25	20	-	-	PUNCT
ijassa-1405	25	21	complete	complete	ADJ
ijassa-1405	25	22	scheduling	scheduling	NOUN
ijassa-1405	25	23	problem	problem	NOUN
ijassa-1405	25	24	on	on	ADP
ijassa-1405	25	25	two	two	NUM
ijassa-1405	25	26	parallel	parallel	ADJ
ijassa-1405	25	27	identical	identical	ADJ
ijassa-1405	25	28	machines	machine	NOUN
ijassa-1405	25	29	with	with	ADP
ijassa-1405	25	30	priority	priority	NOUN
ijassa-1405	25	31	delays	delay	NOUN
ijassa-1405	25	32	for	for	ADP
ijassa-1405	25	33	jobs	job	NOUN
ijassa-1405	25	34	or	or	CCONJ
ijassa-1405	25	35	for	for	ADP
ijassa-1405	25	36	jobs	job	NOUN
ijassa-1405	25	37	of	of	ADP
ijassa-1405	25	38	length	length	NOUN
ijassa-1405	25	39	1	1	NUM
ijassa-1405	25	40	or	or	CCONJ
ijassa-1405	25	41	2	2	NUM
ijassa-1405	25	42	with	with	ADP
ijassa-1405	25	43	minimization	minimization	NOUN
ijassa-1405	25	44	of	of	ADP
ijassa-1405	25	45	execution	execution	NOUN
ijassa-1405	25	46	time	time	NOUN
ijassa-1405	25	47	.	.	PUNCT
ijassa-1405	26	1	an	an	DET
ijassa-1405	26	2	application	application	NOUN
ijassa-1405	26	3	of	of	ADP
ijassa-1405	26	4	these	these	DET
ijassa-1405	26	5	methods	method	NOUN
ijassa-1405	26	6	for	for	ADP
ijassa-1405	26	7	finding	find	VERB
ijassa-1405	26	8	the	the	DET
ijassa-1405	26	9	optimal	optimal	ADJ
ijassa-1405	26	10	solution	solution	NOUN
ijassa-1405	26	11	for	for	ADP
ijassa-1405	26	12	p2	p2	PROPN
ijassa-1405	26	13	|	|	ADV
ijassa-1405	26	14	pred	pre	VERB
ijassa-1405	26	15	,	,	PUNCT
ijassa-1405	26	16	pj	pj	PROPN
ijassa-1405	26	17	=	=	NOUN
ijassa-1405	26	18	1	1	NUM
ijassa-1405	26	19	|cmax	|cmax	NOUN
ijassa-1405	26	20	using	use	VERB
ijassa-1405	26	21	the	the	DET
ijassa-1405	26	22	coffman	coffman	PROPN
ijassa-1405	26	23	and	and	CCONJ
ijassa-1405	26	24	sethi	sethi	PROPN
ijassa-1405	26	25	algorithms	algorithm	NOUN
ijassa-1405	26	26	has	have	AUX
ijassa-1405	26	27	been	be	AUX
ijassa-1405	26	28	implemented	implement	VERB
ijassa-1405	26	29	.	.	PUNCT
ijassa-1405	27	1	in	in	ADP
ijassa-1405	27	2	[	[	X
ijassa-1405	27	3	4	4	NUM
ijassa-1405	27	4	]	]	PUNCT
ijassa-1405	27	5	,	,	PUNCT
ijassa-1405	27	6	the	the	DET
ijassa-1405	27	7	metric	metric	ADJ
ijassa-1405	27	8	approach	approach	NOUN
ijassa-1405	27	9	was	be	AUX
ijassa-1405	27	10	developed	develop	VERB
ijassa-1405	27	11	for	for	ADP
ijassa-1405	27	12	planning	plan	VERB
ijassa-1405	27	13	a	a	DET
ijassa-1405	27	14	two	two	NUM
ijassa-1405	27	15	-	-	PUNCT
ijassa-1405	27	16	station	station	NOUN
ijassa-1405	27	17	single	single	ADJ
ijassa-1405	27	18	-	-	PUNCT
ijassa-1405	27	19	track	track	NOUN
ijassa-1405	27	20	railway	railway	NOUN
ijassa-1405	27	21	.	.	PUNCT
ijassa-1405	28	1	new	new	ADJ
ijassa-1405	28	2	metrics	metric	NOUN
ijassa-1405	28	3	were	be	AUX
ijassa-1405	28	4	proposed	propose	VERB
ijassa-1405	28	5	and	and	CCONJ
ijassa-1405	28	6	computational	computational	ADJ
ijassa-1405	28	7	tests	test	NOUN
ijassa-1405	28	8	were	be	AUX
ijassa-1405	28	9	carried	carry	VERB
ijassa-1405	28	10	out	out	ADP
ijassa-1405	28	11	.	.	PUNCT
ijassa-1405	29	1	the	the	DET
ijassa-1405	29	2	pairwise	pairwise	NOUN
ijassa-1405	29	3	similarity	similarity	NOUN
ijassa-1405	29	4	method	method	NOUN
ijassa-1405	29	5	generalizes	generalize	VERB
ijassa-1405	29	6	the	the	DET
ijassa-1405	29	7	metric	metric	ADJ
ijassa-1405	29	8	approach	approach	NOUN
ijassa-1405	29	9	.	.	PUNCT
ijassa-1405	30	1	it	it	PRON
ijassa-1405	30	2	allows	allow	VERB
ijassa-1405	30	3	for	for	ADP
ijassa-1405	30	4	different	different	ADJ
ijassa-1405	30	5	structures	structure	NOUN
ijassa-1405	30	6	of	of	ADP
ijassa-1405	30	7	instances	instance	NOUN
ijassa-1405	30	8	and	and	CCONJ
ijassa-1405	30	9	involves	involve	VERB
ijassa-1405	30	10	pairwise	pairwise	NOUN
ijassa-1405	30	11	dissimilarity	dissimilarity	NOUN
ijassa-1405	30	12	functions	function	NOUN
ijassa-1405	30	13	for	for	ADP
ijassa-1405	30	14	which	which	DET
ijassa-1405	30	15	satisfaction	satisfaction	NOUN
ijassa-1405	30	16	of	of	ADP
ijassa-1405	30	17	the	the	DET
ijassa-1405	30	18	axioms	axiom	NOUN
ijassa-1405	30	19	of	of	ADP
ijassa-1405	30	20	metric	metric	ADJ
ijassa-1405	30	21	is	be	AUX
ijassa-1405	30	22	not	not	PART
ijassa-1405	30	23	required	require	VERB
ijassa-1405	30	24	.	.	PUNCT
ijassa-1405	31	1	this	this	DET
ijassa-1405	31	2	paper	paper	NOUN
ijassa-1405	31	3	proposes	propose	VERB
ijassa-1405	31	4	a	a	DET
ijassa-1405	31	5	general	general	ADJ
ijassa-1405	31	6	method	method	NOUN
ijassa-1405	31	7	for	for	ADP
ijassa-1405	31	8	assessing	assess	VERB
ijassa-1405	31	9	heuristics	heuristic	NOUN
ijassa-1405	31	10	called	call	VERB
ijassa-1405	31	11	the	the	DET
ijassa-1405	31	12	pairwise	pairwise	NOUN
ijassa-1405	31	13	similarity	similarity	NOUN
ijassa-1405	31	14	method	method	NOUN
ijassa-1405	31	15	.	.	PUNCT
ijassa-1405	32	1	it	it	PRON
ijassa-1405	32	2	is	be	AUX
ijassa-1405	32	3	applied	apply	VERB
ijassa-1405	32	4	to	to	ADP
ijassa-1405	32	5	two	two	NUM
ijassa-1405	32	6	discrete	discrete	ADJ
ijassa-1405	32	7	optimization	optimization	NOUN
ijassa-1405	32	8	problems	problem	NOUN
ijassa-1405	32	9	:	:	PUNCT
ijassa-1405	32	10	the	the	DET
ijassa-1405	32	11	problem	problem	NOUN
ijassa-1405	32	12	of	of	ADP
ijassa-1405	32	13	majority	majority	NOUN
ijassa-1405	32	14	domination	domination	NOUN
ijassa-1405	32	15	on	on	ADP
ijassa-1405	32	16	graphs	graph	NOUN
ijassa-1405	32	17	with	with	ADP
ijassa-1405	32	18	a	a	DET
ijassa-1405	32	19	limited	limited	ADJ
ijassa-1405	32	20	degree	degree	NOUN
ijassa-1405	32	21	of	of	ADP
ijassa-1405	32	22	vertices	vertex	NOUN
ijassa-1405	32	23	and	and	CCONJ
ijassa-1405	32	24	the	the	DET
ijassa-1405	32	25	maximum	maximum	ADJ
ijassa-1405	32	26	cut	cut	NOUN
ijassa-1405	32	27	problem	problem	NOUN
ijassa-1405	32	28	.	.	PUNCT
ijassa-1405	33	1	the	the	DET
ijassa-1405	33	2	focus	focus	NOUN
ijassa-1405	33	3	is	be	AUX
ijassa-1405	33	4	on	on	ADP
ijassa-1405	33	5	finding	find	VERB
ijassa-1405	33	6	instances	instance	NOUN
ijassa-1405	33	7	with	with	ADP
ijassa-1405	33	8	the	the	DET
ijassa-1405	33	9	required	required	ADJ
ijassa-1405	33	10	characteristics	characteristic	NOUN
ijassa-1405	33	11	and	and	CCONJ
ijassa-1405	33	12	using	use	VERB
ijassa-1405	33	13	them	they	PRON
ijassa-1405	33	14	to	to	PART
ijassa-1405	33	15	obtain	obtain	VERB
ijassa-1405	33	16	efficient	efficient	ADJ
ijassa-1405	33	17	solutions	solution	NOUN
ijassa-1405	33	18	for	for	ADP
ijassa-1405	33	19	other	other	ADJ
ijassa-1405	33	20	instances	instance	NOUN
ijassa-1405	33	21	.	.	PUNCT
ijassa-1405	34	1	relations	relation	NOUN
ijassa-1405	34	2	are	be	AUX
ijassa-1405	34	3	established	establish	VERB
ijassa-1405	34	4	between	between	ADP
ijassa-1405	34	5	the	the	DET
ijassa-1405	34	6	change	change	NOUN
ijassa-1405	34	7	in	in	ADP
ijassa-1405	34	8	the	the	DET
ijassa-1405	34	9	value	value	NOUN
ijassa-1405	34	10	of	of	ADP
ijassa-1405	34	11	the	the	DET
ijassa-1405	34	12	objective	objective	ADJ
ijassa-1405	34	13	function	function	NOUN
ijassa-1405	34	14	and	and	CCONJ
ijassa-1405	34	15	the	the	DET
ijassa-1405	34	16	difference	difference	NOUN
ijassa-1405	34	17	between	between	ADP
ijassa-1405	34	18	the	the	DET
ijassa-1405	34	19	graphs	graph	NOUN
ijassa-1405	34	20	of	of	ADP
ijassa-1405	34	21	the	the	DET
ijassa-1405	34	22	problems	problem	NOUN
ijassa-1405	34	23	under	under	ADP
ijassa-1405	34	24	consideration	consideration	NOUN
ijassa-1405	34	25	.	.	PUNCT
ijassa-1405	35	1	the	the	DET
ijassa-1405	35	2	structure	structure	NOUN
ijassa-1405	35	3	of	of	ADP
ijassa-1405	35	4	the	the	DET
ijassa-1405	35	5	paper	paper	NOUN
ijassa-1405	35	6	is	be	AUX
ijassa-1405	35	7	as	as	SCONJ
ijassa-1405	35	8	follows	follow	VERB
ijassa-1405	35	9	.	.	PUNCT
ijassa-1405	36	1	section	section	NOUN
ijassa-1405	36	2	2	2	NUM
ijassa-1405	36	3	introduces	introduce	VERB
ijassa-1405	36	4	the	the	DET
ijassa-1405	36	5	pairwise	pairwise	NOUN
ijassa-1405	36	6	similarity	similarity	NOUN
ijassa-1405	36	7	method	method	NOUN
ijassa-1405	36	8	and	and	CCONJ
ijassa-1405	36	9	describes	describe	VERB
ijassa-1405	36	10	the	the	DET
ijassa-1405	36	11	algorithms	algorithm	NOUN
ijassa-1405	36	12	that	that	PRON
ijassa-1405	36	13	make	make	VERB
ijassa-1405	36	14	it	it	PRON
ijassa-1405	36	15	up	up	ADP
ijassa-1405	36	16	.	.	PUNCT
ijassa-1405	37	1	in	in	ADP
ijassa-1405	37	2	section	section	NOUN
ijassa-1405	37	3	3.1	3.1	NUM
ijassa-1405	37	4	,	,	PUNCT
ijassa-1405	37	5	the	the	DET
ijassa-1405	37	6	pairwise	pairwise	NOUN
ijassa-1405	37	7	similarity	similarity	NOUN
ijassa-1405	37	8	method	method	NOUN
ijassa-1405	37	9	is	be	AUX
ijassa-1405	37	10	applied	apply	VERB
ijassa-1405	37	11	for	for	ADP
ijassa-1405	37	12	finding	find	VERB
ijassa-1405	37	13	the	the	DET
ijassa-1405	37	14	strict	strict	ADJ
ijassa-1405	37	15	majority	majority	NOUN
ijassa-1405	37	16	domination	domination	NOUN
ijassa-1405	37	17	number	number	NOUN
ijassa-1405	37	18	in	in	ADP
ijassa-1405	37	19	a	a	DET
ijassa-1405	37	20	graph	graph	NOUN
ijassa-1405	37	21	with	with	ADP
ijassa-1405	37	22	cycles	cycle	NOUN
ijassa-1405	37	23	in	in	ADP
ijassa-1405	37	24	the	the	DET
ijassa-1405	37	25	framework	framework	NOUN
ijassa-1405	37	26	of	of	ADP
ijassa-1405	37	27	a	a	DET
ijassa-1405	37	28	two	two	NUM
ijassa-1405	37	29	-	-	PUNCT
ijassa-1405	37	30	level	level	NOUN
ijassa-1405	37	31	voting	voting	NOUN
ijassa-1405	37	32	model	model	NOUN
ijassa-1405	37	33	.	.	PUNCT
ijassa-1405	38	1	in	in	ADP
ijassa-1405	38	2	particular	particular	ADJ
ijassa-1405	38	3	,	,	PUNCT
ijassa-1405	38	4	it	it	PRON
ijassa-1405	38	5	is	be	AUX
ijassa-1405	38	6	proved	prove	VERB
ijassa-1405	38	7	that	that	SCONJ
ijassa-1405	38	8	graphs	graph	NOUN
ijassa-1405	38	9	with	with	ADP
ijassa-1405	38	10	a	a	DET
ijassa-1405	38	11	limited	limited	ADJ
ijassa-1405	38	12	cyclomatic	cyclomatic	ADJ
ijassa-1405	38	13	number	number	NOUN
ijassa-1405	38	14	form	form	VERB
ijassa-1405	38	15	a	a	DET
ijassa-1405	38	16	“	"	PUNCT
ijassa-1405	38	17	semisimple	semisimple	ADJ
ijassa-1405	38	18	”	"	PUNCT
ijassa-1405	38	19	special	special	ADJ
ijassa-1405	38	20	case	case	NOUN
ijassa-1405	38	21	,	,	PUNCT
ijassa-1405	38	22	a	a	DET
ijassa-1405	38	23	pairwise	pairwise	NOUN
ijassa-1405	38	24	dissimilarity	dissimilarity	NOUN
ijassa-1405	38	25	function	function	NOUN
ijassa-1405	38	26	is	be	AUX
ijassa-1405	38	27	introduced	introduce	VERB
ijassa-1405	38	28	for	for	ADP
ijassa-1405	38	29	them	they	PRON
ijassa-1405	38	30	,	,	PUNCT
ijassa-1405	38	31	and	and	CCONJ
ijassa-1405	38	32	an	an	DET
ijassa-1405	38	33	approximate	approximate	ADJ
ijassa-1405	38	34	algorithm	algorithm	NOUN
ijassa-1405	38	35	of	of	ADP
ijassa-1405	38	36	polynomial	polynomial	ADJ
ijassa-1405	38	37	complexity	complexity	NOUN
ijassa-1405	38	38	is	be	AUX
ijassa-1405	38	39	constructed	construct	VERB
ijassa-1405	38	40	that	that	PRON
ijassa-1405	38	41	has	have	VERB
ijassa-1405	38	42	a	a	DET
ijassa-1405	38	43	guaranteed	guarantee	VERB
ijassa-1405	38	44	bound	bind	VERB
ijassa-1405	38	45	for	for	ADP
ijassa-1405	38	46	the	the	DET
ijassa-1405	38	47	absolute	absolute	ADJ
ijassa-1405	38	48	error	error	NOUN
ijassa-1405	38	49	of	of	ADP
ijassa-1405	38	50	the	the	DET
ijassa-1405	38	51	objective	objective	ADJ
ijassa-1405	38	52	function	function	NOUN
ijassa-1405	38	53	.	.	PUNCT
ijassa-1405	39	1	in	in	ADP
ijassa-1405	39	2	section	section	NOUN
ijassa-1405	39	3	3.2	3.2	NUM
ijassa-1405	39	4	,	,	PUNCT
ijassa-1405	39	5	the	the	DET
ijassa-1405	39	6	pairwise	pairwise	NOUN
ijassa-1405	39	7	similarity	similarity	NOUN
ijassa-1405	39	8	method	method	NOUN
ijassa-1405	39	9	is	be	AUX
ijassa-1405	39	10	applied	apply	VERB
ijassa-1405	39	11	to	to	ADP
ijassa-1405	39	12	the	the	DET
ijassa-1405	39	13	maximum	maximum	ADJ
ijassa-1405	39	14	cut	cut	NOUN
ijassa-1405	39	15	problem	problem	NOUN
ijassa-1405	39	16	in	in	ADP
ijassa-1405	39	17	the	the	DET
ijassa-1405	39	18	case	case	NOUN
ijassa-1405	39	19	where	where	SCONJ
ijassa-1405	39	20	it	it	PRON
ijassa-1405	39	21	is	be	AUX
ijassa-1405	39	22	difficult	difficult	ADJ
ijassa-1405	39	23	to	to	PART
ijassa-1405	39	24	analytically	analytically	ADV
ijassa-1405	39	25	obtain	obtain	VERB
ijassa-1405	39	26	an	an	DET
ijassa-1405	39	27	absolute	absolute	ADJ
ijassa-1405	39	28	upper	upper	ADJ
ijassa-1405	39	29	bound	bind	VERB
ijassa-1405	39	30	for	for	ADP
ijassa-1405	39	31	the	the	DET
ijassa-1405	39	32	error	error	NOUN
ijassa-1405	39	33	and	and	CCONJ
ijassa-1405	39	34	the	the	DET
ijassa-1405	39	35	estimates	estimate	NOUN
ijassa-1405	39	36	are	be	AUX
ijassa-1405	39	37	based	base	VERB
ijassa-1405	39	38	on	on	ADP
ijassa-1405	39	39	numerical	numerical	PROPN
ijassa-1405	39	40	simulation	simulation	PROPN
ijassa-1405	39	41	.	.	PUNCT
ijassa-1405	40	1	in	in	ADP
ijassa-1405	40	2	conclusion	conclusion	NOUN
ijassa-1405	40	3	,	,	PUNCT
ijassa-1405	40	4	a	a	DET
ijassa-1405	40	5	research	research	NOUN
ijassa-1405	40	6	program	program	NOUN
ijassa-1405	40	7	for	for	ADP
ijassa-1405	40	8	further	further	ADJ
ijassa-1405	40	9	study	study	NOUN
ijassa-1405	40	10	of	of	ADP
ijassa-1405	40	11	the	the	DET
ijassa-1405	40	12	proposed	propose	VERB
ijassa-1405	40	13	method	method	NOUN
ijassa-1405	40	14	is	be	AUX
ijassa-1405	40	15	outlined	outline	VERB
ijassa-1405	40	16	.	.	PUNCT
ijassa-1405	41	1	2	2	X
ijassa-1405	41	2	.	.	X
ijassa-1405	41	3	pairwise	pairwise	NOUN
ijassa-1405	41	4	similarity	similarity	NOUN
ijassa-1405	41	5	method	method	NOUN
ijassa-1405	41	6	we	we	PRON
ijassa-1405	41	7	first	first	ADV
ijassa-1405	41	8	introduce	introduce	VERB
ijassa-1405	41	9	the	the	DET
ijassa-1405	41	10	formal	formal	ADJ
ijassa-1405	41	11	definitions	definition	NOUN
ijassa-1405	41	12	needed	need	VERB
ijassa-1405	41	13	to	to	PART
ijassa-1405	41	14	construct	construct	VERB
ijassa-1405	41	15	the	the	DET
ijassa-1405	41	16	pairwise	pairwise	NOUN
ijassa-1405	41	17	similarity	similarity	NOUN
ijassa-1405	41	18	method	method	NOUN
ijassa-1405	41	19	.	.	PUNCT
ijassa-1405	42	1	definition	definition	NOUN
ijassa-1405	42	2	2.1	2.1	NUM
ijassa-1405	42	3	.	.	PUNCT
ijassa-1405	43	1	for	for	ADP
ijassa-1405	43	2	an	an	DET
ijassa-1405	43	3	np	np	NOUN
ijassa-1405	43	4	-	-	PUNCT
ijassa-1405	43	5	hard	hard	ADJ
ijassa-1405	43	6	problem	problem	NOUN
ijassa-1405	43	7	p	p	NOUN
ijassa-1405	43	8	and	and	CCONJ
ijassa-1405	43	9	a	a	DET
ijassa-1405	43	10	pattern	pattern	NOUN
ijassa-1405	43	11	α	α	NOUN
ijassa-1405	43	12	,	,	PUNCT
ijassa-1405	43	13	the	the	DET
ijassa-1405	43	14	special	special	ADJ
ijassa-1405	43	15	case	case	NOUN
ijassa-1405	43	16	pα	pα	INTJ
ijassa-1405	43	17	is	be	AUX
ijassa-1405	43	18	the	the	DET
ijassa-1405	43	19	subclass	subclass	NOUN
ijassa-1405	43	20	of	of	ADP
ijassa-1405	43	21	p	p	NOUN
ijassa-1405	43	22	comprising	comprise	VERB
ijassa-1405	43	23	all	all	DET
ijassa-1405	43	24	instances	instance	NOUN
ijassa-1405	43	25	a	a	DET
ijassa-1405	43	26	∈	∈	NOUN
ijassa-1405	43	27	pα	pα	NOUN
ijassa-1405	43	28	that	that	PRON
ijassa-1405	43	29	satisfy	satisfy	VERB
ijassa-1405	44	1	α	α	PROPN
ijassa-1405	44	2	.	.	PUNCT
ijassa-1405	45	1	definition	definition	NOUN
ijassa-1405	45	2	2.2	2.2	NUM
ijassa-1405	45	3	.	.	PUNCT
ijassa-1405	46	1	a	a	DET
ijassa-1405	46	2	simple	simple	ADJ
ijassa-1405	46	3	special	special	ADJ
ijassa-1405	46	4	case	case	NOUN
ijassa-1405	46	5	pα	pα	INTJ
ijassa-1405	46	6	simple	simple	ADJ
ijassa-1405	46	7	is	be	AUX
ijassa-1405	46	8	a	a	DET
ijassa-1405	46	9	special	special	ADJ
ijassa-1405	46	10	case	case	NOUN
ijassa-1405	46	11	for	for	ADP
ijassa-1405	46	12	which	which	PRON
ijassa-1405	46	13	there	there	PRON
ijassa-1405	46	14	is	be	VERB
ijassa-1405	46	15	a	a	DET
ijassa-1405	46	16	polynomial	polynomial	ADJ
ijassa-1405	46	17	(	(	PUNCT
ijassa-1405	46	18	or	or	CCONJ
ijassa-1405	46	19	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	46	20	)	)	PUNCT
ijassa-1405	46	21	algorithm	algorithm	NOUN
ijassa-1405	46	22	that	that	PRON
ijassa-1405	46	23	finds	find	VERB
ijassa-1405	46	24	the	the	DET
ijassa-1405	46	25	exact	exact	ADJ
ijassa-1405	46	26	solution	solution	NOUN
ijassa-1405	46	27	for	for	ADP
ijassa-1405	46	28	all	all	DET
ijassa-1405	46	29	instances	instance	NOUN
ijassa-1405	46	30	a	a	DET
ijassa-1405	46	31	∈	∈	NOUN
ijassa-1405	46	32	pα	pα	NOUN
ijassa-1405	46	33	simple	simple	NOUN
ijassa-1405	46	34	.	.	PUNCT
ijassa-1405	47	1	definition	definition	NOUN
ijassa-1405	47	2	2.3	2.3	NUM
ijassa-1405	47	3	.	.	PUNCT
ijassa-1405	48	1	a	a	DET
ijassa-1405	48	2	semisimple	semisimple	ADJ
ijassa-1405	48	3	special	special	ADJ
ijassa-1405	48	4	case	case	NOUN
ijassa-1405	48	5	pα	pα	INTJ
ijassa-1405	48	6	ssimple	ssimple	ADJ
ijassa-1405	48	7	is	be	AUX
ijassa-1405	48	8	a	a	DET
ijassa-1405	48	9	special	special	ADJ
ijassa-1405	48	10	case	case	NOUN
ijassa-1405	48	11	for	for	ADP
ijassa-1405	48	12	which	which	PRON
ijassa-1405	48	13	there	there	PRON
ijassa-1405	48	14	is	be	VERB
ijassa-1405	48	15	a	a	DET
ijassa-1405	48	16	polynomial	polynomial	ADJ
ijassa-1405	48	17	(	(	PUNCT
ijassa-1405	48	18	or	or	CCONJ
ijassa-1405	48	19	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	48	20	)	)	PUNCT
ijassa-1405	48	21	algorithm	algorithm	NOUN
ijassa-1405	48	22	that	that	PRON
ijassa-1405	48	23	finds	find	VERB
ijassa-1405	48	24	an	an	DET
ijassa-1405	48	25	approximate	approximate	ADJ
ijassa-1405	48	26	solution	solution	NOUN
ijassa-1405	48	27	with	with	ADP
ijassa-1405	48	28	a	a	DET
ijassa-1405	48	29	guaranteed	guarantee	VERB
ijassa-1405	48	30	error	error	NOUN
ijassa-1405	48	31	for	for	ADP
ijassa-1405	48	32	all	all	DET
ijassa-1405	48	33	instances	instance	NOUN
ijassa-1405	48	34	a	a	DET
ijassa-1405	48	35	∈	∈	NOUN
ijassa-1405	48	36	pα	pα	INTJ
ijassa-1405	48	37	ssimple	ssimple	ADJ
ijassa-1405	48	38	.	.	PUNCT
ijassa-1405	49	1	definition	definition	NOUN
ijassa-1405	49	2	2.4	2.4	NUM
ijassa-1405	49	3	.	.	PUNCT
ijassa-1405	50	1	a	a	DET
ijassa-1405	50	2	numerical	numerical	ADJ
ijassa-1405	50	3	special	special	ADJ
ijassa-1405	50	4	case	case	NOUN
ijassa-1405	50	5	pα	pα	INTJ
ijassa-1405	50	6	num	num	ADJ
ijassa-1405	50	7	is	be	AUX
ijassa-1405	50	8	a	a	DET
ijassa-1405	50	9	special	special	ADJ
ijassa-1405	50	10	case	case	NOUN
ijassa-1405	50	11	for	for	ADP
ijassa-1405	50	12	which	which	PRON
ijassa-1405	50	13	there	there	PRON
ijassa-1405	50	14	exist	exist	VERB
ijassa-1405	50	15	a	a	DET
ijassa-1405	50	16	polynomial	polynomial	ADJ
ijassa-1405	50	17	(	(	PUNCT
ijassa-1405	50	18	or	or	CCONJ
ijassa-1405	50	19	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	50	20	)	)	PUNCT
ijassa-1405	50	21	algorithm	algorithm	NOUN
ijassa-1405	50	22	and	and	CCONJ
ijassa-1405	50	23	an	an	DET
ijassa-1405	50	24	error	error	NOUN
ijassa-1405	50	25	estimate	estimate	NOUN
ijassa-1405	50	26	such	such	ADJ
ijassa-1405	50	27	that	that	SCONJ
ijassa-1405	50	28	this	this	DET
ijassa-1405	50	29	estimate	estimate	NOUN
ijassa-1405	50	30	for	for	ADP
ijassa-1405	50	31	the	the	DET
ijassa-1405	50	32	algorithm	algorithm	NOUN
ijassa-1405	50	33	is	be	AUX
ijassa-1405	50	34	not	not	PART
ijassa-1405	50	35	proved	prove	VERB
ijassa-1405	50	36	analytically	analytically	ADV
ijassa-1405	50	37	,	,	PUNCT
ijassa-1405	50	38	but	but	CCONJ
ijassa-1405	50	39	is	be	AUX
ijassa-1405	50	40	confirmed	confirm	VERB
ijassa-1405	50	41	by	by	ADP
ijassa-1405	50	42	numerical	numerical	ADJ
ijassa-1405	50	43	experiments	experiment	NOUN
ijassa-1405	50	44	on	on	ADP
ijassa-1405	50	45	pα	pα	PROPN
ijassa-1405	50	46	num	num	PROPN
ijassa-1405	50	47	.	.	PUNCT
ijassa-1405	51	1	copyright	copyright	NOUN
ijassa-1405	51	2	©	©	PROPN
ijassa-1405	51	3	2023	2023	NUM
ijassa-1405	51	4	assa	assa	NOUN
ijassa-1405	51	5	.	.	PUNCT
ijassa-1405	52	1	adv	adv	PROPN
ijassa-1405	52	2	syst	syst	PROPN
ijassa-1405	52	3	sci	sci	PROPN
ijassa-1405	52	4	appl	appl	PROPN
ijassa-1405	52	5	(	(	PUNCT
ijassa-1405	52	6	2023	2023	NUM
ijassa-1405	52	7	)	)	PUNCT
ijassa-1405	52	8	166	166	NUM
ijassa-1405	52	9	d.	d.	PROPN
ijassa-1405	52	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	52	11	,	,	PUNCT
ijassa-1405	52	12	p.	p.	PROPN
ijassa-1405	52	13	chebotarev	chebotarev	PROPN
ijassa-1405	52	14	,	,	PUNCT
ijassa-1405	52	15	m.	m.	NOUN
ijassa-1405	52	16	goubko	goubko	NOUN
ijassa-1405	52	17	,	,	PUNCT
ijassa-1405	52	18	m.	m.	NOUN
ijassa-1405	52	19	somov	somov	PROPN
ijassa-1405	52	20	,	,	PUNCT
ijassa-1405	52	21	n.	n.	PROPN
ijassa-1405	52	22	shushko	shushko	PROPN
ijassa-1405	52	23	definition	definition	NOUN
ijassa-1405	52	24	2.5	2.5	NUM
ijassa-1405	52	25	.	.	PUNCT
ijassa-1405	53	1	a	a	DET
ijassa-1405	53	2	hard	hard	ADJ
ijassa-1405	53	3	special	special	ADJ
ijassa-1405	53	4	case	case	NOUN
ijassa-1405	53	5	pα	pα	INTJ
ijassa-1405	53	6	hard	hard	ADV
ijassa-1405	53	7	is	be	AUX
ijassa-1405	53	8	a	a	DET
ijassa-1405	53	9	special	special	ADJ
ijassa-1405	53	10	case	case	NOUN
ijassa-1405	53	11	for	for	ADP
ijassa-1405	53	12	which	which	PRON
ijassa-1405	53	13	there	there	PRON
ijassa-1405	53	14	is	be	VERB
ijassa-1405	53	15	no	no	DET
ijassa-1405	53	16	polynomial	polynomial	ADJ
ijassa-1405	53	17	(	(	PUNCT
ijassa-1405	53	18	or	or	CCONJ
ijassa-1405	53	19	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	53	20	)	)	PUNCT
ijassa-1405	53	21	algorithm	algorithm	NOUN
ijassa-1405	53	22	that	that	PRON
ijassa-1405	53	23	finds	find	VERB
ijassa-1405	53	24	exact	exact	ADJ
ijassa-1405	53	25	solutions	solution	NOUN
ijassa-1405	53	26	for	for	ADP
ijassa-1405	53	27	all	all	DET
ijassa-1405	53	28	instances	instance	NOUN
ijassa-1405	53	29	a	a	DET
ijassa-1405	53	30	∈	∈	NOUN
ijassa-1405	53	31	pα	pα	NOUN
ijassa-1405	53	32	hard	hard	ADV
ijassa-1405	53	33	.	.	PUNCT
ijassa-1405	54	1	in	in	ADP
ijassa-1405	54	2	what	what	PRON
ijassa-1405	54	3	follows	follow	VERB
ijassa-1405	54	4	,	,	PUNCT
ijassa-1405	54	5	by	by	ADP
ijassa-1405	54	6	special	special	ADJ
ijassa-1405	54	7	cases	case	NOUN
ijassa-1405	54	8	,	,	PUNCT
ijassa-1405	54	9	unless	unless	SCONJ
ijassa-1405	54	10	otherwise	otherwise	ADV
ijassa-1405	54	11	indicated	indicate	VERB
ijassa-1405	54	12	,	,	PUNCT
ijassa-1405	54	13	we	we	PRON
ijassa-1405	54	14	mean	mean	VERB
ijassa-1405	54	15	simple	simple	ADJ
ijassa-1405	54	16	,	,	PUNCT
ijassa-1405	54	17	semisimple	semisimple	NOUN
ijassa-1405	54	18	,	,	PUNCT
ijassa-1405	54	19	or	or	CCONJ
ijassa-1405	54	20	numerically	numerically	ADV
ijassa-1405	54	21	simple	simple	ADJ
ijassa-1405	54	22	special	special	ADJ
ijassa-1405	54	23	cases	case	NOUN
ijassa-1405	54	24	.	.	PUNCT
ijassa-1405	55	1	we	we	PRON
ijassa-1405	55	2	now	now	ADV
ijassa-1405	55	3	define	define	VERB
ijassa-1405	55	4	the	the	DET
ijassa-1405	55	5	pairwise	pairwise	NOUN
ijassa-1405	55	6	dissimilarity	dissimilarity	NOUN
ijassa-1405	55	7	function	function	NOUN
ijassa-1405	55	8	.	.	PUNCT
ijassa-1405	56	1	definition	definition	NOUN
ijassa-1405	56	2	2.6	2.6	NUM
ijassa-1405	56	3	.	.	PUNCT
ijassa-1405	57	1	a	a	DET
ijassa-1405	57	2	pairwise	pairwise	NOUN
ijassa-1405	57	3	dissimilarity	dissimilarity	NOUN
ijassa-1405	57	4	function	function	NOUN
ijassa-1405	57	5	is	be	AUX
ijassa-1405	57	6	a	a	DET
ijassa-1405	57	7	function	function	NOUN
ijassa-1405	57	8	that	that	PRON
ijassa-1405	57	9	measures	measure	VERB
ijassa-1405	57	10	the	the	DET
ijassa-1405	57	11	difference	difference	NOUN
ijassa-1405	57	12	between	between	ADP
ijassa-1405	57	13	instances	instance	NOUN
ijassa-1405	57	14	according	accord	VERB
ijassa-1405	57	15	to	to	ADP
ijassa-1405	57	16	some	some	DET
ijassa-1405	57	17	criterion	criterion	NOUN
ijassa-1405	57	18	.	.	PUNCT
ijassa-1405	58	1	given	give	VERB
ijassa-1405	58	2	a	a	DET
ijassa-1405	58	3	simple	simple	ADJ
ijassa-1405	58	4	special	special	ADJ
ijassa-1405	58	5	case	case	NOUN
ijassa-1405	58	6	pα	pα	INTJ
ijassa-1405	58	7	simple	simple	ADJ
ijassa-1405	58	8	and	and	CCONJ
ijassa-1405	58	9	the	the	DET
ijassa-1405	58	10	corresponding	corresponding	ADJ
ijassa-1405	58	11	polynomial	polynomial	ADJ
ijassa-1405	58	12	or	or	CCONJ
ijassa-1405	58	13	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	58	14	algorithm	algorithm	NOUN
ijassa-1405	58	15	,	,	PUNCT
ijassa-1405	58	16	for	for	SCONJ
ijassa-1405	58	17	any	any	DET
ijassa-1405	58	18	b	b	PROPN
ijassa-1405	58	19	∈	∈	PROPN
ijassa-1405	58	20	pα	pα	VERB
ijassa-1405	58	21	simple	simple	ADJ
ijassa-1405	58	22	and	and	CCONJ
ijassa-1405	58	23	a	a	DET
ijassa-1405	58	24	̸∈	̸∈	PROPN
ijassa-1405	58	25	pα	pα	PROPN
ijassa-1405	58	26	simple	simple	NOUN
ijassa-1405	58	27	,	,	PUNCT
ijassa-1405	58	28	the	the	DET
ijassa-1405	58	29	absolute	absolute	ADJ
ijassa-1405	58	30	(	(	PUNCT
ijassa-1405	58	31	or	or	CCONJ
ijassa-1405	58	32	relative	relative	ADJ
ijassa-1405	58	33	)	)	PUNCT
ijassa-1405	58	34	error	error	NOUN
ijassa-1405	58	35	of	of	ADP
ijassa-1405	58	36	the	the	DET
ijassa-1405	58	37	objective	objective	ADJ
ijassa-1405	58	38	function	function	NOUN
ijassa-1405	58	39	for	for	ADP
ijassa-1405	58	40	a	a	PRON
ijassa-1405	58	41	when	when	SCONJ
ijassa-1405	58	42	the	the	DET
ijassa-1405	58	43	polynomial	polynomial	ADJ
ijassa-1405	58	44	(	(	PUNCT
ijassa-1405	58	45	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	58	46	)	)	PUNCT
ijassa-1405	58	47	exact	exact	ADJ
ijassa-1405	58	48	solution	solution	NOUN
ijassa-1405	58	49	for	for	ADP
ijassa-1405	58	50	b	b	NOUN
ijassa-1405	58	51	is	be	AUX
ijassa-1405	58	52	applied	apply	VERB
ijassa-1405	58	53	to	to	ADP
ijassa-1405	58	54	a	a	PRON
ijassa-1405	58	55	will	will	AUX
ijassa-1405	58	56	be	be	AUX
ijassa-1405	58	57	used	use	VERB
ijassa-1405	58	58	as	as	ADP
ijassa-1405	58	59	the	the	DET
ijassa-1405	58	60	value	value	NOUN
ijassa-1405	58	61	of	of	ADP
ijassa-1405	58	62	the	the	DET
ijassa-1405	58	63	dissimilarity	dissimilarity	NOUN
ijassa-1405	58	64	function	function	NOUN
ijassa-1405	58	65	,	,	PUNCT
ijassa-1405	58	66	denoted	denote	VERB
ijassa-1405	58	67	by	by	ADP
ijassa-1405	58	68	τ	τ	PROPN
ijassa-1405	58	69	,	,	PUNCT
ijassa-1405	58	70	on	on	ADP
ijassa-1405	58	71	the	the	DET
ijassa-1405	58	72	pair	pair	NOUN
ijassa-1405	58	73	(	(	PUNCT
ijassa-1405	58	74	a	a	DET
ijassa-1405	58	75	,	,	PUNCT
ijassa-1405	58	76	b	b	NOUN
ijassa-1405	58	77	)	)	PUNCT
ijassa-1405	58	78	.	.	PUNCT
ijassa-1405	59	1	the	the	DET
ijassa-1405	59	2	steps	step	NOUN
ijassa-1405	59	3	of	of	ADP
ijassa-1405	59	4	the	the	DET
ijassa-1405	59	5	pairwise	pairwise	NOUN
ijassa-1405	59	6	similarity	similarity	NOUN
ijassa-1405	59	7	method	method	NOUN
ijassa-1405	59	8	are	be	AUX
ijassa-1405	59	9	described	describe	VERB
ijassa-1405	59	10	below	below	ADV
ijassa-1405	59	11	.	.	PUNCT
ijassa-1405	60	1	note	note	VERB
ijassa-1405	60	2	that	that	SCONJ
ijassa-1405	60	3	different	different	ADJ
ijassa-1405	60	4	values	value	NOUN
ijassa-1405	60	5	,	,	PUNCT
ijassa-1405	60	6	such	such	ADJ
ijassa-1405	60	7	as	as	ADP
ijassa-1405	60	8	relative	relative	ADJ
ijassa-1405	60	9	error	error	NOUN
ijassa-1405	60	10	,	,	PUNCT
ijassa-1405	60	11	rate	rate	NOUN
ijassa-1405	60	12	of	of	ADP
ijassa-1405	60	13	convergence	convergence	NOUN
ijassa-1405	60	14	of	of	ADP
ijassa-1405	60	15	the	the	DET
ijassa-1405	60	16	method	method	NOUN
ijassa-1405	60	17	,	,	PUNCT
ijassa-1405	60	18	convergence	convergence	NOUN
ijassa-1405	60	19	scores	score	NOUN
ijassa-1405	60	20	of	of	ADP
ijassa-1405	60	21	several	several	ADJ
ijassa-1405	60	22	methods	method	NOUN
ijassa-1405	60	23	,	,	PUNCT
ijassa-1405	60	24	number	number	NOUN
ijassa-1405	60	25	of	of	ADP
ijassa-1405	60	26	operations	operation	NOUN
ijassa-1405	60	27	,	,	PUNCT
ijassa-1405	60	28	etc	etc	X
ijassa-1405	60	29	.	.	X
ijassa-1405	60	30	,	,	PUNCT
ijassa-1405	60	31	can	can	AUX
ijassa-1405	60	32	be	be	AUX
ijassa-1405	60	33	used	use	VERB
ijassa-1405	60	34	to	to	PART
ijassa-1405	60	35	construct	construct	VERB
ijassa-1405	60	36	dissimilarity	dissimilarity	NOUN
ijassa-1405	60	37	functions	function	NOUN
ijassa-1405	60	38	in	in	ADP
ijassa-1405	60	39	the	the	DET
ijassa-1405	60	40	pairwise	pairwise	NOUN
ijassa-1405	60	41	similarity	similarity	NOUN
ijassa-1405	60	42	method	method	NOUN
ijassa-1405	60	43	.	.	PUNCT
ijassa-1405	61	1	let	let	VERB
ijassa-1405	61	2	us	we	PRON
ijassa-1405	61	3	move	move	VERB
ijassa-1405	61	4	on	on	ADP
ijassa-1405	61	5	to	to	ADP
ijassa-1405	61	6	the	the	DET
ijassa-1405	61	7	main	main	ADJ
ijassa-1405	61	8	definitions	definition	NOUN
ijassa-1405	61	9	assuming	assume	VERB
ijassa-1405	61	10	that	that	SCONJ
ijassa-1405	61	11	the	the	DET
ijassa-1405	61	12	problem	problem	NOUN
ijassa-1405	61	13	under	under	ADP
ijassa-1405	61	14	consideration	consideration	NOUN
ijassa-1405	61	15	is	be	AUX
ijassa-1405	61	16	a	a	DET
ijassa-1405	61	17	linear	linear	ADJ
ijassa-1405	61	18	programming	programming	NOUN
ijassa-1405	61	19	problem	problem	NOUN
ijassa-1405	61	20	with	with	ADP
ijassa-1405	61	21	one	one	NUM
ijassa-1405	61	22	objective	objective	ADJ
ijassa-1405	61	23	function	function	NOUN
ijassa-1405	61	24	.	.	PUNCT
ijassa-1405	62	1	in	in	ADP
ijassa-1405	62	2	the	the	DET
ijassa-1405	62	3	pairwise	pairwise	NOUN
ijassa-1405	62	4	similarity	similarity	NOUN
ijassa-1405	62	5	method	method	NOUN
ijassa-1405	62	6	,	,	PUNCT
ijassa-1405	62	7	a	a	DET
ijassa-1405	62	8	solution	solution	NOUN
ijassa-1405	62	9	xb	xb	X
ijassa-1405	62	10	to	to	ADP
ijassa-1405	62	11	the	the	DET
ijassa-1405	62	12	instance	instance	PROPN
ijassa-1405	62	13	b	b	PROPN
ijassa-1405	62	14	obtained	obtain	VERB
ijassa-1405	62	15	using	use	VERB
ijassa-1405	62	16	a	a	DET
ijassa-1405	62	17	polynomial	polynomial	ADJ
ijassa-1405	62	18	(	(	PUNCT
ijassa-1405	62	19	or	or	CCONJ
ijassa-1405	62	20	pseudopolynomial	pseudopolynomial	ADJ
ijassa-1405	62	21	)	)	PUNCT
ijassa-1405	62	22	algorithm	algorithm	NOUN
ijassa-1405	62	23	is	be	AUX
ijassa-1405	62	24	applied	apply	VERB
ijassa-1405	62	25	to	to	ADP
ijassa-1405	62	26	an	an	DET
ijassa-1405	62	27	instance	instance	NOUN
ijassa-1405	62	28	a	a	PRON
ijassa-1405	62	29	,	,	PUNCT
ijassa-1405	62	30	for	for	ADP
ijassa-1405	62	31	which	which	PRON
ijassa-1405	62	32	it	it	PRON
ijassa-1405	62	33	may	may	AUX
ijassa-1405	62	34	violate	violate	VERB
ijassa-1405	62	35	the	the	DET
ijassa-1405	62	36	internal	internal	ADJ
ijassa-1405	62	37	constraints	constraint	NOUN
ijassa-1405	62	38	.	.	PUNCT
ijassa-1405	63	1	depending	depend	VERB
ijassa-1405	63	2	on	on	ADP
ijassa-1405	63	3	how	how	SCONJ
ijassa-1405	63	4	the	the	DET
ijassa-1405	63	5	solution	solution	NOUN
ijassa-1405	63	6	xb	xb	PROPN
ijassa-1405	63	7	is	be	AUX
ijassa-1405	63	8	applied	apply	VERB
ijassa-1405	63	9	,	,	PUNCT
ijassa-1405	63	10	we	we	PRON
ijassa-1405	63	11	consider	consider	VERB
ijassa-1405	63	12	three	three	NUM
ijassa-1405	63	13	strategies	strategy	NOUN
ijassa-1405	63	14	.	.	PUNCT
ijassa-1405	64	1	1	1	X
ijassa-1405	64	2	.	.	X
ijassa-1405	64	3	evaluation	evaluation	NOUN
ijassa-1405	64	4	of	of	ADP
ijassa-1405	64	5	instance	instance	NOUN
ijassa-1405	64	6	a	a	PRON
ijassa-1405	64	7	:	:	PUNCT
ijassa-1405	64	8	using	use	VERB
ijassa-1405	64	9	the	the	DET
ijassa-1405	64	10	obtained	obtain	VERB
ijassa-1405	64	11	solution	solution	NOUN
ijassa-1405	64	12	xb	xb	PROPN
ijassa-1405	64	13	to	to	PART
ijassa-1405	64	14	evaluate	evaluate	VERB
ijassa-1405	64	15	the	the	DET
ijassa-1405	64	16	solution	solution	NOUN
ijassa-1405	64	17	xa	xa	PROPN
ijassa-1405	64	18	,	,	PUNCT
ijassa-1405	64	19	regardless	regardless	ADV
ijassa-1405	64	20	of	of	ADP
ijassa-1405	64	21	the	the	DET
ijassa-1405	64	22	feasibility	feasibility	NOUN
ijassa-1405	64	23	of	of	ADP
ijassa-1405	64	24	the	the	DET
ijassa-1405	64	25	resulting	result	VERB
ijassa-1405	64	26	solution	solution	NOUN
ijassa-1405	64	27	.	.	PUNCT
ijassa-1405	65	1	2	2	X
ijassa-1405	65	2	.	.	X
ijassa-1405	65	3	relaxation	relaxation	NOUN
ijassa-1405	65	4	of	of	ADP
ijassa-1405	65	5	instance	instance	NOUN
ijassa-1405	65	6	a	a	PRON
ijassa-1405	65	7	:	:	PUNCT
ijassa-1405	65	8	using	use	VERB
ijassa-1405	65	9	the	the	DET
ijassa-1405	65	10	obtained	obtain	VERB
ijassa-1405	65	11	solution	solution	NOUN
ijassa-1405	65	12	xb	xb	PROPN
ijassa-1405	65	13	to	to	PART
ijassa-1405	65	14	evaluate	evaluate	VERB
ijassa-1405	65	15	the	the	DET
ijassa-1405	65	16	solution	solution	NOUN
ijassa-1405	65	17	xa	xa	PROPN
ijassa-1405	65	18	,	,	PUNCT
ijassa-1405	65	19	taking	take	VERB
ijassa-1405	65	20	into	into	ADP
ijassa-1405	65	21	account	account	NOUN
ijassa-1405	65	22	which	which	PRON
ijassa-1405	65	23	restrictions	restriction	NOUN
ijassa-1405	65	24	of	of	ADP
ijassa-1405	65	25	instance	instance	NOUN
ijassa-1405	65	26	a	a	PRON
ijassa-1405	65	27	are	be	AUX
ijassa-1405	65	28	violated	violate	VERB
ijassa-1405	65	29	when	when	SCONJ
ijassa-1405	65	30	xb	xb	PROPN
ijassa-1405	65	31	is	be	AUX
ijassa-1405	65	32	applied	apply	VERB
ijassa-1405	65	33	to	to	ADP
ijassa-1405	65	34	a.	a.	NOUN
ijassa-1405	65	35	to	to	PART
ijassa-1405	65	36	implement	implement	VERB
ijassa-1405	65	37	this	this	DET
ijassa-1405	65	38	strategy	strategy	NOUN
ijassa-1405	65	39	,	,	PUNCT
ijassa-1405	65	40	it	it	PRON
ijassa-1405	65	41	is	be	AUX
ijassa-1405	65	42	necessary	necessary	ADJ
ijassa-1405	65	43	to	to	PART
ijassa-1405	65	44	check	check	VERB
ijassa-1405	65	45	the	the	DET
ijassa-1405	65	46	resulting	result	VERB
ijassa-1405	65	47	solution	solution	NOUN
ijassa-1405	65	48	for	for	ADP
ijassa-1405	65	49	feasibility	feasibility	NOUN
ijassa-1405	65	50	.	.	PUNCT
ijassa-1405	66	1	that	that	PRON
ijassa-1405	66	2	is	be	AUX
ijassa-1405	66	3	,	,	PUNCT
ijassa-1405	66	4	if	if	SCONJ
ijassa-1405	66	5	instance	instance	NOUN
ijassa-1405	66	6	b	b	PROPN
ijassa-1405	66	7	is	be	AUX
ijassa-1405	66	8	a	a	DET
ijassa-1405	66	9	relaxation	relaxation	NOUN
ijassa-1405	66	10	of	of	ADP
ijassa-1405	66	11	instance	instance	NOUN
ijassa-1405	66	12	a	a	PRON
ijassa-1405	66	13	,	,	PUNCT
ijassa-1405	66	14	then	then	ADV
ijassa-1405	66	15	a	a	DET
ijassa-1405	66	16	procedure	procedure	NOUN
ijassa-1405	66	17	for	for	ADP
ijassa-1405	66	18	checking	check	VERB
ijassa-1405	66	19	the	the	DET
ijassa-1405	66	20	satisfaction	satisfaction	NOUN
ijassa-1405	66	21	of	of	ADP
ijassa-1405	66	22	constraints	constraint	NOUN
ijassa-1405	66	23	is	be	AUX
ijassa-1405	66	24	needed	need	VERB
ijassa-1405	66	25	in	in	ADP
ijassa-1405	66	26	order	order	NOUN
ijassa-1405	66	27	to	to	PART
ijassa-1405	66	28	determine	determine	VERB
ijassa-1405	66	29	which	which	DET
ijassa-1405	66	30	particular	particular	ADJ
ijassa-1405	66	31	restrictions	restriction	NOUN
ijassa-1405	66	32	of	of	ADP
ijassa-1405	66	33	instance	instance	NOUN
ijassa-1405	66	34	a	a	PRON
ijassa-1405	66	35	are	be	AUX
ijassa-1405	66	36	violated	violate	VERB
ijassa-1405	66	37	by	by	ADP
ijassa-1405	66	38	solution	solution	NOUN
ijassa-1405	66	39	xb	xb	PROPN
ijassa-1405	66	40	.	.	PROPN
ijassa-1405	67	1	3	3	X
ijassa-1405	67	2	.	.	X
ijassa-1405	67	3	constructing	construct	VERB
ijassa-1405	67	4	a	a	DET
ijassa-1405	67	5	valid	valid	ADJ
ijassa-1405	67	6	solution	solution	NOUN
ijassa-1405	67	7	for	for	ADP
ijassa-1405	67	8	instance	instance	NOUN
ijassa-1405	67	9	a	a	PRON
ijassa-1405	67	10	using	use	VERB
ijassa-1405	67	11	the	the	DET
ijassa-1405	67	12	obtained	obtain	VERB
ijassa-1405	67	13	solution	solution	NOUN
ijassa-1405	67	14	xb	xb	PROPN
ijassa-1405	67	15	as	as	ADP
ijassa-1405	67	16	an	an	DET
ijassa-1405	67	17	approximate	approximate	ADJ
ijassa-1405	67	18	solution	solution	NOUN
ijassa-1405	67	19	to	to	PART
ijassa-1405	67	20	instance	instance	VERB
ijassa-1405	67	21	a.	a.	NOUN
ijassa-1405	67	22	to	to	PART
ijassa-1405	67	23	do	do	VERB
ijassa-1405	67	24	this	this	PRON
ijassa-1405	67	25	,	,	PUNCT
ijassa-1405	67	26	it	it	PRON
ijassa-1405	67	27	is	be	AUX
ijassa-1405	67	28	necessary	necessary	ADJ
ijassa-1405	67	29	to	to	PART
ijassa-1405	67	30	check	check	VERB
ijassa-1405	67	31	the	the	DET
ijassa-1405	67	32	feasibility	feasibility	NOUN
ijassa-1405	67	33	of	of	ADP
ijassa-1405	67	34	xb	xb	PROPN
ijassa-1405	67	35	and	and	CCONJ
ijassa-1405	67	36	,	,	PUNCT
ijassa-1405	67	37	if	if	SCONJ
ijassa-1405	67	38	some	some	DET
ijassa-1405	67	39	constraints	constraint	NOUN
ijassa-1405	67	40	are	be	AUX
ijassa-1405	67	41	violated	violate	VERB
ijassa-1405	67	42	,	,	PUNCT
ijassa-1405	67	43	find	find	VERB
ijassa-1405	67	44	the	the	DET
ijassa-1405	67	45	new	new	ADJ
ijassa-1405	67	46	solution	solution	NOUN
ijassa-1405	67	47	x∗	x∗	PROPN
ijassa-1405	68	1	b	b	X
ijassa-1405	68	2	closest	close	ADJ
ijassa-1405	68	3	to	to	ADP
ijassa-1405	68	4	xb	xb	PROPN
ijassa-1405	68	5	among	among	ADP
ijassa-1405	68	6	the	the	DET
ijassa-1405	68	7	solutions	solution	NOUN
ijassa-1405	68	8	that	that	PRON
ijassa-1405	68	9	satisfy	satisfy	VERB
ijassa-1405	68	10	all	all	DET
ijassa-1405	68	11	the	the	DET
ijassa-1405	68	12	constraints	constraint	NOUN
ijassa-1405	68	13	of	of	ADP
ijassa-1405	68	14	a.	a.	NOUN
ijassa-1405	68	15	thus	thus	ADV
ijassa-1405	68	16	,	,	PUNCT
ijassa-1405	68	17	to	to	PART
ijassa-1405	68	18	obtain	obtain	VERB
ijassa-1405	68	19	xa	xa	X
ijassa-1405	68	20	=	=	PUNCT
ijassa-1405	68	21	x∗	x∗	PROPN
ijassa-1405	69	1	b	b	X
ijassa-1405	69	2	,	,	PUNCT
ijassa-1405	69	3	it	it	PRON
ijassa-1405	69	4	is	be	AUX
ijassa-1405	69	5	necessary	necessary	ADJ
ijassa-1405	69	6	to	to	PART
ijassa-1405	69	7	construct	construct	VERB
ijassa-1405	69	8	a	a	DET
ijassa-1405	69	9	function	function	NOUN
ijassa-1405	69	10	transforming	transform	VERB
ijassa-1405	69	11	xb	xb	NOUN
ijassa-1405	69	12	into	into	ADP
ijassa-1405	69	13	x∗	x∗	PROPN
ijassa-1405	69	14	b.	b.	PROPN
ijassa-1405	70	1	thus	thus	ADV
ijassa-1405	70	2	,	,	PUNCT
ijassa-1405	70	3	the	the	DET
ijassa-1405	70	4	pairwise	pairwise	NOUN
ijassa-1405	70	5	similarity	similarity	NOUN
ijassa-1405	70	6	method	method	NOUN
ijassa-1405	70	7	consists	consist	VERB
ijassa-1405	70	8	of	of	ADP
ijassa-1405	70	9	the	the	DET
ijassa-1405	70	10	following	follow	VERB
ijassa-1405	70	11	steps	step	NOUN
ijassa-1405	70	12	.	.	PUNCT
ijassa-1405	71	1	1	1	X
ijassa-1405	71	2	.	.	X
ijassa-1405	71	3	find	find	VERB
ijassa-1405	71	4	one	one	NUM
ijassa-1405	71	5	or	or	CCONJ
ijassa-1405	71	6	more	more	ADJ
ijassa-1405	71	7	special	special	ADJ
ijassa-1405	71	8	cases	case	NOUN
ijassa-1405	71	9	of	of	ADP
ijassa-1405	71	10	the	the	DET
ijassa-1405	71	11	problem	problem	NOUN
ijassa-1405	71	12	.	.	PUNCT
ijassa-1405	72	1	for	for	ADP
ijassa-1405	72	2	many	many	ADJ
ijassa-1405	72	3	discrete	discrete	ADJ
ijassa-1405	72	4	optimization	optimization	NOUN
ijassa-1405	72	5	problems	problem	NOUN
ijassa-1405	72	6	,	,	PUNCT
ijassa-1405	72	7	some	some	DET
ijassa-1405	72	8	special	special	ADJ
ijassa-1405	72	9	cases	case	NOUN
ijassa-1405	72	10	are	be	AUX
ijassa-1405	72	11	known	know	VERB
ijassa-1405	72	12	.	.	PUNCT
ijassa-1405	73	1	below	below	ADP
ijassa-1405	73	2	we	we	PRON
ijassa-1405	73	3	present	present	VERB
ijassa-1405	73	4	guidelines	guideline	NOUN
ijassa-1405	73	5	for	for	ADP
ijassa-1405	73	6	finding	find	VERB
ijassa-1405	73	7	new	new	ADJ
ijassa-1405	73	8	special	special	ADJ
ijassa-1405	73	9	cases	case	NOUN
ijassa-1405	73	10	.	.	PUNCT
ijassa-1405	74	1	2	2	X
ijassa-1405	74	2	.	.	X
ijassa-1405	74	3	construct	construct	VERB
ijassa-1405	74	4	a	a	DET
ijassa-1405	74	5	pairwise	pairwise	NOUN
ijassa-1405	74	6	dissimilarity	dissimilarity	NOUN
ijassa-1405	74	7	function	function	NOUN
ijassa-1405	74	8	that	that	PRON
ijassa-1405	74	9	allows	allow	VERB
ijassa-1405	74	10	one	one	PRON
ijassa-1405	74	11	to	to	PART
ijassa-1405	74	12	estimate	estimate	VERB
ijassa-1405	74	13	the	the	DET
ijassa-1405	74	14	distance	distance	NOUN
ijassa-1405	74	15	from	from	ADP
ijassa-1405	74	16	any	any	DET
ijassa-1405	74	17	instance	instance	NOUN
ijassa-1405	74	18	to	to	ADP
ijassa-1405	74	19	each	each	PRON
ijassa-1405	74	20	of	of	ADP
ijassa-1405	74	21	the	the	DET
ijassa-1405	74	22	special	special	ADJ
ijassa-1405	74	23	cases	case	NOUN
ijassa-1405	74	24	.	.	PUNCT
ijassa-1405	75	1	an	an	DET
ijassa-1405	75	2	algorithm	algorithm	NOUN
ijassa-1405	75	3	for	for	ADP
ijassa-1405	75	4	building	build	VERB
ijassa-1405	75	5	such	such	DET
ijassa-1405	75	6	a	a	DET
ijassa-1405	75	7	function	function	NOUN
ijassa-1405	75	8	is	be	AUX
ijassa-1405	75	9	proposed	propose	VERB
ijassa-1405	75	10	below	below	ADV
ijassa-1405	75	11	.	.	PUNCT
ijassa-1405	76	1	3	3	X
ijassa-1405	76	2	.	.	PUNCT
ijassa-1405	76	3	given	give	VERB
ijassa-1405	76	4	an	an	DET
ijassa-1405	76	5	instance	instance	NOUN
ijassa-1405	76	6	a	a	PRON
ijassa-1405	76	7	,	,	PUNCT
ijassa-1405	76	8	find	find	VERB
ijassa-1405	76	9	the	the	DET
ijassa-1405	76	10	closest	close	ADJ
ijassa-1405	76	11	special	special	ADJ
ijassa-1405	76	12	case	case	NOUN
ijassa-1405	76	13	using	use	VERB
ijassa-1405	76	14	the	the	DET
ijassa-1405	76	15	chosen	choose	VERB
ijassa-1405	76	16	pairwise	pairwise	NOUN
ijassa-1405	76	17	dissimilarity	dissimilarity	NOUN
ijassa-1405	76	18	function	function	NOUN
ijassa-1405	76	19	.	.	PUNCT
ijassa-1405	77	1	4	4	X
ijassa-1405	77	2	.	.	X
ijassa-1405	77	3	find	find	VERB
ijassa-1405	77	4	the	the	DET
ijassa-1405	77	5	solution	solution	NOUN
ijassa-1405	77	6	to	to	ADP
ijassa-1405	77	7	the	the	DET
ijassa-1405	77	8	closest	close	ADJ
ijassa-1405	77	9	to	to	ADP
ijassa-1405	77	10	a	a	DET
ijassa-1405	77	11	instance	instance	NOUN
ijassa-1405	77	12	that	that	PRON
ijassa-1405	77	13	belongs	belong	VERB
ijassa-1405	77	14	to	to	ADP
ijassa-1405	77	15	a	a	DET
ijassa-1405	77	16	special	special	ADJ
ijassa-1405	77	17	case	case	NOUN
ijassa-1405	77	18	.	.	PUNCT
ijassa-1405	78	1	5	5	X
ijassa-1405	78	2	.	.	NUM
ijassa-1405	78	3	estimate	estimate	VERB
ijassa-1405	78	4	the	the	DET
ijassa-1405	78	5	guaranteed	guarantee	VERB
ijassa-1405	78	6	error	error	NOUN
ijassa-1405	78	7	of	of	ADP
ijassa-1405	78	8	the	the	DET
ijassa-1405	78	9	obtained	obtain	VERB
ijassa-1405	78	10	solution	solution	NOUN
ijassa-1405	78	11	using	use	VERB
ijassa-1405	78	12	the	the	DET
ijassa-1405	78	13	chosen	choose	VERB
ijassa-1405	78	14	pairwise	pairwise	NOUN
ijassa-1405	78	15	dissimilarity	dissimilarity	NOUN
ijassa-1405	78	16	function	function	NOUN
ijassa-1405	78	17	.	.	PUNCT
ijassa-1405	79	1	6	6	X
ijassa-1405	79	2	.	.	X
ijassa-1405	79	3	choose	choose	VERB
ijassa-1405	79	4	a	a	DET
ijassa-1405	79	5	strategy	strategy	NOUN
ijassa-1405	79	6	for	for	ADP
ijassa-1405	79	7	applying	apply	VERB
ijassa-1405	79	8	the	the	DET
ijassa-1405	79	9	solution	solution	NOUN
ijassa-1405	79	10	of	of	ADP
ijassa-1405	79	11	item	item	NOUN
ijassa-1405	79	12	4	4	NUM
ijassa-1405	79	13	to	to	PART
ijassa-1405	79	14	instance	instance	VERB
ijassa-1405	79	15	a.	a.	NOUN
ijassa-1405	79	16	–	–	PUNCT
ijassa-1405	79	17	for	for	ADP
ijassa-1405	79	18	the	the	DET
ijassa-1405	79	19	“	"	PUNCT
ijassa-1405	79	20	evaluation	evaluation	NOUN
ijassa-1405	79	21	of	of	ADP
ijassa-1405	79	22	instance	instance	NOUN
ijassa-1405	79	23	a	a	DET
ijassa-1405	79	24	”	"	PUNCT
ijassa-1405	79	25	strategy	strategy	NOUN
ijassa-1405	79	26	,	,	PUNCT
ijassa-1405	79	27	we	we	PRON
ijassa-1405	79	28	use	use	VERB
ijassa-1405	79	29	xb	xb	PROPN
ijassa-1405	79	30	without	without	ADP
ijassa-1405	79	31	adjustment	adjustment	NOUN
ijassa-1405	79	32	.	.	PUNCT
ijassa-1405	80	1	copyright	copyright	NOUN
ijassa-1405	80	2	©	©	PROPN
ijassa-1405	80	3	2023	2023	NUM
ijassa-1405	80	4	assa	assa	NOUN
ijassa-1405	80	5	.	.	PUNCT
ijassa-1405	81	1	adv	adv	PROPN
ijassa-1405	81	2	syst	syst	PROPN
ijassa-1405	81	3	sci	sci	PROPN
ijassa-1405	81	4	appl	appl	PROPN
ijassa-1405	81	5	(	(	PUNCT
ijassa-1405	81	6	2023	2023	NUM
ijassa-1405	81	7	)	)	PUNCT
ijassa-1405	81	8	pairwise	pairwise	NOUN
ijassa-1405	81	9	similarity	similarity	NOUN
ijassa-1405	81	10	estimation	estimation	NOUN
ijassa-1405	81	11	for	for	ADP
ijassa-1405	81	12	discrete	discrete	ADJ
ijassa-1405	81	13	optimization	optimization	NOUN
ijassa-1405	81	14	problems	problem	NOUN
ijassa-1405	81	15	167	167	NUM
ijassa-1405	81	16	–	–	PUNCT
ijassa-1405	81	17	for	for	ADP
ijassa-1405	81	18	the	the	DET
ijassa-1405	81	19	strategy	strategy	NOUN
ijassa-1405	81	20	“	"	PUNCT
ijassa-1405	81	21	relaxation	relaxation	NOUN
ijassa-1405	81	22	of	of	ADP
ijassa-1405	81	23	instance	instance	NOUN
ijassa-1405	81	24	a	a	PRON
ijassa-1405	81	25	”	"	PUNCT
ijassa-1405	81	26	,	,	PUNCT
ijassa-1405	81	27	we	we	PRON
ijassa-1405	81	28	use	use	VERB
ijassa-1405	81	29	xb	xb	PROPN
ijassa-1405	81	30	,	,	PUNCT
ijassa-1405	81	31	taking	take	VERB
ijassa-1405	81	32	into	into	ADP
ijassa-1405	81	33	account	account	NOUN
ijassa-1405	81	34	information	information	NOUN
ijassa-1405	81	35	about	about	ADP
ijassa-1405	81	36	whether	whether	SCONJ
ijassa-1405	81	37	the	the	DET
ijassa-1405	81	38	constraints	constraint	NOUN
ijassa-1405	81	39	of	of	ADP
ijassa-1405	81	40	the	the	DET
ijassa-1405	81	41	original	original	ADJ
ijassa-1405	81	42	instance	instance	NOUN
ijassa-1405	81	43	are	be	AUX
ijassa-1405	81	44	violated	violate	VERB
ijassa-1405	81	45	,	,	PUNCT
ijassa-1405	81	46	and	and	CCONJ
ijassa-1405	81	47	if	if	SCONJ
ijassa-1405	81	48	so	so	ADV
ijassa-1405	81	49	,	,	PUNCT
ijassa-1405	81	50	which	which	PRON
ijassa-1405	81	51	ones	one	NOUN
ijassa-1405	81	52	.	.	PUNCT
ijassa-1405	81	53	–	–	PUNCT
ijassa-1405	81	54	for	for	ADP
ijassa-1405	81	55	the	the	DET
ijassa-1405	81	56	strategy	strategy	NOUN
ijassa-1405	81	57	“	"	PUNCT
ijassa-1405	81	58	constructing	construct	VERB
ijassa-1405	81	59	a	a	DET
ijassa-1405	81	60	valid	valid	ADJ
ijassa-1405	81	61	solution	solution	NOUN
ijassa-1405	81	62	for	for	ADP
ijassa-1405	81	63	instance	instance	NOUN
ijassa-1405	81	64	a	a	PRON
ijassa-1405	81	65	”	"	PUNCT
ijassa-1405	81	66	,	,	PUNCT
ijassa-1405	81	67	we	we	PRON
ijassa-1405	81	68	check	check	VERB
ijassa-1405	81	69	the	the	DET
ijassa-1405	81	70	obtained	obtain	VERB
ijassa-1405	81	71	solution	solution	NOUN
ijassa-1405	81	72	for	for	ADP
ijassa-1405	81	73	feasibility	feasibility	NOUN
ijassa-1405	81	74	,	,	PUNCT
ijassa-1405	81	75	and	and	CCONJ
ijassa-1405	81	76	if	if	SCONJ
ijassa-1405	81	77	some	some	DET
ijassa-1405	81	78	restrictions	restriction	NOUN
ijassa-1405	81	79	are	be	AUX
ijassa-1405	81	80	violated	violate	VERB
ijassa-1405	81	81	,	,	PUNCT
ijassa-1405	81	82	then	then	ADV
ijassa-1405	81	83	use	use	VERB
ijassa-1405	81	84	the	the	DET
ijassa-1405	81	85	function	function	NOUN
ijassa-1405	81	86	transforming	transform	VERB
ijassa-1405	81	87	xb	xb	PROPN
ijassa-1405	81	88	into	into	ADP
ijassa-1405	81	89	xa	xa	PROPN
ijassa-1405	81	90	=	=	PROPN
ijassa-1405	81	91	x∗	x∗	PROPN
ijassa-1405	81	92	b.	b.	PROPN
ijassa-1405	81	93	finding	find	VERB
ijassa-1405	81	94	special	special	ADJ
ijassa-1405	81	95	cases	case	NOUN
ijassa-1405	81	96	is	be	AUX
ijassa-1405	81	97	a	a	DET
ijassa-1405	81	98	non	non	ADJ
ijassa-1405	81	99	-	-	ADJ
ijassa-1405	81	100	trivial	trivial	ADJ
ijassa-1405	81	101	task	task	NOUN
ijassa-1405	81	102	,	,	PUNCT
ijassa-1405	81	103	the	the	DET
ijassa-1405	81	104	solution	solution	NOUN
ijassa-1405	81	105	of	of	ADP
ijassa-1405	81	106	which	which	PRON
ijassa-1405	81	107	is	be	AUX
ijassa-1405	81	108	based	base	VERB
ijassa-1405	81	109	on	on	ADP
ijassa-1405	81	110	studying	study	VERB
ijassa-1405	81	111	the	the	DET
ijassa-1405	81	112	special	special	ADJ
ijassa-1405	81	113	properties	property	NOUN
ijassa-1405	81	114	of	of	ADP
ijassa-1405	81	115	the	the	DET
ijassa-1405	81	116	problem	problem	NOUN
ijassa-1405	81	117	under	under	ADP
ijassa-1405	81	118	consideration	consideration	NOUN
ijassa-1405	81	119	.	.	PUNCT
ijassa-1405	82	1	for	for	ADP
ijassa-1405	82	2	example	example	NOUN
ijassa-1405	82	3	,	,	PUNCT
ijassa-1405	82	4	for	for	ADP
ijassa-1405	82	5	the	the	DET
ijassa-1405	82	6	classes	class	NOUN
ijassa-1405	82	7	of	of	ADP
ijassa-1405	82	8	problems	problem	NOUN
ijassa-1405	82	9	where	where	SCONJ
ijassa-1405	82	10	the	the	DET
ijassa-1405	82	11	graph	graph	NOUN
ijassa-1405	82	12	included	include	VERB
ijassa-1405	82	13	in	in	ADP
ijassa-1405	82	14	a	a	DET
ijassa-1405	82	15	constraint	constraint	NOUN
ijassa-1405	82	16	is	be	AUX
ijassa-1405	82	17	a	a	DET
ijassa-1405	82	18	tree	tree	NOUN
ijassa-1405	82	19	,	,	PUNCT
ijassa-1405	82	20	there	there	PRON
ijassa-1405	82	21	are	be	VERB
ijassa-1405	82	22	often	often	ADV
ijassa-1405	82	23	fast	fast	ADJ
ijassa-1405	82	24	exact	exact	ADJ
ijassa-1405	82	25	algorithms	algorithm	NOUN
ijassa-1405	82	26	based	base	VERB
ijassa-1405	82	27	on	on	ADP
ijassa-1405	82	28	classical	classical	ADJ
ijassa-1405	82	29	tree	tree	NOUN
ijassa-1405	82	30	traversal	traversal	NOUN
ijassa-1405	82	31	algorithms	algorithm	NOUN
ijassa-1405	82	32	.	.	PUNCT
ijassa-1405	83	1	expanding	expand	VERB
ijassa-1405	83	2	the	the	DET
ijassa-1405	83	3	set	set	NOUN
ijassa-1405	83	4	of	of	ADP
ijassa-1405	83	5	special	special	ADJ
ijassa-1405	83	6	cases	case	NOUN
ijassa-1405	83	7	allows	allow	VERB
ijassa-1405	83	8	one	one	NUM
ijassa-1405	83	9	to	to	PART
ijassa-1405	83	10	more	more	ADV
ijassa-1405	83	11	accurately	accurately	ADV
ijassa-1405	83	12	determine	determine	VERB
ijassa-1405	83	13	the	the	DET
ijassa-1405	83	14	absolute	absolute	ADJ
ijassa-1405	83	15	error	error	NOUN
ijassa-1405	83	16	of	of	ADP
ijassa-1405	83	17	the	the	DET
ijassa-1405	83	18	original	original	ADJ
ijassa-1405	83	19	instance	instance	NOUN
ijassa-1405	83	20	.	.	PUNCT
ijassa-1405	84	1	we	we	PRON
ijassa-1405	84	2	now	now	ADV
ijassa-1405	84	3	give	give	VERB
ijassa-1405	84	4	some	some	DET
ijassa-1405	84	5	guidelines	guideline	NOUN
ijassa-1405	84	6	that	that	PRON
ijassa-1405	84	7	help	help	AUX
ijassa-1405	84	8	find	find	VERB
ijassa-1405	84	9	special	special	ADJ
ijassa-1405	84	10	cases	case	NOUN
ijassa-1405	84	11	.	.	PUNCT
ijassa-1405	85	1	the	the	DET
ijassa-1405	85	2	most	most	ADV
ijassa-1405	85	3	obvious	obvious	ADJ
ijassa-1405	85	4	way	way	NOUN
ijassa-1405	85	5	is	be	AUX
ijassa-1405	85	6	to	to	PART
ijassa-1405	85	7	expand	expand	VERB
ijassa-1405	85	8	the	the	DET
ijassa-1405	85	9	known	know	VERB
ijassa-1405	85	10	special	special	ADJ
ijassa-1405	85	11	cases	case	NOUN
ijassa-1405	85	12	by	by	ADP
ijassa-1405	85	13	slightly	slightly	ADV
ijassa-1405	85	14	changing	change	VERB
ijassa-1405	85	15	the	the	DET
ijassa-1405	85	16	original	original	ADJ
ijassa-1405	85	17	pattern	pattern	NOUN
ijassa-1405	85	18	.	.	PUNCT
ijassa-1405	86	1	section	section	NOUN
ijassa-1405	86	2	3.1	3.1	NUM
ijassa-1405	86	3	gives	give	VERB
ijassa-1405	86	4	an	an	DET
ijassa-1405	86	5	instance	instance	NOUN
ijassa-1405	86	6	of	of	ADP
ijassa-1405	86	7	such	such	DET
ijassa-1405	86	8	an	an	DET
ijassa-1405	86	9	extension	extension	NOUN
ijassa-1405	86	10	by	by	ADP
ijassa-1405	86	11	adding	add	VERB
ijassa-1405	86	12	additional	additional	ADJ
ijassa-1405	86	13	edges	edge	NOUN
ijassa-1405	86	14	to	to	ADP
ijassa-1405	86	15	the	the	DET
ijassa-1405	86	16	trees	tree	NOUN
ijassa-1405	86	17	to	to	PART
ijassa-1405	86	18	form	form	VERB
ijassa-1405	86	19	cycles	cycle	NOUN
ijassa-1405	86	20	.	.	PUNCT
ijassa-1405	87	1	the	the	DET
ijassa-1405	87	2	second	second	ADJ
ijassa-1405	87	3	way	way	NOUN
ijassa-1405	87	4	is	be	AUX
ijassa-1405	87	5	based	base	VERB
ijassa-1405	87	6	on	on	ADP
ijassa-1405	87	7	the	the	DET
ijassa-1405	87	8	following	follow	VERB
ijassa-1405	87	9	statement	statement	NOUN
ijassa-1405	87	10	.	.	PUNCT
ijassa-1405	88	1	if	if	SCONJ
ijassa-1405	88	2	for	for	ADP
ijassa-1405	88	3	problem	problem	NOUN
ijassa-1405	88	4	p	p	NOUN
ijassa-1405	88	5	there	there	PRON
ijassa-1405	88	6	exists	exist	VERB
ijassa-1405	88	7	an	an	DET
ijassa-1405	88	8	approximate	approximate	ADJ
ijassa-1405	88	9	algorithm	algorithm	NOUN
ijassa-1405	88	10	ã	ã	PROPN
ijassa-1405	88	11	,	,	PUNCT
ijassa-1405	88	12	then	then	ADV
ijassa-1405	88	13	among	among	ADP
ijassa-1405	88	14	the	the	DET
ijassa-1405	88	15	instances	instance	NOUN
ijassa-1405	88	16	of	of	ADP
ijassa-1405	88	17	p	p	NOUN
ijassa-1405	88	18	one	one	PRON
ijassa-1405	88	19	can	can	AUX
ijassa-1405	88	20	single	single	VERB
ijassa-1405	88	21	out	out	ADP
ijassa-1405	88	22	a	a	DET
ijassa-1405	88	23	subset	subset	NOUN
ijassa-1405	88	24	of	of	ADP
ijassa-1405	88	25	instances	instance	NOUN
ijassa-1405	88	26	p	p	NOUN
ijassa-1405	88	27	∗	∗	NOUN
ijassa-1405	88	28	for	for	ADP
ijassa-1405	88	29	which	which	PRON
ijassa-1405	88	30	this	this	DET
ijassa-1405	88	31	algorithm	algorithm	NOUN
ijassa-1405	88	32	provides	provide	VERB
ijassa-1405	88	33	exact	exact	ADJ
ijassa-1405	88	34	solutions	solution	NOUN
ijassa-1405	88	35	.	.	PUNCT
ijassa-1405	89	1	to	to	PART
ijassa-1405	89	2	implement	implement	VERB
ijassa-1405	89	3	this	this	DET
ijassa-1405	89	4	guideline	guideline	NOUN
ijassa-1405	89	5	,	,	PUNCT
ijassa-1405	89	6	it	it	PRON
ijassa-1405	89	7	is	be	AUX
ijassa-1405	89	8	necessary	necessary	ADJ
ijassa-1405	89	9	to	to	PART
ijassa-1405	89	10	solve	solve	VERB
ijassa-1405	89	11	a	a	DET
ijassa-1405	89	12	number	number	NOUN
ijassa-1405	89	13	of	of	ADP
ijassa-1405	89	14	randomly	randomly	ADV
ijassa-1405	89	15	selected	select	VERB
ijassa-1405	89	16	instances	instance	NOUN
ijassa-1405	89	17	of	of	ADP
ijassa-1405	89	18	problem	problem	NOUN
ijassa-1405	89	19	p	p	NOUN
ijassa-1405	89	20	with	with	ADP
ijassa-1405	89	21	different	different	ADJ
ijassa-1405	89	22	parameters	parameter	NOUN
ijassa-1405	89	23	using	use	VERB
ijassa-1405	89	24	the	the	DET
ijassa-1405	89	25	exact	exact	ADJ
ijassa-1405	89	26	algorithm	algorithm	NOUN
ijassa-1405	89	27	a	a	PRON
ijassa-1405	89	28	and	and	CCONJ
ijassa-1405	89	29	the	the	DET
ijassa-1405	89	30	approximate	approximate	ADJ
ijassa-1405	89	31	algorithm	algorithm	NOUN
ijassa-1405	89	32	ã.	ã.	PROPN
ijassa-1405	89	33	next	next	ADV
ijassa-1405	89	34	,	,	PUNCT
ijassa-1405	89	35	a	a	DET
ijassa-1405	89	36	subset	subset	NOUN
ijassa-1405	89	37	of	of	ADP
ijassa-1405	89	38	instances	instance	NOUN
ijassa-1405	89	39	p	p	NOUN
ijassa-1405	89	40	∗	∗	NOUN
ijassa-1405	89	41	⊂	⊂	PROPN
ijassa-1405	89	42	p	p	X
ijassa-1405	89	43	for	for	ADP
ijassa-1405	89	44	which	which	PRON
ijassa-1405	89	45	exact	exact	ADJ
ijassa-1405	89	46	solutions	solution	NOUN
ijassa-1405	89	47	(	(	PUNCT
ijassa-1405	89	48	or	or	CCONJ
ijassa-1405	89	49	solutions	solution	NOUN
ijassa-1405	89	50	with	with	ADP
ijassa-1405	89	51	a	a	DET
ijassa-1405	89	52	guaranteed	guarantee	VERB
ijassa-1405	89	53	error	error	NOUN
ijassa-1405	89	54	)	)	PUNCT
ijassa-1405	89	55	were	be	AUX
ijassa-1405	89	56	obtained	obtain	VERB
ijassa-1405	89	57	by	by	ADP
ijassa-1405	89	58	the	the	DET
ijassa-1405	89	59	approximate	approximate	ADJ
ijassa-1405	89	60	algorithm	algorithm	NOUN
ijassa-1405	89	61	ã	ã	PROPN
ijassa-1405	89	62	must	must	AUX
ijassa-1405	89	63	be	be	AUX
ijassa-1405	89	64	selected	select	VERB
ijassa-1405	89	65	.	.	PUNCT
ijassa-1405	90	1	note	note	VERB
ijassa-1405	90	2	that	that	SCONJ
ijassa-1405	90	3	the	the	DET
ijassa-1405	90	4	subset	subset	NOUN
ijassa-1405	90	5	of	of	ADP
ijassa-1405	90	6	instances	instance	NOUN
ijassa-1405	90	7	p	p	NOUN
ijassa-1405	90	8	∗	∗	NOUN
ijassa-1405	90	9	is	be	AUX
ijassa-1405	90	10	,	,	PUNCT
ijassa-1405	90	11	by	by	ADP
ijassa-1405	90	12	definition	definition	NOUN
ijassa-1405	90	13	,	,	PUNCT
ijassa-1405	90	14	a	a	DET
ijassa-1405	90	15	numerically	numerically	ADV
ijassa-1405	90	16	simple	simple	ADJ
ijassa-1405	90	17	special	special	ADJ
ijassa-1405	90	18	case	case	NOUN
ijassa-1405	90	19	.	.	PUNCT
ijassa-1405	91	1	then	then	ADV
ijassa-1405	91	2	it	it	PRON
ijassa-1405	91	3	is	be	AUX
ijassa-1405	91	4	necessary	necessary	ADJ
ijassa-1405	91	5	to	to	PART
ijassa-1405	91	6	determine	determine	VERB
ijassa-1405	91	7	whether	whether	SCONJ
ijassa-1405	91	8	there	there	PRON
ijassa-1405	91	9	is	be	VERB
ijassa-1405	91	10	a	a	DET
ijassa-1405	91	11	subset	subset	NOUN
ijassa-1405	91	12	of	of	ADP
ijassa-1405	91	13	instances	instance	NOUN
ijassa-1405	91	14	p	p	X
ijassa-1405	91	15	∗∗	∗∗	PROPN
ijassa-1405	91	16	⊆	⊆	NUM
ijassa-1405	91	17	p	p	NOUN
ijassa-1405	91	18	∗	∗	NOUN
ijassa-1405	91	19	for	for	ADP
ijassa-1405	91	20	which	which	PRON
ijassa-1405	91	21	some	some	DET
ijassa-1405	91	22	pattern	pattern	NOUN
ijassa-1405	91	23	α	α	PRON
ijassa-1405	91	24	can	can	AUX
ijassa-1405	91	25	be	be	AUX
ijassa-1405	91	26	formulated	formulate	VERB
ijassa-1405	91	27	.	.	PUNCT
ijassa-1405	92	1	if	if	SCONJ
ijassa-1405	92	2	the	the	DET
ijassa-1405	92	3	pattern	pattern	NOUN
ijassa-1405	92	4	α	α	NOUN
ijassa-1405	92	5	is	be	AUX
ijassa-1405	92	6	found	find	VERB
ijassa-1405	92	7	,	,	PUNCT
ijassa-1405	92	8	then	then	ADV
ijassa-1405	92	9	the	the	DET
ijassa-1405	92	10	resulting	result	VERB
ijassa-1405	92	11	set	set	NOUN
ijassa-1405	92	12	of	of	ADP
ijassa-1405	92	13	instances	instance	NOUN
ijassa-1405	92	14	p	p	X
ijassa-1405	92	15	∗∗	∗∗	PROPN
ijassa-1405	92	16	is	be	AUX
ijassa-1405	92	17	,	,	PUNCT
ijassa-1405	92	18	by	by	ADP
ijassa-1405	92	19	definition	definition	NOUN
ijassa-1405	92	20	,	,	PUNCT
ijassa-1405	92	21	a	a	DET
ijassa-1405	92	22	simple	simple	ADJ
ijassa-1405	92	23	or	or	CCONJ
ijassa-1405	92	24	semisimple	semisimple	ADJ
ijassa-1405	92	25	special	special	ADJ
ijassa-1405	92	26	case	case	NOUN
ijassa-1405	92	27	.	.	PUNCT
ijassa-1405	93	1	the	the	DET
ijassa-1405	93	2	third	third	ADJ
ijassa-1405	93	3	way	way	NOUN
ijassa-1405	93	4	involves	involve	VERB
ijassa-1405	93	5	an	an	DET
ijassa-1405	93	6	exact	exact	ADJ
ijassa-1405	93	7	combinatorial	combinatorial	ADJ
ijassa-1405	93	8	algorithm	algorithm	NOUN
ijassa-1405	93	9	a	a	NOUN
ijassa-1405	93	10	,	,	PUNCT
ijassa-1405	93	11	for	for	ADP
ijassa-1405	93	12	which	which	PRON
ijassa-1405	93	13	the	the	DET
ijassa-1405	93	14	rate	rate	NOUN
ijassa-1405	93	15	of	of	ADP
ijassa-1405	93	16	convergence	convergence	NOUN
ijassa-1405	93	17	is	be	AUX
ijassa-1405	93	18	investigated	investigate	VERB
ijassa-1405	93	19	.	.	PUNCT
ijassa-1405	94	1	if	if	SCONJ
ijassa-1405	94	2	for	for	ADP
ijassa-1405	94	3	problem	problem	NOUN
ijassa-1405	94	4	p	p	X
ijassa-1405	94	5	it	it	PRON
ijassa-1405	94	6	is	be	AUX
ijassa-1405	94	7	possible	possible	ADJ
ijassa-1405	94	8	to	to	PART
ijassa-1405	94	9	select	select	VERB
ijassa-1405	94	10	a	a	DET
ijassa-1405	94	11	subset	subset	NOUN
ijassa-1405	94	12	of	of	ADP
ijassa-1405	94	13	instances	instance	NOUN
ijassa-1405	94	14	p	p	NOUN
ijassa-1405	94	15	∗	∗	NOUN
ijassa-1405	94	16	⊂	⊂	PROPN
ijassa-1405	94	17	p	p	X
ijassa-1405	94	18	for	for	ADP
ijassa-1405	94	19	which	which	DET
ijassa-1405	94	20	algorithm	algorithm	NOUN
ijassa-1405	94	21	a	a	DET
ijassa-1405	94	22	converges	converge	NOUN
ijassa-1405	94	23	fast	fast	VERB
ijassa-1405	94	24	enough	enough	ADV
ijassa-1405	94	25	,	,	PUNCT
ijassa-1405	94	26	then	then	ADV
ijassa-1405	94	27	one	one	PRON
ijassa-1405	94	28	may	may	AUX
ijassa-1405	94	29	try	try	VERB
ijassa-1405	94	30	to	to	PART
ijassa-1405	94	31	construct	construct	VERB
ijassa-1405	94	32	a	a	DET
ijassa-1405	94	33	heuristic	heuristic	ADJ
ijassa-1405	94	34	algorithm	algorithm	NOUN
ijassa-1405	94	35	ã	ã	PROPN
ijassa-1405	94	36	based	base	VERB
ijassa-1405	94	37	on	on	ADP
ijassa-1405	94	38	a	a	PRON
ijassa-1405	94	39	,	,	PUNCT
ijassa-1405	94	40	which	which	PRON
ijassa-1405	94	41	provides	provide	VERB
ijassa-1405	94	42	an	an	DET
ijassa-1405	94	43	exact	exact	ADJ
ijassa-1405	94	44	solution	solution	NOUN
ijassa-1405	94	45	or	or	CCONJ
ijassa-1405	94	46	an	an	DET
ijassa-1405	94	47	approximate	approximate	ADJ
ijassa-1405	94	48	solution	solution	NOUN
ijassa-1405	94	49	with	with	ADP
ijassa-1405	94	50	a	a	DET
ijassa-1405	94	51	guaranteed	guarantee	VERB
ijassa-1405	94	52	error	error	NOUN
ijassa-1405	94	53	for	for	ADP
ijassa-1405	94	54	all	all	DET
ijassa-1405	94	55	instances	instance	NOUN
ijassa-1405	94	56	in	in	ADP
ijassa-1405	94	57	p	p	DET
ijassa-1405	94	58	∗.	∗.	PROPN
ijassa-1405	94	59	note	note	NOUN
ijassa-1405	94	60	that	that	SCONJ
ijassa-1405	94	61	the	the	DET
ijassa-1405	94	62	concept	concept	NOUN
ijassa-1405	94	63	of	of	ADP
ijassa-1405	94	64	fast	fast	ADJ
ijassa-1405	94	65	convergence	convergence	NOUN
ijassa-1405	94	66	of	of	ADP
ijassa-1405	94	67	an	an	DET
ijassa-1405	94	68	algorithm	algorithm	NOUN
ijassa-1405	94	69	in	in	ADP
ijassa-1405	94	70	this	this	DET
ijassa-1405	94	71	context	context	NOUN
ijassa-1405	94	72	is	be	AUX
ijassa-1405	94	73	used	use	VERB
ijassa-1405	94	74	informally	informally	ADV
ijassa-1405	94	75	,	,	PUNCT
ijassa-1405	94	76	since	since	SCONJ
ijassa-1405	94	77	the	the	DET
ijassa-1405	94	78	formalization	formalization	NOUN
ijassa-1405	94	79	depends	depend	VERB
ijassa-1405	94	80	on	on	ADP
ijassa-1405	94	81	a	a	DET
ijassa-1405	94	82	specific	specific	ADJ
ijassa-1405	94	83	problem	problem	NOUN
ijassa-1405	94	84	.	.	PUNCT
ijassa-1405	95	1	to	to	PART
ijassa-1405	95	2	implement	implement	VERB
ijassa-1405	95	3	this	this	DET
ijassa-1405	95	4	guideline	guideline	NOUN
ijassa-1405	95	5	,	,	PUNCT
ijassa-1405	95	6	it	it	PRON
ijassa-1405	95	7	is	be	AUX
ijassa-1405	95	8	necessary	necessary	ADJ
ijassa-1405	95	9	to	to	PART
ijassa-1405	95	10	randomly	randomly	VERB
ijassa-1405	95	11	select	select	VERB
ijassa-1405	95	12	a	a	DET
ijassa-1405	95	13	number	number	NOUN
ijassa-1405	95	14	of	of	ADP
ijassa-1405	95	15	instances	instance	NOUN
ijassa-1405	95	16	of	of	ADP
ijassa-1405	95	17	p	p	NOUN
ijassa-1405	95	18	with	with	ADP
ijassa-1405	95	19	different	different	ADJ
ijassa-1405	95	20	parameters	parameter	NOUN
ijassa-1405	95	21	and	and	CCONJ
ijassa-1405	95	22	solve	solve	VERB
ijassa-1405	95	23	them	they	PRON
ijassa-1405	95	24	using	use	VERB
ijassa-1405	95	25	a.	a.	NOUN
ijassa-1405	95	26	next	next	ADV
ijassa-1405	95	27	,	,	PUNCT
ijassa-1405	95	28	we	we	PRON
ijassa-1405	95	29	should	should	AUX
ijassa-1405	95	30	single	single	VERB
ijassa-1405	95	31	out	out	ADP
ijassa-1405	95	32	a	a	DET
ijassa-1405	95	33	subset	subset	NOUN
ijassa-1405	95	34	of	of	ADP
ijassa-1405	95	35	instances	instance	NOUN
ijassa-1405	95	36	p	p	NOUN
ijassa-1405	95	37	∗	∗	NOUN
ijassa-1405	95	38	⊂	⊂	PROPN
ijassa-1405	95	39	p	p	X
ijassa-1405	95	40	for	for	ADP
ijassa-1405	95	41	which	which	PRON
ijassa-1405	95	42	a	a	PRON
ijassa-1405	95	43	obtains	obtain	VERB
ijassa-1405	95	44	exact	exact	ADJ
ijassa-1405	95	45	solutions	solution	NOUN
ijassa-1405	95	46	fairly	fairly	ADV
ijassa-1405	95	47	quickly	quickly	ADV
ijassa-1405	95	48	.	.	PUNCT
ijassa-1405	96	1	then	then	ADV
ijassa-1405	96	2	it	it	PRON
ijassa-1405	96	3	is	be	AUX
ijassa-1405	96	4	necessary	necessary	ADJ
ijassa-1405	96	5	to	to	PART
ijassa-1405	96	6	build	build	VERB
ijassa-1405	96	7	a	a	DET
ijassa-1405	96	8	heuristic	heuristic	ADJ
ijassa-1405	96	9	algorithm	algorithm	NOUN
ijassa-1405	96	10	based	base	VERB
ijassa-1405	96	11	on	on	ADP
ijassa-1405	96	12	the	the	DET
ijassa-1405	96	13	steps	step	NOUN
ijassa-1405	96	14	of	of	ADP
ijassa-1405	96	15	a	a	PRON
ijassa-1405	96	16	,	,	PUNCT
ijassa-1405	96	17	which	which	PRON
ijassa-1405	96	18	are	be	AUX
ijassa-1405	96	19	carried	carry	VERB
ijassa-1405	96	20	out	out	ADP
ijassa-1405	96	21	in	in	ADP
ijassa-1405	96	22	the	the	DET
ijassa-1405	96	23	course	course	NOUN
ijassa-1405	96	24	of	of	ADP
ijassa-1405	96	25	solving	solve	VERB
ijassa-1405	96	26	the	the	DET
ijassa-1405	96	27	instances	instance	NOUN
ijassa-1405	96	28	in	in	ADP
ijassa-1405	96	29	p	p	X
ijassa-1405	96	30	∗.	∗.	PROPN
ijassa-1405	96	31	as	as	ADP
ijassa-1405	96	32	a	a	DET
ijassa-1405	96	33	result	result	NOUN
ijassa-1405	96	34	,	,	PUNCT
ijassa-1405	96	35	we	we	PRON
ijassa-1405	96	36	get	get	VERB
ijassa-1405	96	37	p	p	NOUN
ijassa-1405	96	38	∗	∗	NOUN
ijassa-1405	96	39	as	as	ADP
ijassa-1405	96	40	a	a	DET
ijassa-1405	96	41	numerically	numerically	ADV
ijassa-1405	96	42	simple	simple	ADJ
ijassa-1405	96	43	special	special	ADJ
ijassa-1405	96	44	case	case	NOUN
ijassa-1405	96	45	.	.	PUNCT
ijassa-1405	97	1	further	far	ADV
ijassa-1405	97	2	,	,	PUNCT
ijassa-1405	97	3	similarly	similarly	ADV
ijassa-1405	97	4	to	to	ADP
ijassa-1405	97	5	the	the	DET
ijassa-1405	97	6	second	second	ADJ
ijassa-1405	97	7	way	way	NOUN
ijassa-1405	97	8	,	,	PUNCT
ijassa-1405	97	9	we	we	PRON
ijassa-1405	97	10	look	look	VERB
ijassa-1405	97	11	for	for	ADP
ijassa-1405	97	12	a	a	DET
ijassa-1405	97	13	pattern	pattern	NOUN
ijassa-1405	97	14	α	α	NOUN
ijassa-1405	97	15	that	that	PRON
ijassa-1405	97	16	describes	describe	VERB
ijassa-1405	97	17	some	some	DET
ijassa-1405	97	18	subset	subset	NOUN
ijassa-1405	97	19	of	of	ADP
ijassa-1405	97	20	instances	instance	NOUN
ijassa-1405	97	21	p	p	X
ijassa-1405	97	22	∗∗	∗∗	PROPN
ijassa-1405	98	1	⊆	⊆	NUM
ijassa-1405	98	2	p	p	X
ijassa-1405	98	3	∗.	∗.	PROPN
ijassa-1405	98	4	if	if	SCONJ
ijassa-1405	98	5	such	such	DET
ijassa-1405	98	6	a	a	DET
ijassa-1405	98	7	pattern	pattern	NOUN
ijassa-1405	98	8	has	have	AUX
ijassa-1405	98	9	been	be	AUX
ijassa-1405	98	10	found	find	VERB
ijassa-1405	98	11	,	,	PUNCT
ijassa-1405	98	12	then	then	ADV
ijassa-1405	98	13	p	p	PROPN
ijassa-1405	98	14	∗∗	∗∗	PROPN
ijassa-1405	98	15	is	be	AUX
ijassa-1405	98	16	a	a	DET
ijassa-1405	98	17	simple	simple	ADJ
ijassa-1405	98	18	special	special	ADJ
ijassa-1405	98	19	case	case	NOUN
ijassa-1405	98	20	.	.	PUNCT
ijassa-1405	99	1	we	we	PRON
ijassa-1405	99	2	now	now	ADV
ijassa-1405	99	3	turn	turn	VERB
ijassa-1405	99	4	to	to	ADP
ijassa-1405	99	5	the	the	DET
ijassa-1405	99	6	construction	construction	NOUN
ijassa-1405	99	7	of	of	ADP
ijassa-1405	99	8	a	a	DET
ijassa-1405	99	9	pairwise	pairwise	NOUN
ijassa-1405	99	10	dissimilarity	dissimilarity	NOUN
ijassa-1405	99	11	function	function	NOUN
ijassa-1405	99	12	.	.	PUNCT
ijassa-1405	100	1	this	this	PRON
ijassa-1405	100	2	includes	include	VERB
ijassa-1405	100	3	the	the	DET
ijassa-1405	100	4	following	follow	VERB
ijassa-1405	100	5	steps	step	NOUN
ijassa-1405	100	6	.	.	PUNCT
ijassa-1405	101	1	1	1	X
ijassa-1405	101	2	.	.	X
ijassa-1405	101	3	find	find	VERB
ijassa-1405	101	4	a	a	DET
ijassa-1405	101	5	special	special	ADJ
ijassa-1405	101	6	case	case	NOUN
ijassa-1405	101	7	p	p	X
ijassa-1405	101	8	∗.	∗.	PROPN
ijassa-1405	101	9	2	2	NUM
ijassa-1405	101	10	.	.	PUNCT
ijassa-1405	102	1	fix	fix	VERB
ijassa-1405	102	2	all	all	DET
ijassa-1405	102	3	parameters	parameter	NOUN
ijassa-1405	102	4	of	of	ADP
ijassa-1405	102	5	the	the	DET
ijassa-1405	102	6	p	p	PROPN
ijassa-1405	102	7	∗	∗	NOUN
ijassa-1405	102	8	problem	problem	NOUN
ijassa-1405	102	9	,	,	PUNCT
ijassa-1405	102	10	except	except	SCONJ
ijassa-1405	102	11	for	for	ADP
ijassa-1405	102	12	one	one	NUM
ijassa-1405	102	13	parameter	parameter	NOUN
ijassa-1405	102	14	q.	q.	NOUN
ijassa-1405	102	15	3	3	X
ijassa-1405	102	16	.	.	PUNCT
ijassa-1405	102	17	solve	solve	VERB
ijassa-1405	102	18	some	some	DET
ijassa-1405	102	19	set	set	NOUN
ijassa-1405	102	20	of	of	ADP
ijassa-1405	102	21	instances	instance	NOUN
ijassa-1405	102	22	of	of	ADP
ijassa-1405	102	23	the	the	DET
ijassa-1405	102	24	problem	problem	NOUN
ijassa-1405	102	25	p	p	NOUN
ijassa-1405	102	26	∗	∗	NOUN
ijassa-1405	102	27	for	for	ADP
ijassa-1405	102	28	various	various	ADJ
ijassa-1405	102	29	q.	q.	PROPN
ijassa-1405	102	30	4	4	NUM
ijassa-1405	102	31	.	.	PUNCT
ijassa-1405	102	32	determine	determine	VERB
ijassa-1405	102	33	the	the	DET
ijassa-1405	102	34	relationship	relationship	NOUN
ijassa-1405	102	35	βq	βq	VERB
ijassa-1405	102	36	between	between	ADP
ijassa-1405	102	37	q	q	PROPN
ijassa-1405	102	38	and	and	CCONJ
ijassa-1405	102	39	the	the	DET
ijassa-1405	102	40	exact	exact	ADJ
ijassa-1405	102	41	value	value	NOUN
ijassa-1405	102	42	of	of	ADP
ijassa-1405	102	43	the	the	DET
ijassa-1405	102	44	objective	objective	ADJ
ijassa-1405	102	45	function	function	NOUN
ijassa-1405	102	46	.	.	PUNCT
ijassa-1405	103	1	5	5	X
ijassa-1405	103	2	.	.	X
ijassa-1405	103	3	construct	construct	VERB
ijassa-1405	103	4	a	a	DET
ijassa-1405	103	5	pairwise	pairwise	NOUN
ijassa-1405	103	6	dissimilarity	dissimilarity	NOUN
ijassa-1405	103	7	function	function	NOUN
ijassa-1405	103	8	ρq	ρq	AUX
ijassa-1405	103	9	that	that	PRON
ijassa-1405	103	10	approximately	approximately	ADV
ijassa-1405	103	11	represents	represent	VERB
ijassa-1405	103	12	βq	βq	ADJ
ijassa-1405	103	13	.	.	PUNCT
ijassa-1405	104	1	6	6	X
ijassa-1405	104	2	.	.	X
ijassa-1405	104	3	repeat	repeat	NOUN
ijassa-1405	104	4	steps	step	NOUN
ijassa-1405	104	5	(	(	PUNCT
ijassa-1405	104	6	2)–(5	2)–(5	NOUN
ijassa-1405	104	7	)	)	PUNCT
ijassa-1405	104	8	for	for	ADP
ijassa-1405	104	9	the	the	DET
ijassa-1405	104	10	other	other	ADJ
ijassa-1405	104	11	problem	problem	NOUN
ijassa-1405	104	12	parameters	parameter	NOUN
ijassa-1405	104	13	.	.	PUNCT
ijassa-1405	105	1	7	7	X
ijassa-1405	105	2	.	.	X
ijassa-1405	105	3	as	as	ADP
ijassa-1405	105	4	the	the	DET
ijassa-1405	105	5	resulting	result	VERB
ijassa-1405	105	6	pairwise	pairwise	NOUN
ijassa-1405	105	7	dissimilarity	dissimilarity	NOUN
ijassa-1405	105	8	function	function	NOUN
ijassa-1405	105	9	,	,	PUNCT
ijassa-1405	105	10	consider	consider	VERB
ijassa-1405	105	11	the	the	DET
ijassa-1405	105	12	sum	sum	NOUN
ijassa-1405	105	13	ρ	ρ	PROPN
ijassa-1405	105	14	=	=	SYM
ijassa-1405	106	1	∑n	∑n	NUM
ijassa-1405	106	2	q=1	q=1	PROPN
ijassa-1405	106	3	ρ	ρ	NOUN
ijassa-1405	106	4	q	q	NOUN
ijassa-1405	106	5	of	of	ADP
ijassa-1405	106	6	partial	partial	ADJ
ijassa-1405	106	7	functions	function	NOUN
ijassa-1405	106	8	for	for	ADP
ijassa-1405	106	9	all	all	DET
ijassa-1405	106	10	parameters	parameter	NOUN
ijassa-1405	106	11	of	of	ADP
ijassa-1405	106	12	problem	problem	NOUN
ijassa-1405	106	13	p	p	X
ijassa-1405	106	14	.	.	PUNCT
ijassa-1405	107	1	copyright	copyright	NOUN
ijassa-1405	107	2	©	©	PROPN
ijassa-1405	107	3	2023	2023	NUM
ijassa-1405	107	4	assa	assa	NOUN
ijassa-1405	107	5	.	.	PUNCT
ijassa-1405	108	1	adv	adv	PROPN
ijassa-1405	108	2	syst	syst	PROPN
ijassa-1405	108	3	sci	sci	PROPN
ijassa-1405	108	4	appl	appl	PROPN
ijassa-1405	108	5	(	(	PUNCT
ijassa-1405	108	6	2023	2023	NUM
ijassa-1405	108	7	)	)	PUNCT
ijassa-1405	108	8	168	168	NUM
ijassa-1405	108	9	d.	d.	PROPN
ijassa-1405	108	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	108	11	,	,	PUNCT
ijassa-1405	108	12	p.	p.	PROPN
ijassa-1405	108	13	chebotarev	chebotarev	PROPN
ijassa-1405	108	14	,	,	PUNCT
ijassa-1405	108	15	m.	m.	NOUN
ijassa-1405	108	16	goubko	goubko	NOUN
ijassa-1405	108	17	,	,	PUNCT
ijassa-1405	108	18	m.	m.	NOUN
ijassa-1405	108	19	somov	somov	PROPN
ijassa-1405	108	20	,	,	PUNCT
ijassa-1405	108	21	n.	n.	PROPN
ijassa-1405	108	22	shushko	shushko	VERB
ijassa-1405	108	23	an	an	DET
ijassa-1405	108	24	example	example	NOUN
ijassa-1405	108	25	of	of	ADP
ijassa-1405	108	26	the	the	DET
ijassa-1405	108	27	application	application	NOUN
ijassa-1405	108	28	of	of	ADP
ijassa-1405	108	29	this	this	DET
ijassa-1405	108	30	procedure	procedure	NOUN
ijassa-1405	108	31	is	be	AUX
ijassa-1405	108	32	the	the	DET
ijassa-1405	108	33	variation	variation	NOUN
ijassa-1405	108	34	of	of	ADP
ijassa-1405	108	35	the	the	DET
ijassa-1405	108	36	cyclomatic	cyclomatic	ADJ
ijassa-1405	108	37	number	number	NOUN
ijassa-1405	108	38	of	of	ADP
ijassa-1405	108	39	a	a	DET
ijassa-1405	108	40	graph	graph	NOUN
ijassa-1405	108	41	in	in	ADP
ijassa-1405	108	42	section	section	NOUN
ijassa-1405	108	43	3.1	3.1	NUM
ijassa-1405	108	44	,	,	PUNCT
ijassa-1405	108	45	where	where	SCONJ
ijassa-1405	108	46	the	the	DET
ijassa-1405	108	47	pairwise	pairwise	NOUN
ijassa-1405	108	48	similarity	similarity	NOUN
ijassa-1405	108	49	method	method	NOUN
ijassa-1405	108	50	is	be	AUX
ijassa-1405	108	51	used	use	VERB
ijassa-1405	108	52	to	to	PART
ijassa-1405	108	53	build	build	VERB
ijassa-1405	108	54	an	an	DET
ijassa-1405	108	55	analytical	analytical	ADJ
ijassa-1405	108	56	estimate	estimate	NOUN
ijassa-1405	108	57	with	with	ADP
ijassa-1405	108	58	a	a	DET
ijassa-1405	108	59	limited	limited	ADJ
ijassa-1405	108	60	absolute	absolute	ADJ
ijassa-1405	108	61	error	error	NOUN
ijassa-1405	108	62	.	.	PUNCT
ijassa-1405	109	1	note	note	VERB
ijassa-1405	109	2	that	that	SCONJ
ijassa-1405	109	3	,	,	PUNCT
ijassa-1405	109	4	due	due	ADP
ijassa-1405	109	5	to	to	ADP
ijassa-1405	109	6	the	the	DET
ijassa-1405	109	7	complexity	complexity	NOUN
ijassa-1405	109	8	of	of	ADP
ijassa-1405	109	9	the	the	DET
ijassa-1405	109	10	problem	problem	NOUN
ijassa-1405	109	11	,	,	PUNCT
ijassa-1405	109	12	the	the	DET
ijassa-1405	109	13	pairwise	pairwise	NOUN
ijassa-1405	109	14	dissimilarity	dissimilarity	NOUN
ijassa-1405	109	15	function	function	NOUN
ijassa-1405	109	16	can	can	AUX
ijassa-1405	109	17	not	not	PART
ijassa-1405	109	18	always	always	ADV
ijassa-1405	109	19	be	be	AUX
ijassa-1405	109	20	found	find	VERB
ijassa-1405	109	21	analytically	analytically	ADV
ijassa-1405	109	22	.	.	PUNCT
ijassa-1405	110	1	in	in	ADP
ijassa-1405	110	2	this	this	DET
ijassa-1405	110	3	case	case	NOUN
ijassa-1405	110	4	,	,	PUNCT
ijassa-1405	110	5	it	it	PRON
ijassa-1405	110	6	is	be	AUX
ijassa-1405	110	7	proposed	propose	VERB
ijassa-1405	110	8	to	to	PART
ijassa-1405	110	9	evaluate	evaluate	VERB
ijassa-1405	110	10	the	the	DET
ijassa-1405	110	11	pairwise	pairwise	NOUN
ijassa-1405	110	12	dissimilarity	dissimilarity	NOUN
ijassa-1405	110	13	function	function	NOUN
ijassa-1405	110	14	numerically	numerically	ADV
ijassa-1405	110	15	.	.	PUNCT
ijassa-1405	111	1	for	for	ADP
ijassa-1405	111	2	instance	instance	NOUN
ijassa-1405	111	3	,	,	PUNCT
ijassa-1405	111	4	in	in	ADP
ijassa-1405	111	5	section	section	NOUN
ijassa-1405	111	6	3.2	3.2	NUM
ijassa-1405	111	7	the	the	DET
ijassa-1405	111	8	pairwise	pairwise	NOUN
ijassa-1405	111	9	dissimilarity	dissimilarity	NOUN
ijassa-1405	111	10	function	function	NOUN
ijassa-1405	111	11	is	be	AUX
ijassa-1405	111	12	evaluated	evaluate	VERB
ijassa-1405	111	13	using	use	VERB
ijassa-1405	111	14	computational	computational	ADJ
ijassa-1405	111	15	experiments	experiment	NOUN
ijassa-1405	111	16	.	.	PUNCT
ijassa-1405	112	1	it	it	PRON
ijassa-1405	112	2	is	be	AUX
ijassa-1405	112	3	proposed	propose	VERB
ijassa-1405	112	4	to	to	PART
ijassa-1405	112	5	majorize	majorize	VERB
ijassa-1405	112	6	from	from	ADP
ijassa-1405	112	7	above	above	ADV
ijassa-1405	112	8	and	and	CCONJ
ijassa-1405	112	9	tabulate	tabulate	VERB
ijassa-1405	112	10	the	the	DET
ijassa-1405	112	11	numerical	numerical	ADJ
ijassa-1405	112	12	values	value	NOUN
ijassa-1405	112	13	of	of	ADP
ijassa-1405	112	14	the	the	DET
ijassa-1405	112	15	pairwise	pairwise	NOUN
ijassa-1405	112	16	dissimilarity	dissimilarity	NOUN
ijassa-1405	112	17	function	function	NOUN
ijassa-1405	112	18	.	.	PUNCT
ijassa-1405	113	1	3	3	X
ijassa-1405	113	2	.	.	X
ijassa-1405	113	3	applications	application	NOUN
ijassa-1405	113	4	of	of	ADP
ijassa-1405	113	5	the	the	DET
ijassa-1405	113	6	pairwise	pairwise	NOUN
ijassa-1405	113	7	similarity	similarity	NOUN
ijassa-1405	113	8	method	method	NOUN
ijassa-1405	113	9	3.1	3.1	NUM
ijassa-1405	113	10	.	.	PUNCT
ijassa-1405	113	11	majority	majority	NOUN
ijassa-1405	113	12	domination	domination	NOUN
ijassa-1405	113	13	problem	problem	NOUN
ijassa-1405	113	14	in	in	ADP
ijassa-1405	113	15	this	this	DET
ijassa-1405	113	16	section	section	NOUN
ijassa-1405	113	17	,	,	PUNCT
ijassa-1405	113	18	the	the	DET
ijassa-1405	113	19	pairwise	pairwise	NOUN
ijassa-1405	113	20	similarity	similarity	NOUN
ijassa-1405	113	21	method	method	NOUN
ijassa-1405	113	22	is	be	AUX
ijassa-1405	113	23	illustrated	illustrate	VERB
ijassa-1405	113	24	by	by	ADP
ijassa-1405	113	25	the	the	DET
ijassa-1405	113	26	its	its	PRON
ijassa-1405	113	27	application	application	NOUN
ijassa-1405	113	28	to	to	ADP
ijassa-1405	113	29	the	the	DET
ijassa-1405	113	30	problem	problem	NOUN
ijassa-1405	113	31	of	of	ADP
ijassa-1405	113	32	finding	find	VERB
ijassa-1405	113	33	the	the	DET
ijassa-1405	113	34	strict	strict	ADJ
ijassa-1405	113	35	majority	majority	NOUN
ijassa-1405	113	36	domination	domination	NOUN
ijassa-1405	113	37	number	number	NOUN
ijassa-1405	113	38	for	for	ADP
ijassa-1405	113	39	a	a	DET
ijassa-1405	113	40	graph	graph	NOUN
ijassa-1405	113	41	with	with	ADP
ijassa-1405	113	42	cycles	cycle	NOUN
ijassa-1405	113	43	within	within	ADP
ijassa-1405	113	44	the	the	DET
ijassa-1405	113	45	two	two	NUM
ijassa-1405	113	46	-	-	PUNCT
ijassa-1405	113	47	tier	tier	NOUN
ijassa-1405	113	48	voting	voting	NOUN
ijassa-1405	113	49	model	model	NOUN
ijassa-1405	113	50	.	.	PUNCT
ijassa-1405	114	1	the	the	DET
ijassa-1405	114	2	pairwise	pairwise	PROPN
ijassa-1405	114	3	dissimilarity	dissimilarity	NOUN
ijassa-1405	114	4	function	function	NOUN
ijassa-1405	114	5	is	be	AUX
ijassa-1405	114	6	built	build	VERB
ijassa-1405	114	7	using	use	VERB
ijassa-1405	114	8	the	the	DET
ijassa-1405	114	9	procedure	procedure	NOUN
ijassa-1405	114	10	described	describe	VERB
ijassa-1405	114	11	in	in	ADP
ijassa-1405	114	12	section	section	NOUN
ijassa-1405	114	13	2	2	NUM
ijassa-1405	114	14	.	.	PUNCT
ijassa-1405	115	1	the	the	DET
ijassa-1405	115	2	special	special	ADJ
ijassa-1405	115	3	case	case	NOUN
ijassa-1405	115	4	is	be	AUX
ijassa-1405	115	5	constructed	construct	VERB
ijassa-1405	115	6	by	by	ADP
ijassa-1405	115	7	extending	extend	VERB
ijassa-1405	115	8	the	the	DET
ijassa-1405	115	9	well	well	ADV
ijassa-1405	115	10	-	-	PUNCT
ijassa-1405	115	11	known	know	VERB
ijassa-1405	115	12	special	special	ADJ
ijassa-1405	115	13	case	case	NOUN
ijassa-1405	115	14	,	,	PUNCT
ijassa-1405	115	15	where	where	SCONJ
ijassa-1405	115	16	the	the	DET
ijassa-1405	115	17	constraint	constraint	NOUN
ijassa-1405	115	18	graph	graph	NOUN
ijassa-1405	115	19	is	be	AUX
ijassa-1405	115	20	a	a	DET
ijassa-1405	115	21	tree	tree	NOUN
ijassa-1405	115	22	.	.	PUNCT
ijassa-1405	116	1	in	in	ADP
ijassa-1405	116	2	social	social	ADJ
ijassa-1405	116	3	and	and	CCONJ
ijassa-1405	116	4	technical	technical	ADJ
ijassa-1405	116	5	systems	system	NOUN
ijassa-1405	116	6	,	,	PUNCT
ijassa-1405	116	7	two	two	NUM
ijassa-1405	116	8	-	-	PUNCT
ijassa-1405	116	9	tier	tier	NOUN
ijassa-1405	116	10	majority	majority	NOUN
ijassa-1405	116	11	procedures	procedure	NOUN
ijassa-1405	116	12	are	be	AUX
ijassa-1405	116	13	often	often	ADV
ijassa-1405	116	14	used	use	VERB
ijassa-1405	116	15	to	to	PART
ijassa-1405	116	16	make	make	VERB
ijassa-1405	116	17	decisions	decision	NOUN
ijassa-1405	116	18	.	.	PUNCT
ijassa-1405	117	1	in	in	ADP
ijassa-1405	117	2	such	such	ADJ
ijassa-1405	117	3	procedures	procedure	NOUN
ijassa-1405	117	4	,	,	PUNCT
ijassa-1405	117	5	at	at	ADP
ijassa-1405	117	6	the	the	DET
ijassa-1405	117	7	first	first	ADJ
ijassa-1405	117	8	stage	stage	NOUN
ijassa-1405	117	9	,	,	PUNCT
ijassa-1405	117	10	majority	majority	NOUN
ijassa-1405	117	11	voting	voting	NOUN
ijassa-1405	117	12	is	be	AUX
ijassa-1405	117	13	carried	carry	VERB
ijassa-1405	117	14	out	out	ADP
ijassa-1405	117	15	in	in	ADP
ijassa-1405	117	16	local	local	ADJ
ijassa-1405	117	17	groups	group	NOUN
ijassa-1405	117	18	of	of	ADP
ijassa-1405	117	19	agents	agent	NOUN
ijassa-1405	117	20	,	,	PUNCT
ijassa-1405	117	21	at	at	ADP
ijassa-1405	117	22	the	the	DET
ijassa-1405	117	23	second	second	ADJ
ijassa-1405	117	24	stage	stage	NOUN
ijassa-1405	117	25	,	,	PUNCT
ijassa-1405	117	26	the	the	DET
ijassa-1405	117	27	results	result	NOUN
ijassa-1405	117	28	of	of	ADP
ijassa-1405	117	29	group	group	NOUN
ijassa-1405	117	30	voting	voting	NOUN
ijassa-1405	117	31	are	be	AUX
ijassa-1405	117	32	aggregated	aggregate	VERB
ijassa-1405	117	33	,	,	PUNCT
ijassa-1405	117	34	also	also	ADV
ijassa-1405	117	35	using	use	VERB
ijassa-1405	117	36	majority	majority	NOUN
ijassa-1405	117	37	,	,	PUNCT
ijassa-1405	117	38	into	into	ADP
ijassa-1405	117	39	the	the	DET
ijassa-1405	117	40	final	final	ADJ
ijassa-1405	117	41	decision	decision	NOUN
ijassa-1405	117	42	[	[	X
ijassa-1405	117	43	3	3	NUM
ijassa-1405	117	44	]	]	PUNCT
ijassa-1405	117	45	.	.	PUNCT
ijassa-1405	118	1	one	one	NUM
ijassa-1405	118	2	of	of	ADP
ijassa-1405	118	3	the	the	DET
ijassa-1405	118	4	central	central	ADJ
ijassa-1405	118	5	questions	question	NOUN
ijassa-1405	118	6	in	in	ADP
ijassa-1405	118	7	the	the	DET
ijassa-1405	118	8	analysis	analysis	NOUN
ijassa-1405	118	9	of	of	ADP
ijassa-1405	118	10	twotier	twoti	ADJ
ijassa-1405	118	11	procedures	procedure	NOUN
ijassa-1405	118	12	is	be	AUX
ijassa-1405	118	13	:	:	PUNCT
ijassa-1405	118	14	“	"	PUNCT
ijassa-1405	118	15	for	for	ADP
ijassa-1405	118	16	what	what	PRON
ijassa-1405	118	17	minimum	minimum	ADJ
ijassa-1405	118	18	proportion	proportion	NOUN
ijassa-1405	118	19	of	of	ADP
ijassa-1405	118	20	agents	agent	NOUN
ijassa-1405	118	21	that	that	PRON
ijassa-1405	118	22	support	support	VERB
ijassa-1405	118	23	a	a	DET
ijassa-1405	118	24	proposal	proposal	NOUN
ijassa-1405	118	25	can	can	AUX
ijassa-1405	118	26	it	it	PRON
ijassa-1405	118	27	ultimately	ultimately	ADV
ijassa-1405	118	28	be	be	AUX
ijassa-1405	118	29	accepted	accept	VERB
ijassa-1405	118	30	by	by	ADP
ijassa-1405	118	31	this	this	DET
ijassa-1405	118	32	procedure	procedure	NOUN
ijassa-1405	118	33	?	?	PUNCT
ijassa-1405	118	34	”	"	PUNCT
ijassa-1405	118	35	for	for	ADP
ijassa-1405	118	36	a	a	DET
ijassa-1405	118	37	given	give	VERB
ijassa-1405	118	38	graph	graph	NOUN
ijassa-1405	118	39	of	of	ADP
ijassa-1405	118	40	information	information	NOUN
ijassa-1405	118	41	connections	connection	NOUN
ijassa-1405	118	42	between	between	ADP
ijassa-1405	118	43	the	the	DET
ijassa-1405	118	44	agents	agent	NOUN
ijassa-1405	118	45	,	,	PUNCT
ijassa-1405	118	46	the	the	DET
ijassa-1405	118	47	minimum	minimum	ADJ
ijassa-1405	118	48	difference	difference	NOUN
ijassa-1405	118	49	between	between	ADP
ijassa-1405	118	50	the	the	DET
ijassa-1405	118	51	number	number	NOUN
ijassa-1405	118	52	of	of	ADP
ijassa-1405	118	53	agents	agent	NOUN
ijassa-1405	118	54	that	that	PRON
ijassa-1405	118	55	support	support	VERB
ijassa-1405	118	56	an	an	DET
ijassa-1405	118	57	accepted	accept	VERB
ijassa-1405	118	58	proposal	proposal	NOUN
ijassa-1405	118	59	and	and	CCONJ
ijassa-1405	118	60	the	the	DET
ijassa-1405	118	61	number	number	NOUN
ijassa-1405	118	62	of	of	ADP
ijassa-1405	118	63	agents	agent	NOUN
ijassa-1405	118	64	that	that	PRON
ijassa-1405	118	65	do	do	AUX
ijassa-1405	118	66	not	not	PART
ijassa-1405	118	67	support	support	VERB
ijassa-1405	118	68	it	it	PRON
ijassa-1405	118	69	is	be	AUX
ijassa-1405	118	70	called	call	VERB
ijassa-1405	118	71	the	the	DET
ijassa-1405	118	72	strict	strict	ADJ
ijassa-1405	118	73	majority	majority	NOUN
ijassa-1405	118	74	domination	domination	NOUN
ijassa-1405	118	75	number	number	NOUN
ijassa-1405	118	76	of	of	ADP
ijassa-1405	118	77	the	the	DET
ijassa-1405	118	78	graph	graph	NOUN
ijassa-1405	118	79	.	.	PUNCT
ijassa-1405	119	1	we	we	PRON
ijassa-1405	119	2	will	will	AUX
ijassa-1405	119	3	use	use	VERB
ijassa-1405	119	4	the	the	DET
ijassa-1405	119	5	following	following	ADJ
ijassa-1405	119	6	notation	notation	NOUN
ijassa-1405	119	7	.	.	PUNCT
ijassa-1405	120	1	g	g	NOUN
ijassa-1405	120	2	=	=	SYM
ijassa-1405	120	3	(	(	PUNCT
ijassa-1405	120	4	v	v	NOUN
ijassa-1405	120	5	,	,	PUNCT
ijassa-1405	120	6	e	e	NOUN
ijassa-1405	120	7	)	)	PUNCT
ijassa-1405	120	8	,	,	PUNCT
ijassa-1405	120	9	|v	|v	PROPN
ijassa-1405	120	10	|	|	NOUN
ijassa-1405	120	11	=	=	SYM
ijassa-1405	120	12	n	n	CCONJ
ijassa-1405	120	13	,	,	PUNCT
ijassa-1405	120	14	is	be	AUX
ijassa-1405	120	15	a	a	DET
ijassa-1405	120	16	graph	graph	NOUN
ijassa-1405	120	17	,	,	PUNCT
ijassa-1405	120	18	each	each	DET
ijassa-1405	120	19	vertex	vertex	NOUN
ijassa-1405	120	20	of	of	ADP
ijassa-1405	120	21	which	which	PRON
ijassa-1405	120	22	has	have	VERB
ijassa-1405	120	23	a	a	DET
ijassa-1405	120	24	loop	loop	NOUN
ijassa-1405	120	25	.	.	PUNCT
ijassa-1405	121	1	vertex	vertex	NOUN
ijassa-1405	121	2	v	v	ADP
ijassa-1405	121	3	∈	∈	PROPN
ijassa-1405	121	4	v	v	NOUN
ijassa-1405	121	5	has	have	VERB
ijassa-1405	121	6	the	the	DET
ijassa-1405	121	7	set	set	NOUN
ijassa-1405	121	8	of	of	ADP
ijassa-1405	121	9	neighbors	neighbor	NOUN
ijassa-1405	121	10	nv	nv	PROPN
ijassa-1405	122	1	=	=	PUNCT
ijassa-1405	122	2	{	{	PUNCT
ijassa-1405	122	3	w	w	PROPN
ijassa-1405	122	4	∈	∈	PROPN
ijassa-1405	122	5	v	v	NOUN
ijassa-1405	122	6	:	:	PUNCT
ijassa-1405	122	7	{	{	PUNCT
ijassa-1405	122	8	v	v	NOUN
ijassa-1405	122	9	,	,	PUNCT
ijassa-1405	122	10	w	w	NOUN
ijassa-1405	122	11	}	}	PUNCT
ijassa-1405	122	12	∈	∈	PROPN
ijassa-1405	122	13	e	e	NOUN
ijassa-1405	122	14	}	}	PUNCT
ijassa-1405	122	15	,	,	PUNCT
ijassa-1405	122	16	which	which	PRON
ijassa-1405	122	17	includes	include	VERB
ijassa-1405	122	18	v.	v.	CCONJ
ijassa-1405	122	19	we	we	PRON
ijassa-1405	122	20	will	will	AUX
ijassa-1405	122	21	write	write	VERB
ijassa-1405	122	22	nv(g	nv(g	PUNCT
ijassa-1405	122	23	)	)	PUNCT
ijassa-1405	122	24	when	when	SCONJ
ijassa-1405	122	25	several	several	ADJ
ijassa-1405	122	26	graphs	graph	NOUN
ijassa-1405	122	27	share	share	VERB
ijassa-1405	122	28	the	the	DET
ijassa-1405	122	29	same	same	ADJ
ijassa-1405	122	30	vertex	vertex	NOUN
ijassa-1405	122	31	set	set	NOUN
ijassa-1405	122	32	.	.	PUNCT
ijassa-1405	123	1	an	an	DET
ijassa-1405	123	2	opinion	opinion	NOUN
ijassa-1405	123	3	function	function	NOUN
ijassa-1405	123	4	f	f	NOUN
ijassa-1405	123	5	:	:	PUNCT
ijassa-1405	123	6	v	v	X
ijassa-1405	123	7	→	→	SYM
ijassa-1405	123	8	{	{	PUNCT
ijassa-1405	123	9	−1	−1	NOUN
ijassa-1405	123	10	,	,	PUNCT
ijassa-1405	123	11	1	1	NUM
ijassa-1405	123	12	}	}	PUNCT
ijassa-1405	123	13	associates	associate	VERB
ijassa-1405	123	14	an	an	DET
ijassa-1405	123	15	opinion	opinion	NOUN
ijassa-1405	123	16	with	with	ADP
ijassa-1405	123	17	each	each	DET
ijassa-1405	123	18	vertex	vertex	NOUN
ijassa-1405	123	19	.	.	PUNCT
ijassa-1405	124	1	the	the	DET
ijassa-1405	124	2	opinion	opinion	NOUN
ijassa-1405	124	3	function	function	NOUN
ijassa-1405	124	4	is	be	AUX
ijassa-1405	124	5	extended	extend	VERB
ijassa-1405	124	6	to	to	ADP
ijassa-1405	124	7	subsets	subset	NOUN
ijassa-1405	124	8	w	w	ADP
ijassa-1405	124	9	⊆	⊆	NUM
ijassa-1405	124	10	v	v	NOUN
ijassa-1405	124	11	as	as	ADP
ijassa-1405	124	12	the	the	DET
ijassa-1405	124	13	sum	sum	NOUN
ijassa-1405	124	14	of	of	ADP
ijassa-1405	124	15	the	the	DET
ijassa-1405	124	16	opinions	opinion	NOUN
ijassa-1405	124	17	of	of	ADP
ijassa-1405	124	18	the	the	DET
ijassa-1405	124	19	vertices	vertex	NOUN
ijassa-1405	124	20	that	that	PRON
ijassa-1405	124	21	belong	belong	VERB
ijassa-1405	124	22	to	to	ADP
ijassa-1405	124	23	w	w	PROPN
ijassa-1405	124	24	:	:	PUNCT
ijassa-1405	124	25	f(w	f(w	PROPN
ijassa-1405	124	26	)	)	PUNCT
ijassa-1405	125	1	=	=	PUNCT
ijassa-1405	125	2	∑	∑	PROPN
ijassa-1405	125	3	v∈w	v∈w	PROPN
ijassa-1405	125	4	f(v	f(v	NOUN
ijassa-1405	125	5	)	)	PUNCT
ijassa-1405	125	6	.	.	PUNCT
ijassa-1405	126	1	each	each	DET
ijassa-1405	126	2	vertex	vertex	NOUN
ijassa-1405	126	3	v	v	ADP
ijassa-1405	126	4	∈	∈	NOUN
ijassa-1405	126	5	v	v	NOUN
ijassa-1405	126	6	votes	vote	NOUN
ijassa-1405	126	7	“	"	PUNCT
ijassa-1405	126	8	for	for	ADP
ijassa-1405	126	9	”	"	PUNCT
ijassa-1405	126	10	if	if	SCONJ
ijassa-1405	126	11	f(nv	f(nv	NOUN
ijassa-1405	126	12	)	)	PUNCT
ijassa-1405	126	13	>	>	X
ijassa-1405	126	14	0	0	PUNCT
ijassa-1405	126	15	or	or	CCONJ
ijassa-1405	126	16	“	"	PUNCT
ijassa-1405	126	17	against	against	ADP
ijassa-1405	126	18	”	"	PUNCT
ijassa-1405	126	19	otherwise	otherwise	ADV
ijassa-1405	126	20	.	.	PUNCT
ijassa-1405	127	1	a	a	DET
ijassa-1405	127	2	pair	pair	NOUN
ijassa-1405	127	3	(	(	PUNCT
ijassa-1405	127	4	g	g	NOUN
ijassa-1405	127	5	,	,	PUNCT
ijassa-1405	127	6	f	f	X
ijassa-1405	127	7	)	)	PUNCT
ijassa-1405	127	8	≡	≡	PROPN
ijassa-1405	127	9	gf	gf	PROPN
ijassa-1405	127	10	will	will	AUX
ijassa-1405	127	11	be	be	AUX
ijassa-1405	127	12	called	call	VERB
ijassa-1405	127	13	a	a	DET
ijassa-1405	127	14	configuration	configuration	NOUN
ijassa-1405	127	15	.	.	PUNCT
ijassa-1405	128	1	let	let	VERB
ijassa-1405	128	2	v	v	NOUN
ijassa-1405	128	3	+	+	NOUN
ijassa-1405	129	1	=	=	SYM
ijassa-1405	129	2	{	{	PUNCT
ijassa-1405	129	3	v	v	NUM
ijassa-1405	129	4	∈	∈	NOUN
ijassa-1405	129	5	v	v	NOUN
ijassa-1405	129	6	:	:	PUNCT
ijassa-1405	129	7	f(nv	f(nv	NOUN
ijassa-1405	129	8	)	)	PUNCT
ijassa-1405	129	9	>	>	X
ijassa-1405	129	10	0	0	X
ijassa-1405	129	11	}	}	PUNCT
ijassa-1405	129	12	be	be	AUX
ijassa-1405	129	13	the	the	DET
ijassa-1405	129	14	set	set	NOUN
ijassa-1405	129	15	of	of	ADP
ijassa-1405	129	16	vertices	vertex	NOUN
ijassa-1405	129	17	voting	vote	VERB
ijassa-1405	129	18	“	"	PUNCT
ijassa-1405	129	19	for	for	ADP
ijassa-1405	129	20	”	"	PUNCT
ijassa-1405	129	21	.	.	PUNCT
ijassa-1405	130	1	definition	definition	NOUN
ijassa-1405	130	2	3.1	3.1	NUM
ijassa-1405	130	3	.	.	PUNCT
ijassa-1405	131	1	given	give	VERB
ijassa-1405	131	2	a	a	DET
ijassa-1405	131	3	configuration	configuration	NOUN
ijassa-1405	131	4	,	,	PUNCT
ijassa-1405	131	5	a	a	DET
ijassa-1405	131	6	proposal	proposal	NOUN
ijassa-1405	131	7	put	put	VERB
ijassa-1405	131	8	to	to	ADP
ijassa-1405	131	9	a	a	DET
ijassa-1405	131	10	vote	vote	NOUN
ijassa-1405	131	11	is	be	AUX
ijassa-1405	131	12	accepted	accept	VERB
ijassa-1405	131	13	if	if	SCONJ
ijassa-1405	131	14	|v	|v	ADP
ijassa-1405	131	15	+	+	ADV
ijassa-1405	131	16	|	|	ADV
ijassa-1405	131	17	>	>	X
ijassa-1405	131	18	|v	|v	PROPN
ijassa-1405	131	19	|/2	|/2	PROPN
ijassa-1405	131	20	and	and	CCONJ
ijassa-1405	131	21	rejected	reject	VERB
ijassa-1405	131	22	otherwise	otherwise	ADV
ijassa-1405	131	23	;	;	PUNCT
ijassa-1405	131	24	acceptance	acceptance	NOUN
ijassa-1405	131	25	or	or	CCONJ
ijassa-1405	131	26	rejection	rejection	NOUN
ijassa-1405	131	27	are	be	AUX
ijassa-1405	131	28	the	the	DET
ijassa-1405	131	29	possible	possible	ADJ
ijassa-1405	131	30	results	result	NOUN
ijassa-1405	131	31	of	of	ADP
ijassa-1405	131	32	the	the	DET
ijassa-1405	131	33	vote	vote	NOUN
ijassa-1405	131	34	.	.	PUNCT
ijassa-1405	132	1	an	an	DET
ijassa-1405	132	2	opinion	opinion	NOUN
ijassa-1405	132	3	function	function	NOUN
ijassa-1405	132	4	for	for	ADP
ijassa-1405	132	5	which	which	PRON
ijassa-1405	132	6	a	a	DET
ijassa-1405	132	7	proposal	proposal	NOUN
ijassa-1405	132	8	is	be	AUX
ijassa-1405	132	9	accepted	accept	VERB
ijassa-1405	132	10	is	be	AUX
ijassa-1405	132	11	called	call	VERB
ijassa-1405	132	12	a	a	DET
ijassa-1405	132	13	strict	strict	ADJ
ijassa-1405	132	14	majority	majority	NOUN
ijassa-1405	132	15	function	function	NOUN
ijassa-1405	132	16	for	for	ADP
ijassa-1405	132	17	g.	g.	PROPN
ijassa-1405	132	18	definition	definition	NOUN
ijassa-1405	132	19	3.2	3.2	NUM
ijassa-1405	132	20	.	.	PUNCT
ijassa-1405	133	1	the	the	DET
ijassa-1405	133	2	strict	strict	ADJ
ijassa-1405	133	3	majority	majority	NOUN
ijassa-1405	133	4	domination	domination	NOUN
ijassa-1405	133	5	number	number	NOUN
ijassa-1405	133	6	of	of	ADP
ijassa-1405	133	7	a	a	DET
ijassa-1405	133	8	graph	graph	NOUN
ijassa-1405	133	9	g	g	PROPN
ijassa-1405	133	10	is	be	AUX
ijassa-1405	133	11	γ(g	γ(g	PROPN
ijassa-1405	133	12	)	)	PUNCT
ijassa-1405	133	13	=	=	PUNCT
ijassa-1405	134	1	minf∈f+f(v	minf∈f+f(v	PROPN
ijassa-1405	134	2	)	)	PUNCT
ijassa-1405	134	3	,	,	PUNCT
ijassa-1405	134	4	where	where	SCONJ
ijassa-1405	134	5	f+	f+	PROPN
ijassa-1405	134	6	is	be	AUX
ijassa-1405	134	7	the	the	DET
ijassa-1405	134	8	set	set	NOUN
ijassa-1405	134	9	of	of	ADP
ijassa-1405	134	10	strict	strict	ADJ
ijassa-1405	134	11	majority	majority	NOUN
ijassa-1405	134	12	functions	function	NOUN
ijassa-1405	134	13	for	for	ADP
ijassa-1405	134	14	g.	g.	PROPN
ijassa-1405	134	15	a	a	DET
ijassa-1405	134	16	strict	strict	ADJ
ijassa-1405	134	17	majority	majority	NOUN
ijassa-1405	134	18	function	function	NOUN
ijassa-1405	134	19	f	f	PROPN
ijassa-1405	134	20	will	will	AUX
ijassa-1405	134	21	be	be	AUX
ijassa-1405	134	22	called	call	VERB
ijassa-1405	134	23	optimal	optimal	ADJ
ijassa-1405	134	24	whenever	whenever	SCONJ
ijassa-1405	134	25	f(v	f(v	NOUN
ijassa-1405	134	26	)	)	PUNCT
ijassa-1405	135	1	=	=	PUNCT
ijassa-1405	135	2	γ(g	γ(g	PROPN
ijassa-1405	135	3	)	)	PUNCT
ijassa-1405	135	4	.	.	PUNCT
ijassa-1405	136	1	finding	find	VERB
ijassa-1405	136	2	the	the	DET
ijassa-1405	136	3	strict	strict	ADJ
ijassa-1405	136	4	majority	majority	NOUN
ijassa-1405	136	5	domination	domination	NOUN
ijassa-1405	136	6	number	number	NOUN
ijassa-1405	136	7	of	of	ADP
ijassa-1405	136	8	a	a	DET
ijassa-1405	136	9	given	give	VERB
ijassa-1405	136	10	graph	graph	NOUN
ijassa-1405	136	11	g	g	PROPN
ijassa-1405	136	12	and	and	CCONJ
ijassa-1405	136	13	the	the	DET
ijassa-1405	136	14	corresponding	corresponding	ADJ
ijassa-1405	136	15	optimal	optimal	ADJ
ijassa-1405	136	16	opinion	opinion	NOUN
ijassa-1405	136	17	function	function	NOUN
ijassa-1405	136	18	is	be	AUX
ijassa-1405	136	19	a	a	DET
ijassa-1405	136	20	discrete	discrete	ADJ
ijassa-1405	136	21	optimization	optimization	NOUN
ijassa-1405	136	22	problem	problem	NOUN
ijassa-1405	136	23	whose	whose	DET
ijassa-1405	136	24	solution	solution	NOUN
ijassa-1405	136	25	space	space	NOUN
ijassa-1405	136	26	is	be	AUX
ijassa-1405	136	27	given	give	VERB
ijassa-1405	136	28	by	by	ADP
ijassa-1405	136	29	2n	2n	NUM
ijassa-1405	136	30	possible	possible	ADJ
ijassa-1405	136	31	opinion	opinion	NOUN
ijassa-1405	136	32	functions	function	NOUN
ijassa-1405	136	33	.	.	PUNCT
ijassa-1405	137	1	for	for	ADP
ijassa-1405	137	2	the	the	DET
ijassa-1405	137	3	case	case	NOUN
ijassa-1405	137	4	of	of	ADP
ijassa-1405	137	5	an	an	DET
ijassa-1405	137	6	arbitrary	arbitrary	ADJ
ijassa-1405	137	7	graph	graph	NOUN
ijassa-1405	137	8	g	g	NOUN
ijassa-1405	137	9	,	,	PUNCT
ijassa-1405	137	10	this	this	PRON
ijassa-1405	137	11	is	be	AUX
ijassa-1405	137	12	an	an	DET
ijassa-1405	137	13	np	np	NOUN
ijassa-1405	137	14	-	-	PUNCT
ijassa-1405	137	15	complete	complete	ADJ
ijassa-1405	137	16	problem	problem	NOUN
ijassa-1405	138	1	[	[	X
ijassa-1405	138	2	1	1	NUM
ijassa-1405	138	3	]	]	PUNCT
ijassa-1405	138	4	,	,	PUNCT
ijassa-1405	138	5	however	however	ADV
ijassa-1405	138	6	,	,	PUNCT
ijassa-1405	138	7	there	there	PRON
ijassa-1405	138	8	are	be	VERB
ijassa-1405	138	9	special	special	ADJ
ijassa-1405	138	10	cases	case	NOUN
ijassa-1405	138	11	for	for	ADP
ijassa-1405	138	12	which	which	PRON
ijassa-1405	138	13	a	a	DET
ijassa-1405	138	14	polynomial	polynomial	ADJ
ijassa-1405	138	15	algorithm	algorithm	NOUN
ijassa-1405	138	16	that	that	PRON
ijassa-1405	138	17	solves	solve	VERB
ijassa-1405	138	18	it	it	PRON
ijassa-1405	138	19	exists	exist	VERB
ijassa-1405	138	20	.	.	PUNCT
ijassa-1405	139	1	in	in	ADP
ijassa-1405	139	2	particular	particular	ADJ
ijassa-1405	139	3	,	,	PUNCT
ijassa-1405	139	4	if	if	SCONJ
ijassa-1405	139	5	g	g	PROPN
ijassa-1405	139	6	is	be	AUX
ijassa-1405	139	7	a	a	DET
ijassa-1405	139	8	tree	tree	NOUN
ijassa-1405	139	9	,	,	PUNCT
ijassa-1405	139	10	then	then	ADV
ijassa-1405	139	11	an	an	DET
ijassa-1405	139	12	optimal	optimal	ADJ
ijassa-1405	139	13	opinion	opinion	NOUN
ijassa-1405	139	14	function	function	NOUN
ijassa-1405	139	15	can	can	AUX
ijassa-1405	139	16	be	be	AUX
ijassa-1405	139	17	constructed	construct	VERB
ijassa-1405	139	18	in	in	ADP
ijassa-1405	139	19	polynomial	polynomial	ADJ
ijassa-1405	139	20	time	time	NOUN
ijassa-1405	139	21	using	use	VERB
ijassa-1405	139	22	a	a	DET
ijassa-1405	139	23	dynamic	dynamic	ADJ
ijassa-1405	139	24	programming	programming	NOUN
ijassa-1405	139	25	algorithm	algorithm	NOUN
ijassa-1405	139	26	[	[	X
ijassa-1405	139	27	9	9	NUM
ijassa-1405	139	28	]	]	PUNCT
ijassa-1405	139	29	.	.	PUNCT
ijassa-1405	140	1	the	the	DET
ijassa-1405	140	2	problems	problem	NOUN
ijassa-1405	140	3	of	of	ADP
ijassa-1405	140	4	finding	find	VERB
ijassa-1405	140	5	the	the	DET
ijassa-1405	140	6	strict	strict	ADJ
ijassa-1405	140	7	majority	majority	NOUN
ijassa-1405	140	8	domination	domination	NOUN
ijassa-1405	140	9	number	number	NOUN
ijassa-1405	140	10	on	on	ADP
ijassa-1405	140	11	trees	tree	NOUN
ijassa-1405	140	12	act	act	VERB
ijassa-1405	140	13	as	as	ADP
ijassa-1405	140	14	a	a	DET
ijassa-1405	140	15	simple	simple	ADJ
ijassa-1405	140	16	special	special	ADJ
ijassa-1405	140	17	case	case	NOUN
ijassa-1405	140	18	in	in	ADP
ijassa-1405	140	19	the	the	DET
ijassa-1405	140	20	application	application	NOUN
ijassa-1405	140	21	of	of	ADP
ijassa-1405	140	22	the	the	DET
ijassa-1405	140	23	pairwise	pairwise	NOUN
ijassa-1405	140	24	similarity	similarity	NOUN
ijassa-1405	140	25	method	method	NOUN
ijassa-1405	140	26	described	describe	VERB
ijassa-1405	140	27	below	below	ADV
ijassa-1405	140	28	.	.	PUNCT
ijassa-1405	141	1	in	in	ADP
ijassa-1405	141	2	accordance	accordance	NOUN
ijassa-1405	141	3	with	with	ADP
ijassa-1405	141	4	the	the	DET
ijassa-1405	141	5	general	general	ADJ
ijassa-1405	141	6	scheme	scheme	NOUN
ijassa-1405	141	7	of	of	ADP
ijassa-1405	141	8	the	the	DET
ijassa-1405	141	9	method	method	NOUN
ijassa-1405	141	10	given	give	VERB
ijassa-1405	141	11	in	in	ADP
ijassa-1405	141	12	section	section	NOUN
ijassa-1405	141	13	2	2	NUM
ijassa-1405	141	14	,	,	PUNCT
ijassa-1405	141	15	we	we	PRON
ijassa-1405	141	16	will	will	AUX
ijassa-1405	141	17	show	show	VERB
ijassa-1405	141	18	that	that	SCONJ
ijassa-1405	141	19	the	the	DET
ijassa-1405	141	20	case	case	NOUN
ijassa-1405	141	21	of	of	ADP
ijassa-1405	141	22	graphs	graph	NOUN
ijassa-1405	141	23	with	with	ADP
ijassa-1405	141	24	an	an	DET
ijassa-1405	141	25	upper	upper	ADJ
ijassa-1405	141	26	bounded	bounded	ADJ
ijassa-1405	141	27	cyclomatic	cyclomatic	ADJ
ijassa-1405	141	28	number	number	NOUN
ijassa-1405	141	29	is	be	AUX
ijassa-1405	141	30	a	a	DET
ijassa-1405	141	31	semisimple	semisimple	ADJ
ijassa-1405	141	32	special	special	ADJ
ijassa-1405	141	33	case	case	NOUN
ijassa-1405	141	34	for	for	ADP
ijassa-1405	141	35	copyright	copyright	NOUN
ijassa-1405	141	36	©	©	PROPN
ijassa-1405	141	37	2023	2023	NUM
ijassa-1405	141	38	assa	assa	NOUN
ijassa-1405	141	39	.	.	PUNCT
ijassa-1405	142	1	adv	adv	PROPN
ijassa-1405	142	2	syst	syst	PROPN
ijassa-1405	142	3	sci	sci	PROPN
ijassa-1405	142	4	appl	appl	PROPN
ijassa-1405	142	5	(	(	PUNCT
ijassa-1405	142	6	2023	2023	NUM
ijassa-1405	142	7	)	)	PUNCT
ijassa-1405	142	8	pairwise	pairwise	NOUN
ijassa-1405	142	9	similarity	similarity	NOUN
ijassa-1405	142	10	estimation	estimation	NOUN
ijassa-1405	142	11	for	for	ADP
ijassa-1405	142	12	discrete	discrete	ADJ
ijassa-1405	142	13	optimization	optimization	NOUN
ijassa-1405	142	14	problems	problem	NOUN
ijassa-1405	142	15	169	169	NUM
ijassa-1405	142	16	the	the	DET
ijassa-1405	142	17	problem	problem	NOUN
ijassa-1405	142	18	of	of	ADP
ijassa-1405	142	19	finding	find	VERB
ijassa-1405	142	20	the	the	DET
ijassa-1405	142	21	strict	strict	ADJ
ijassa-1405	142	22	majority	majority	NOUN
ijassa-1405	142	23	domination	domination	NOUN
ijassa-1405	142	24	number	number	NOUN
ijassa-1405	142	25	of	of	ADP
ijassa-1405	142	26	a	a	DET
ijassa-1405	142	27	graph	graph	NOUN
ijassa-1405	142	28	,	,	PUNCT
ijassa-1405	142	29	that	that	ADV
ijassa-1405	142	30	is	is	ADV
ijassa-1405	142	31	,	,	PUNCT
ijassa-1405	142	32	it	it	PRON
ijassa-1405	142	33	allows	allow	VERB
ijassa-1405	142	34	the	the	DET
ijassa-1405	142	35	construction	construction	NOUN
ijassa-1405	142	36	of	of	ADP
ijassa-1405	142	37	an	an	DET
ijassa-1405	142	38	approximate	approximate	ADJ
ijassa-1405	142	39	solution	solution	NOUN
ijassa-1405	142	40	with	with	ADP
ijassa-1405	142	41	a	a	DET
ijassa-1405	142	42	guaranteed	guarantee	VERB
ijassa-1405	142	43	absolute	absolute	ADJ
ijassa-1405	142	44	error	error	NOUN
ijassa-1405	142	45	by	by	ADP
ijassa-1405	142	46	reduction	reduction	NOUN
ijassa-1405	142	47	to	to	ADP
ijassa-1405	142	48	the	the	DET
ijassa-1405	142	49	case	case	NOUN
ijassa-1405	142	50	of	of	ADP
ijassa-1405	142	51	a	a	DET
ijassa-1405	142	52	tree	tree	NOUN
ijassa-1405	142	53	.	.	PUNCT
ijassa-1405	143	1	thus	thus	ADV
ijassa-1405	143	2	,	,	PUNCT
ijassa-1405	143	3	a	a	DET
ijassa-1405	143	4	limited	limited	ADJ
ijassa-1405	143	5	number	number	NOUN
ijassa-1405	143	6	of	of	ADP
ijassa-1405	143	7	independent	independent	ADJ
ijassa-1405	143	8	cycles	cycle	NOUN
ijassa-1405	143	9	is	be	AUX
ijassa-1405	143	10	the	the	DET
ijassa-1405	143	11	pattern	pattern	NOUN
ijassa-1405	143	12	α	α	NOUN
ijassa-1405	143	13	around	around	ADP
ijassa-1405	143	14	which	which	PRON
ijassa-1405	143	15	the	the	DET
ijassa-1405	143	16	application	application	NOUN
ijassa-1405	143	17	of	of	ADP
ijassa-1405	143	18	the	the	DET
ijassa-1405	143	19	pairwise	pairwise	NOUN
ijassa-1405	143	20	similarity	similarity	NOUN
ijassa-1405	143	21	method	method	NOUN
ijassa-1405	143	22	can	can	AUX
ijassa-1405	143	23	be	be	AUX
ijassa-1405	143	24	developed	develop	VERB
ijassa-1405	143	25	.	.	PUNCT
ijassa-1405	144	1	in	in	ADP
ijassa-1405	144	2	theorem	theorem	ADJ
ijassa-1405	144	3	3.1	3.1	NUM
ijassa-1405	144	4	below	below	ADV
ijassa-1405	144	5	,	,	PUNCT
ijassa-1405	144	6	we	we	PRON
ijassa-1405	144	7	prove	prove	VERB
ijassa-1405	144	8	that	that	SCONJ
ijassa-1405	144	9	for	for	ADP
ijassa-1405	144	10	any	any	DET
ijassa-1405	144	11	spanning	span	VERB
ijassa-1405	144	12	tree	tree	NOUN
ijassa-1405	144	13	t	t	PROPN
ijassa-1405	144	14	of	of	ADP
ijassa-1405	144	15	graph	graph	NOUN
ijassa-1405	144	16	g	g	NOUN
ijassa-1405	144	17	having	have	VERB
ijassa-1405	144	18	k	k	PROPN
ijassa-1405	144	19	cycles	cycle	NOUN
ijassa-1405	144	20	,	,	PUNCT
ijassa-1405	144	21	γ(g	γ(g	PROPN
ijassa-1405	144	22	)	)	PUNCT
ijassa-1405	144	23	≥	≥	NOUN
ijassa-1405	144	24	γ(t	γ(t	PUNCT
ijassa-1405	144	25	)	)	PUNCT
ijassa-1405	145	1	−	−	PROPN
ijassa-1405	145	2	4k	4k	PRON
ijassa-1405	145	3	holds	hold	VERB
ijassa-1405	145	4	.	.	PUNCT
ijassa-1405	146	1	it	it	PRON
ijassa-1405	146	2	also	also	ADV
ijassa-1405	146	3	follows	follow	VERB
ijassa-1405	146	4	from	from	ADP
ijassa-1405	146	5	the	the	DET
ijassa-1405	146	6	proof	proof	NOUN
ijassa-1405	146	7	that	that	SCONJ
ijassa-1405	146	8	knowing	know	VERB
ijassa-1405	146	9	the	the	DET
ijassa-1405	146	10	optimal	optimal	ADJ
ijassa-1405	146	11	opinion	opinion	NOUN
ijassa-1405	146	12	function	function	NOUN
ijassa-1405	146	13	f	f	PROPN
ijassa-1405	146	14	of	of	ADP
ijassa-1405	146	15	a	a	DET
ijassa-1405	146	16	spanning	span	VERB
ijassa-1405	146	17	tree	tree	NOUN
ijassa-1405	146	18	t	t	PROPN
ijassa-1405	146	19	,	,	PUNCT
ijassa-1405	146	20	one	one	PRON
ijassa-1405	146	21	can	can	AUX
ijassa-1405	146	22	construct	construct	VERB
ijassa-1405	146	23	a	a	DET
ijassa-1405	146	24	strict	strict	ADJ
ijassa-1405	146	25	majority	majority	NOUN
ijassa-1405	146	26	function	function	NOUN
ijassa-1405	146	27	f̃	f̃	PROPN
ijassa-1405	146	28	for	for	ADP
ijassa-1405	146	29	the	the	DET
ijassa-1405	146	30	graph	graph	NOUN
ijassa-1405	146	31	g	g	ADP
ijassa-1405	146	32	such	such	ADJ
ijassa-1405	146	33	that	that	DET
ijassa-1405	146	34	f̃(v	f̃(v	NOUN
ijassa-1405	146	35	)	)	PUNCT
ijassa-1405	146	36	≤	≤	NOUN
ijassa-1405	146	37	γ(t	γ(t	PUNCT
ijassa-1405	146	38	)	)	PUNCT
ijassa-1405	147	1	+	+	CCONJ
ijassa-1405	147	2	2k	2k	NUM
ijassa-1405	147	3	,	,	PUNCT
ijassa-1405	147	4	which	which	PRON
ijassa-1405	147	5	follows	follow	VERB
ijassa-1405	147	6	that	that	SCONJ
ijassa-1405	147	7	the	the	DET
ijassa-1405	147	8	error	error	NOUN
ijassa-1405	147	9	of	of	ADP
ijassa-1405	147	10	the	the	DET
ijassa-1405	147	11	approximate	approximate	ADJ
ijassa-1405	147	12	solution	solution	NOUN
ijassa-1405	147	13	f̃(v	f̃(v	NOUN
ijassa-1405	147	14	)	)	PUNCT
ijassa-1405	147	15	−	−	PROPN
ijassa-1405	147	16	γ(g	γ(g	PROPN
ijassa-1405	147	17	)	)	PUNCT
ijassa-1405	147	18	does	do	AUX
ijassa-1405	147	19	not	not	PART
ijassa-1405	147	20	exceed	exceed	VERB
ijassa-1405	147	21	6k	6k	NOUN
ijassa-1405	147	22	.	.	PUNCT
ijassa-1405	148	1	this	this	DET
ijassa-1405	148	2	theorem	theorem	NOUN
ijassa-1405	148	3	allows	allow	VERB
ijassa-1405	148	4	us	we	PRON
ijassa-1405	148	5	to	to	PART
ijassa-1405	148	6	reduce	reduce	VERB
ijassa-1405	148	7	the	the	DET
ijassa-1405	148	8	search	search	NOUN
ijassa-1405	148	9	for	for	ADP
ijassa-1405	148	10	an	an	DET
ijassa-1405	148	11	approximate	approximate	ADJ
ijassa-1405	148	12	solution	solution	NOUN
ijassa-1405	148	13	for	for	ADP
ijassa-1405	148	14	g	g	NOUN
ijassa-1405	148	15	to	to	ADP
ijassa-1405	148	16	the	the	DET
ijassa-1405	148	17	search	search	NOUN
ijassa-1405	148	18	for	for	ADP
ijassa-1405	148	19	an	an	DET
ijassa-1405	148	20	optimal	optimal	ADJ
ijassa-1405	148	21	opinion	opinion	NOUN
ijassa-1405	148	22	function	function	NOUN
ijassa-1405	148	23	for	for	ADP
ijassa-1405	148	24	a	a	DET
ijassa-1405	148	25	tree	tree	NOUN
ijassa-1405	148	26	t	t	NOUN
ijassa-1405	148	27	,	,	PUNCT
ijassa-1405	148	28	which	which	PRON
ijassa-1405	148	29	can	can	AUX
ijassa-1405	148	30	be	be	AUX
ijassa-1405	148	31	done	do	VERB
ijassa-1405	148	32	in	in	ADP
ijassa-1405	148	33	polynomial	polynomial	ADJ
ijassa-1405	148	34	time	time	NOUN
ijassa-1405	148	35	[	[	X
ijassa-1405	148	36	1	1	NUM
ijassa-1405	148	37	]	]	PUNCT
ijassa-1405	148	38	,	,	PUNCT
ijassa-1405	148	39	while	while	SCONJ
ijassa-1405	148	40	the	the	DET
ijassa-1405	148	41	guaranteed	guarantee	VERB
ijassa-1405	148	42	error	error	NOUN
ijassa-1405	148	43	of	of	ADP
ijassa-1405	148	44	the	the	DET
ijassa-1405	148	45	solution	solution	NOUN
ijassa-1405	148	46	depends	depend	VERB
ijassa-1405	148	47	only	only	ADV
ijassa-1405	148	48	on	on	ADP
ijassa-1405	148	49	the	the	DET
ijassa-1405	148	50	number	number	NOUN
ijassa-1405	148	51	of	of	ADP
ijassa-1405	148	52	cycles	cycle	NOUN
ijassa-1405	148	53	in	in	ADP
ijassa-1405	148	54	the	the	DET
ijassa-1405	148	55	graph	graph	NOUN
ijassa-1405	148	56	,	,	PUNCT
ijassa-1405	148	57	not	not	PART
ijassa-1405	148	58	on	on	ADP
ijassa-1405	148	59	its	its	PRON
ijassa-1405	148	60	order	order	NOUN
ijassa-1405	148	61	or	or	CCONJ
ijassa-1405	148	62	size	size	NOUN
ijassa-1405	148	63	.	.	PUNCT
ijassa-1405	149	1	we	we	PRON
ijassa-1405	149	2	first	first	ADV
ijassa-1405	149	3	introduce	introduce	VERB
ijassa-1405	149	4	a	a	DET
ijassa-1405	149	5	technical	technical	ADJ
ijassa-1405	149	6	notion	notion	NOUN
ijassa-1405	149	7	and	and	CCONJ
ijassa-1405	149	8	prove	prove	VERB
ijassa-1405	149	9	an	an	DET
ijassa-1405	149	10	auxiliary	auxiliary	ADJ
ijassa-1405	149	11	result	result	NOUN
ijassa-1405	149	12	.	.	PUNCT
ijassa-1405	150	1	definition	definition	NOUN
ijassa-1405	150	2	3.3	3.3	NUM
ijassa-1405	150	3	.	.	PUNCT
ijassa-1405	151	1	let	let	VERB
ijassa-1405	151	2	configurations	configuration	NOUN
ijassa-1405	151	3	gf	gf	NOUN
ijassa-1405	151	4	and	and	CCONJ
ijassa-1405	151	5	g′f̃	g′f̃	PROPN
ijassa-1405	151	6	share	share	NOUN
ijassa-1405	151	7	vertex	vertex	NOUN
ijassa-1405	151	8	set	set	VERB
ijassa-1405	151	9	v	v	NOUN
ijassa-1405	151	10	.	.	PUNCT
ijassa-1405	152	1	we	we	PRON
ijassa-1405	152	2	say	say	VERB
ijassa-1405	152	3	that	that	SCONJ
ijassa-1405	152	4	the	the	DET
ijassa-1405	152	5	voting	voting	NOUN
ijassa-1405	152	6	conditions	condition	NOUN
ijassa-1405	152	7	of	of	ADP
ijassa-1405	152	8	v	v	NUM
ijassa-1405	152	9	∈	∈	PROPN
ijassa-1405	152	10	v	v	NOUN
ijassa-1405	152	11	in	in	ADP
ijassa-1405	152	12	g′f̃	g′f̃	PROPN
ijassa-1405	152	13	are	be	AUX
ijassa-1405	152	14	no	no	ADV
ijassa-1405	152	15	worse	bad	ADJ
ijassa-1405	152	16	than	than	ADP
ijassa-1405	152	17	in	in	ADP
ijassa-1405	152	18	gf	gf	PROPN
ijassa-1405	152	19	if	if	SCONJ
ijassa-1405	152	20	v	v	PRON
ijassa-1405	152	21	has	have	VERB
ijassa-1405	152	22	at	at	ADV
ijassa-1405	152	23	least	least	ADJ
ijassa-1405	152	24	as	as	ADP
ijassa-1405	152	25	many	many	ADJ
ijassa-1405	152	26	neighbors	neighbor	NOUN
ijassa-1405	152	27	in	in	ADP
ijassa-1405	152	28	g′f̃	g′f̃	PROPN
ijassa-1405	152	29	with	with	ADP
ijassa-1405	152	30	opinion	opinion	NOUN
ijassa-1405	152	31	+1	+1	INTJ
ijassa-1405	152	32	than	than	ADP
ijassa-1405	152	33	in	in	ADP
ijassa-1405	152	34	gf	gf	NOUN
ijassa-1405	152	35	and	and	CCONJ
ijassa-1405	152	36	no	no	PRON
ijassa-1405	152	37	more	more	ADJ
ijassa-1405	152	38	neighbors	neighbor	NOUN
ijassa-1405	152	39	in	in	ADP
ijassa-1405	152	40	g′f̃	g′f̃	PROPN
ijassa-1405	152	41	with	with	ADP
ijassa-1405	152	42	opinion	opinion	NOUN
ijassa-1405	152	43	−1	−1	NOUN
ijassa-1405	152	44	than	than	ADP
ijassa-1405	152	45	in	in	ADP
ijassa-1405	152	46	gf	gf	PROPN
ijassa-1405	152	47	.	.	PUNCT
ijassa-1405	153	1	lemma	lemma	PROPN
ijassa-1405	153	2	3.1	3.1	NUM
ijassa-1405	153	3	:	:	PUNCT
ijassa-1405	153	4	let	let	VERB
ijassa-1405	153	5	g	g	PRON
ijassa-1405	153	6	be	be	AUX
ijassa-1405	153	7	a	a	DET
ijassa-1405	153	8	graph	graph	NOUN
ijassa-1405	153	9	with	with	ADP
ijassa-1405	153	10	e(g	e(g	NOUN
ijassa-1405	153	11	)	)	PUNCT
ijassa-1405	153	12	̸=	̸=	PROPN
ijassa-1405	153	13	∅	∅	NOUN
ijassa-1405	153	14	and	and	CCONJ
ijassa-1405	153	15	h	h	NOUN
ijassa-1405	153	16	be	be	AUX
ijassa-1405	153	17	the	the	DET
ijassa-1405	153	18	graph	graph	NOUN
ijassa-1405	153	19	obtained	obtain	VERB
ijassa-1405	153	20	from	from	ADP
ijassa-1405	153	21	g	g	NOUN
ijassa-1405	153	22	by	by	ADP
ijassa-1405	153	23	removing	remove	VERB
ijassa-1405	153	24	some	some	DET
ijassa-1405	153	25	edge	edge	NOUN
ijassa-1405	153	26	uv	uv	NOUN
ijassa-1405	153	27	.	.	PUNCT
ijassa-1405	154	1	then	then	ADV
ijassa-1405	154	2	−4	−4	X
ijassa-1405	154	3	≤	≤	ADJ
ijassa-1405	154	4	γ(g)−	γ(g)−	PROPN
ijassa-1405	154	5	γ(h	γ(h	NOUN
ijassa-1405	154	6	)	)	PUNCT
ijassa-1405	154	7	≤	≤	NOUN
ijassa-1405	154	8	2	2	NUM
ijassa-1405	154	9	.	.	PUNCT
ijassa-1405	155	1	(	(	PUNCT
ijassa-1405	155	2	3.1	3.1	NUM
ijassa-1405	155	3	)	)	PUNCT
ijassa-1405	155	4	proof	proof	NOUN
ijassa-1405	155	5	suppose	suppose	VERB
ijassa-1405	155	6	f	f	PROPN
ijassa-1405	155	7	is	be	AUX
ijassa-1405	155	8	an	an	DET
ijassa-1405	155	9	optimal	optimal	ADJ
ijassa-1405	155	10	opinion	opinion	NOUN
ijassa-1405	155	11	function	function	NOUN
ijassa-1405	155	12	for	for	ADP
ijassa-1405	155	13	h	h	NOUN
ijassa-1405	155	14	;	;	PUNCT
ijassa-1405	155	15	therefore	therefore	ADV
ijassa-1405	155	16	,	,	PUNCT
ijassa-1405	155	17	f(v	f(v	PROPN
ijassa-1405	155	18	)	)	PUNCT
ijassa-1405	155	19	=	=	SYM
ijassa-1405	155	20	γ(h	γ(h	NOUN
ijassa-1405	155	21	)	)	PUNCT
ijassa-1405	155	22	.	.	PUNCT
ijassa-1405	156	1	let	let	VERB
ijassa-1405	156	2	us	we	PRON
ijassa-1405	156	3	bound	bind	VERB
ijassa-1405	156	4	γ(g	γ(g	PROPN
ijassa-1405	156	5	)	)	PUNCT
ijassa-1405	156	6	from	from	ADP
ijassa-1405	156	7	above	above	ADP
ijassa-1405	156	8	and	and	CCONJ
ijassa-1405	156	9	below	below	ADV
ijassa-1405	156	10	.	.	PUNCT
ijassa-1405	157	1	to	to	PART
ijassa-1405	157	2	do	do	VERB
ijassa-1405	157	3	this	this	PRON
ijassa-1405	157	4	,	,	PUNCT
ijassa-1405	157	5	consider	consider	VERB
ijassa-1405	157	6	the	the	DET
ijassa-1405	157	7	cases	case	NOUN
ijassa-1405	157	8	where	where	SCONJ
ijassa-1405	157	9	f	f	PROPN
ijassa-1405	157	10	is	be	AUX
ijassa-1405	157	11	not	not	PART
ijassa-1405	157	12	a	a	DET
ijassa-1405	157	13	strict	strict	ADJ
ijassa-1405	157	14	majority	majority	NOUN
ijassa-1405	157	15	function	function	NOUN
ijassa-1405	157	16	for	for	ADP
ijassa-1405	157	17	g	g	NOUN
ijassa-1405	157	18	along	along	ADP
ijassa-1405	157	19	with	with	ADP
ijassa-1405	157	20	modifications	modification	NOUN
ijassa-1405	157	21	of	of	ADP
ijassa-1405	157	22	f	f	PRON
ijassa-1405	157	23	that	that	PRON
ijassa-1405	157	24	make	make	VERB
ijassa-1405	157	25	the	the	DET
ijassa-1405	157	26	resulting	result	VERB
ijassa-1405	157	27	function	function	NOUN
ijassa-1405	157	28	f̃	f̃	PROPN
ijassa-1405	157	29	a	a	DET
ijassa-1405	157	30	strict	strict	ADJ
ijassa-1405	157	31	majority	majority	NOUN
ijassa-1405	157	32	function	function	NOUN
ijassa-1405	157	33	for	for	ADP
ijassa-1405	157	34	g.	g.	PROPN
ijassa-1405	157	35	then	then	ADV
ijassa-1405	157	36	f̃(v	f̃(v	PROPN
ijassa-1405	157	37	)	)	PUNCT
ijassa-1405	157	38	is	be	AUX
ijassa-1405	157	39	an	an	DET
ijassa-1405	157	40	upper	upper	ADJ
ijassa-1405	157	41	bound	bind	VERB
ijassa-1405	157	42	for	for	ADP
ijassa-1405	157	43	γ(g	γ(g	PROPN
ijassa-1405	157	44	)	)	PUNCT
ijassa-1405	157	45	.	.	PUNCT
ijassa-1405	158	1	first	first	ADV
ijassa-1405	158	2	consider	consider	VERB
ijassa-1405	158	3	the	the	DET
ijassa-1405	158	4	cases	case	NOUN
ijassa-1405	158	5	where	where	SCONJ
ijassa-1405	158	6	vertices	vertice	VERB
ijassa-1405	158	7	u	u	NOUN
ijassa-1405	158	8	and/or	and/or	CCONJ
ijassa-1405	158	9	v	v	ADJ
ijassa-1405	158	10	vote	vote	NOUN
ijassa-1405	158	11	“	"	PUNCT
ijassa-1405	158	12	for	for	ADP
ijassa-1405	158	13	”	"	PUNCT
ijassa-1405	158	14	in	in	ADP
ijassa-1405	158	15	hf	hf	NOUN
ijassa-1405	158	16	,	,	PUNCT
ijassa-1405	158	17	while	while	SCONJ
ijassa-1405	158	18	without	without	ADP
ijassa-1405	158	19	this	this	PRON
ijassa-1405	158	20	the	the	DET
ijassa-1405	158	21	proposal	proposal	NOUN
ijassa-1405	158	22	would	would	AUX
ijassa-1405	158	23	be	be	AUX
ijassa-1405	158	24	rejected	reject	VERB
ijassa-1405	158	25	.	.	PUNCT
ijassa-1405	159	1	in	in	ADP
ijassa-1405	159	2	such	such	ADJ
ijassa-1405	159	3	cases	case	NOUN
ijassa-1405	159	4	,	,	PUNCT
ijassa-1405	159	5	after	after	ADP
ijassa-1405	159	6	adding	add	VERB
ijassa-1405	159	7	edge	edge	NOUN
ijassa-1405	159	8	uv	uv	NOUN
ijassa-1405	159	9	,	,	PUNCT
ijassa-1405	159	10	the	the	DET
ijassa-1405	159	11	voting	voting	NOUN
ijassa-1405	159	12	conditions	condition	NOUN
ijassa-1405	159	13	for	for	ADP
ijassa-1405	159	14	u	u	NOUN
ijassa-1405	159	15	and/or	and/or	CCONJ
ijassa-1405	159	16	v	v	PROPN
ijassa-1405	159	17	may	may	AUX
ijassa-1405	159	18	worsen	worsen	VERB
ijassa-1405	159	19	,	,	PUNCT
ijassa-1405	159	20	which	which	PRON
ijassa-1405	159	21	may	may	AUX
ijassa-1405	159	22	lead	lead	VERB
ijassa-1405	159	23	to	to	ADP
ijassa-1405	159	24	the	the	DET
ijassa-1405	159	25	violation	violation	NOUN
ijassa-1405	159	26	of	of	ADP
ijassa-1405	159	27	the	the	DET
ijassa-1405	159	28	strict	strict	ADJ
ijassa-1405	159	29	majority	majority	NOUN
ijassa-1405	159	30	condition	condition	NOUN
ijassa-1405	159	31	for	for	ADP
ijassa-1405	159	32	f	f	PROPN
ijassa-1405	159	33	in	in	ADP
ijassa-1405	159	34	gf	gf	PROPN
ijassa-1405	159	35	.	.	PUNCT
ijassa-1405	160	1	if	if	SCONJ
ijassa-1405	160	2	these	these	DET
ijassa-1405	160	3	vertices	vertice	VERB
ijassa-1405	160	4	vote	vote	VERB
ijassa-1405	160	5	“	"	PUNCT
ijassa-1405	160	6	against	against	ADP
ijassa-1405	160	7	”	"	PUNCT
ijassa-1405	160	8	in	in	ADP
ijassa-1405	160	9	hf	hf	PROPN
ijassa-1405	160	10	,	,	PUNCT
ijassa-1405	160	11	then	then	ADV
ijassa-1405	160	12	changing	change	VERB
ijassa-1405	160	13	the	the	DET
ijassa-1405	160	14	voting	voting	NOUN
ijassa-1405	160	15	conditions	condition	NOUN
ijassa-1405	160	16	for	for	ADP
ijassa-1405	160	17	them	they	PRON
ijassa-1405	160	18	with	with	ADP
ijassa-1405	160	19	the	the	DET
ijassa-1405	160	20	addition	addition	NOUN
ijassa-1405	160	21	of	of	ADP
ijassa-1405	160	22	edge	edge	NOUN
ijassa-1405	160	23	uv	uv	NOUN
ijassa-1405	160	24	does	do	AUX
ijassa-1405	160	25	not	not	PART
ijassa-1405	160	26	cancel	cancel	VERB
ijassa-1405	160	27	the	the	DET
ijassa-1405	160	28	acceptance	acceptance	NOUN
ijassa-1405	160	29	of	of	ADP
ijassa-1405	160	30	the	the	DET
ijassa-1405	160	31	proposal	proposal	NOUN
ijassa-1405	160	32	and	and	CCONJ
ijassa-1405	160	33	preserves	preserve	VERB
ijassa-1405	160	34	the	the	DET
ijassa-1405	160	35	strict	strict	ADJ
ijassa-1405	160	36	majority	majority	NOUN
ijassa-1405	160	37	condition	condition	NOUN
ijassa-1405	160	38	for	for	ADP
ijassa-1405	160	39	f	f	PROPN
ijassa-1405	160	40	in	in	ADP
ijassa-1405	160	41	gf	gf	PROPN
ijassa-1405	160	42	.	.	PUNCT
ijassa-1405	161	1	1	1	X
ijassa-1405	161	2	.	.	X
ijassa-1405	161	3	let	let	VERB
ijassa-1405	161	4	f(u	f(u	PROPN
ijassa-1405	161	5	)	)	PUNCT
ijassa-1405	161	6	=	=	PUNCT
ijassa-1405	161	7	f(v	f(v	NOUN
ijassa-1405	161	8	)	)	PUNCT
ijassa-1405	161	9	=	=	SYM
ijassa-1405	162	1	1	1	X
ijassa-1405	162	2	.	.	PUNCT
ijassa-1405	162	3	in	in	ADP
ijassa-1405	162	4	this	this	DET
ijassa-1405	162	5	case	case	NOUN
ijassa-1405	162	6	,	,	PUNCT
ijassa-1405	162	7	adding	add	VERB
ijassa-1405	162	8	a	a	DET
ijassa-1405	162	9	neighbor	neighbor	NOUN
ijassa-1405	162	10	with	with	ADP
ijassa-1405	162	11	opinion	opinion	NOUN
ijassa-1405	162	12	+1	+1	PRON
ijassa-1405	162	13	will	will	AUX
ijassa-1405	162	14	not	not	PART
ijassa-1405	162	15	worsen	worsen	VERB
ijassa-1405	162	16	the	the	DET
ijassa-1405	162	17	voting	voting	NOUN
ijassa-1405	162	18	conditions	condition	NOUN
ijassa-1405	162	19	for	for	ADP
ijassa-1405	162	20	either	either	DET
ijassa-1405	162	21	vertex	vertex	NOUN
ijassa-1405	162	22	.	.	PUNCT
ijassa-1405	163	1	therefore	therefore	ADV
ijassa-1405	163	2	,	,	PUNCT
ijassa-1405	163	3	f	f	PROPN
ijassa-1405	163	4	remains	remain	VERB
ijassa-1405	163	5	a	a	DET
ijassa-1405	163	6	strict	strict	ADJ
ijassa-1405	163	7	majority	majority	NOUN
ijassa-1405	163	8	function	function	NOUN
ijassa-1405	163	9	on	on	ADP
ijassa-1405	163	10	g	g	NOUN
ijassa-1405	163	11	,	,	PUNCT
ijassa-1405	163	12	but	but	CCONJ
ijassa-1405	163	13	may	may	AUX
ijassa-1405	163	14	cease	cease	VERB
ijassa-1405	163	15	to	to	PART
ijassa-1405	163	16	be	be	AUX
ijassa-1405	163	17	optimal	optimal	ADJ
ijassa-1405	163	18	.	.	PUNCT
ijassa-1405	164	1	hence	hence	ADV
ijassa-1405	164	2	γ(g	γ(g	PROPN
ijassa-1405	164	3	)	)	PUNCT
ijassa-1405	164	4	≤	≤	PROPN
ijassa-1405	164	5	f̃(v	f̃(v	NOUN
ijassa-1405	164	6	)	)	PUNCT
ijassa-1405	164	7	=	=	PUNCT
ijassa-1405	164	8	f(v	f(v	PRON
ijassa-1405	164	9	)	)	PUNCT
ijassa-1405	165	1	=	=	SYM
ijassa-1405	165	2	γ(h	γ(h	NOUN
ijassa-1405	165	3	)	)	PUNCT
ijassa-1405	165	4	.	.	PUNCT
ijassa-1405	166	1	2	2	X
ijassa-1405	166	2	.	.	X
ijassa-1405	166	3	let	let	VERB
ijassa-1405	166	4	f(u	f(u	PROPN
ijassa-1405	166	5	)	)	PUNCT
ijassa-1405	166	6	=	=	PUNCT
ijassa-1405	166	7	f(v	f(v	NOUN
ijassa-1405	166	8	)	)	PUNCT
ijassa-1405	166	9	=	=	SYM
ijassa-1405	167	1	−1	−1	NOUN
ijassa-1405	167	2	.	.	PUNCT
ijassa-1405	168	1	then	then	ADV
ijassa-1405	168	2	the	the	DET
ijassa-1405	168	3	addition	addition	NOUN
ijassa-1405	168	4	of	of	ADP
ijassa-1405	168	5	edge	edge	NOUN
ijassa-1405	168	6	uv	uv	NOUN
ijassa-1405	168	7	worsens	worsen	VERB
ijassa-1405	168	8	the	the	DET
ijassa-1405	168	9	voting	voting	NOUN
ijassa-1405	168	10	conditions	condition	NOUN
ijassa-1405	168	11	for	for	ADP
ijassa-1405	168	12	both	both	CCONJ
ijassa-1405	168	13	u	u	NOUN
ijassa-1405	168	14	and	and	CCONJ
ijassa-1405	168	15	v.	v.	ADP
ijassa-1405	168	16	•	•	NOUN
ijassa-1405	168	17	if	if	SCONJ
ijassa-1405	168	18	u	u	NOUN
ijassa-1405	168	19	and	and	CCONJ
ijassa-1405	168	20	v	v	NUM
ijassa-1405	168	21	vote	vote	NOUN
ijassa-1405	168	22	“	"	PUNCT
ijassa-1405	168	23	for	for	ADP
ijassa-1405	168	24	”	"	PUNCT
ijassa-1405	168	25	in	in	ADP
ijassa-1405	168	26	hf	hf	NOUN
ijassa-1405	168	27	and	and	CCONJ
ijassa-1405	168	28	f(nu(h	f(nu(h	NUM
ijassa-1405	168	29	)	)	PUNCT
ijassa-1405	168	30	)	)	PUNCT
ijassa-1405	169	1	=	=	SYM
ijassa-1405	169	2	1	1	NUM
ijassa-1405	169	3	or	or	CCONJ
ijassa-1405	169	4	f(nv(h	f(nv(h	NOUN
ijassa-1405	169	5	)	)	PUNCT
ijassa-1405	169	6	)	)	PUNCT
ijassa-1405	170	1	=	=	PUNCT
ijassa-1405	170	2	1	1	NUM
ijassa-1405	170	3	,	,	PUNCT
ijassa-1405	170	4	then	then	ADV
ijassa-1405	170	5	after	after	ADP
ijassa-1405	170	6	adding	add	VERB
ijassa-1405	170	7	edge	edge	NOUN
ijassa-1405	170	8	uv	uv	NOUN
ijassa-1405	170	9	,	,	PUNCT
ijassa-1405	170	10	the	the	DET
ijassa-1405	170	11	vote	vote	NOUN
ijassa-1405	170	12	of	of	ADP
ijassa-1405	170	13	one	one	NUM
ijassa-1405	170	14	of	of	ADP
ijassa-1405	170	15	the	the	DET
ijassa-1405	170	16	vertices	vertex	NOUN
ijassa-1405	170	17	changes	change	NOUN
ijassa-1405	170	18	to	to	AUX
ijassa-1405	170	19	”	"	PUNCT
ijassa-1405	170	20	against	against	ADP
ijassa-1405	170	21	”	"	PUNCT
ijassa-1405	170	22	.	.	PUNCT
ijassa-1405	171	1	as	as	ADP
ijassa-1405	171	2	a	a	DET
ijassa-1405	171	3	result	result	NOUN
ijassa-1405	171	4	,	,	PUNCT
ijassa-1405	171	5	f	f	PROPN
ijassa-1405	171	6	may	may	AUX
ijassa-1405	171	7	cease	cease	VERB
ijassa-1405	171	8	to	to	PART
ijassa-1405	171	9	be	be	AUX
ijassa-1405	171	10	a	a	DET
ijassa-1405	171	11	strict	strict	ADJ
ijassa-1405	171	12	majority	majority	NOUN
ijassa-1405	171	13	function	function	NOUN
ijassa-1405	171	14	.	.	PUNCT
ijassa-1405	172	1	to	to	PART
ijassa-1405	172	2	obtain	obtain	VERB
ijassa-1405	172	3	a	a	DET
ijassa-1405	172	4	function	function	NOUN
ijassa-1405	172	5	f̃	f̃	PROPN
ijassa-1405	172	6	having	have	VERB
ijassa-1405	172	7	this	this	DET
ijassa-1405	172	8	property	property	NOUN
ijassa-1405	172	9	,	,	PUNCT
ijassa-1405	172	10	it	it	PRON
ijassa-1405	172	11	is	be	AUX
ijassa-1405	172	12	sufficient	sufficient	ADJ
ijassa-1405	172	13	to	to	PART
ijassa-1405	172	14	change	change	VERB
ijassa-1405	172	15	the	the	DET
ijassa-1405	172	16	opinion	opinion	NOUN
ijassa-1405	172	17	of	of	ADP
ijassa-1405	172	18	u	u	NOUN
ijassa-1405	172	19	or	or	CCONJ
ijassa-1405	172	20	v	v	NOUN
ijassa-1405	172	21	(	(	PUNCT
ijassa-1405	172	22	let	let	VERB
ijassa-1405	172	23	it	it	PRON
ijassa-1405	172	24	be	be	AUX
ijassa-1405	172	25	u	u	NOUN
ijassa-1405	172	26	)	)	PUNCT
ijassa-1405	172	27	from	from	ADP
ijassa-1405	172	28	−1	−1	NOUN
ijassa-1405	172	29	to	to	ADP
ijassa-1405	172	30	+1	+1	PROPN
ijassa-1405	172	31	.	.	PUNCT
ijassa-1405	173	1	then	then	ADV
ijassa-1405	173	2	f̃(nu(g	f̃(nu(g	PROPN
ijassa-1405	173	3	)	)	PUNCT
ijassa-1405	173	4	)	)	PUNCT
ijassa-1405	174	1	=	=	PUNCT
ijassa-1405	174	2	f(nu(h	f(nu(h	PROPN
ijassa-1405	174	3	)	)	PUNCT
ijassa-1405	174	4	)	)	PUNCT
ijassa-1405	174	5	,	,	PUNCT
ijassa-1405	174	6	while	while	SCONJ
ijassa-1405	174	7	f̃(nv(g	f̃(nv(g	ADJ
ijassa-1405	174	8	)	)	PUNCT
ijassa-1405	174	9	)	)	PUNCT
ijassa-1405	175	1	=	=	PUNCT
ijassa-1405	175	2	f(nv(h	f(nv(h	NOUN
ijassa-1405	175	3	)	)	PUNCT
ijassa-1405	175	4	)	)	PUNCT
ijassa-1405	176	1	+	+	CCONJ
ijassa-1405	176	2	1	1	X
ijassa-1405	176	3	.	.	PUNCT
ijassa-1405	176	4	thus	thus	ADV
ijassa-1405	176	5	,	,	PUNCT
ijassa-1405	176	6	after	after	ADP
ijassa-1405	176	7	adding	add	VERB
ijassa-1405	176	8	edge	edge	NOUN
ijassa-1405	176	9	uv	uv	NOUN
ijassa-1405	176	10	and	and	CCONJ
ijassa-1405	176	11	setting	set	VERB
ijassa-1405	176	12	f̃(u	f̃(u	NOUN
ijassa-1405	176	13	)	)	PUNCT
ijassa-1405	176	14	=	=	SYM
ijassa-1405	176	15	f(u	f(u	PROPN
ijassa-1405	176	16	)	)	PUNCT
ijassa-1405	177	1	+	+	NUM
ijassa-1405	177	2	2	2	NUM
ijassa-1405	177	3	,	,	PUNCT
ijassa-1405	177	4	the	the	DET
ijassa-1405	177	5	votes	vote	NOUN
ijassa-1405	177	6	are	be	AUX
ijassa-1405	177	7	preserved	preserve	VERB
ijassa-1405	177	8	and	and	CCONJ
ijassa-1405	177	9	so	so	ADV
ijassa-1405	177	10	f̃	f̃	PROPN
ijassa-1405	177	11	is	be	AUX
ijassa-1405	177	12	a	a	DET
ijassa-1405	177	13	strict	strict	ADJ
ijassa-1405	177	14	majority	majority	NOUN
ijassa-1405	177	15	function	function	NOUN
ijassa-1405	177	16	for	for	ADP
ijassa-1405	177	17	g.	g.	PROPN
ijassa-1405	177	18	hence	hence	ADV
ijassa-1405	177	19	γ(g	γ(g	PROPN
ijassa-1405	177	20	)	)	PUNCT
ijassa-1405	177	21	≤	≤	NUM
ijassa-1405	177	22	f̃(v	f̃(v	NOUN
ijassa-1405	177	23	)	)	PUNCT
ijassa-1405	178	1	=	=	PUNCT
ijassa-1405	178	2	f(v	f(v	PRON
ijassa-1405	178	3	)	)	PUNCT
ijassa-1405	179	1	+	+	CCONJ
ijassa-1405	179	2	2	2	NUM
ijassa-1405	179	3	=	=	SYM
ijassa-1405	179	4	γ(h	γ(h	NOUN
ijassa-1405	179	5	)	)	PUNCT
ijassa-1405	180	1	+	+	CCONJ
ijassa-1405	180	2	2	2	X
ijassa-1405	180	3	.	.	NUM
ijassa-1405	180	4	•	•	NOUN
ijassa-1405	180	5	if	if	SCONJ
ijassa-1405	180	6	u	u	NOUN
ijassa-1405	180	7	or	or	CCONJ
ijassa-1405	180	8	v	v	NUM
ijassa-1405	180	9	votes	vote	NOUN
ijassa-1405	180	10	“	"	PUNCT
ijassa-1405	180	11	for	for	ADP
ijassa-1405	180	12	”	"	PUNCT
ijassa-1405	180	13	and	and	CCONJ
ijassa-1405	180	14	the	the	DET
ijassa-1405	180	15	other	other	ADJ
ijassa-1405	180	16	vertex	vertex	NOUN
ijassa-1405	180	17	votes	vote	NOUN
ijassa-1405	180	18	“	"	PUNCT
ijassa-1405	180	19	against	against	ADP
ijassa-1405	180	20	”	"	PUNCT
ijassa-1405	180	21	in	in	ADP
ijassa-1405	180	22	hf	hf	PROPN
ijassa-1405	180	23	,	,	PUNCT
ijassa-1405	180	24	then	then	ADV
ijassa-1405	180	25	to	to	PART
ijassa-1405	180	26	define	define	VERB
ijassa-1405	180	27	a	a	DET
ijassa-1405	180	28	strict	strict	ADJ
ijassa-1405	180	29	majority	majority	NOUN
ijassa-1405	180	30	function	function	NOUN
ijassa-1405	180	31	f̃	f̃	PROPN
ijassa-1405	180	32	for	for	ADP
ijassa-1405	180	33	g	g	NOUN
ijassa-1405	180	34	,	,	PUNCT
ijassa-1405	180	35	it	it	PRON
ijassa-1405	180	36	suffices	suffice	VERB
ijassa-1405	180	37	to	to	PART
ijassa-1405	180	38	set	set	VERB
ijassa-1405	180	39	f̃(u	f̃(u	PROPN
ijassa-1405	180	40	)	)	PUNCT
ijassa-1405	181	1	=	=	SYM
ijassa-1405	181	2	+1	+1	NOUN
ijassa-1405	181	3	or	or	CCONJ
ijassa-1405	181	4	f̃(v	f̃(v	NOUN
ijassa-1405	181	5	)	)	PUNCT
ijassa-1405	182	1	=	=	SYM
ijassa-1405	182	2	+1	+1	PROPN
ijassa-1405	182	3	.	.	PUNCT
ijassa-1405	183	1	in	in	ADP
ijassa-1405	183	2	this	this	DET
ijassa-1405	183	3	case	case	NOUN
ijassa-1405	183	4	also	also	ADV
ijassa-1405	183	5	γ(g	γ(g	PROPN
ijassa-1405	183	6	)	)	PUNCT
ijassa-1405	183	7	≤	≤	PROPN
ijassa-1405	183	8	f̃(v	f̃(v	NOUN
ijassa-1405	183	9	)	)	PUNCT
ijassa-1405	183	10	=	=	PUNCT
ijassa-1405	183	11	f(v	f(v	PRON
ijassa-1405	183	12	)	)	PUNCT
ijassa-1405	184	1	+	+	CCONJ
ijassa-1405	184	2	2	2	NUM
ijassa-1405	184	3	=	=	SYM
ijassa-1405	184	4	γ(h	γ(h	NOUN
ijassa-1405	184	5	)	)	PUNCT
ijassa-1405	185	1	+	+	NOUN
ijassa-1405	185	2	2	2	X
ijassa-1405	185	3	.	.	X
ijassa-1405	185	4	copyright	copyright	NOUN
ijassa-1405	185	5	©	©	PROPN
ijassa-1405	185	6	2023	2023	NUM
ijassa-1405	185	7	assa	assa	NOUN
ijassa-1405	185	8	.	.	PUNCT
ijassa-1405	186	1	adv	adv	PROPN
ijassa-1405	186	2	syst	syst	PROPN
ijassa-1405	186	3	sci	sci	PROPN
ijassa-1405	186	4	appl	appl	PROPN
ijassa-1405	186	5	(	(	PUNCT
ijassa-1405	186	6	2023	2023	NUM
ijassa-1405	186	7	)	)	PUNCT
ijassa-1405	186	8	170	170	NUM
ijassa-1405	186	9	d.	d.	PROPN
ijassa-1405	186	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	186	11	,	,	PUNCT
ijassa-1405	186	12	p.	p.	PROPN
ijassa-1405	186	13	chebotarev	chebotarev	PROPN
ijassa-1405	186	14	,	,	PUNCT
ijassa-1405	186	15	m.	m.	NOUN
ijassa-1405	186	16	goubko	goubko	NOUN
ijassa-1405	186	17	,	,	PUNCT
ijassa-1405	186	18	m.	m.	NOUN
ijassa-1405	186	19	somov	somov	PROPN
ijassa-1405	186	20	,	,	PUNCT
ijassa-1405	186	21	n.	n.	PROPN
ijassa-1405	186	22	shushko	shushko	PROPN
ijassa-1405	186	23	3	3	NUM
ijassa-1405	186	24	.	.	PUNCT
ijassa-1405	187	1	let	let	VERB
ijassa-1405	187	2	f(u	f(u	PROPN
ijassa-1405	187	3	)	)	PUNCT
ijassa-1405	187	4	=	=	SYM
ijassa-1405	187	5	−1	−1	NOUN
ijassa-1405	187	6	,	,	PUNCT
ijassa-1405	187	7	f(v	f(v	PROPN
ijassa-1405	187	8	)	)	PUNCT
ijassa-1405	187	9	=	=	SYM
ijassa-1405	188	1	1	1	X
ijassa-1405	188	2	.	.	X
ijassa-1405	188	3	for	for	ADP
ijassa-1405	188	4	u	u	NOUN
ijassa-1405	188	5	,	,	PUNCT
ijassa-1405	188	6	adding	add	VERB
ijassa-1405	188	7	edge	edge	NOUN
ijassa-1405	188	8	uv	uv	NOUN
ijassa-1405	188	9	does	do	AUX
ijassa-1405	188	10	not	not	PART
ijassa-1405	188	11	worsen	worsen	VERB
ijassa-1405	188	12	the	the	DET
ijassa-1405	188	13	voting	voting	NOUN
ijassa-1405	188	14	conditions	condition	NOUN
ijassa-1405	188	15	.	.	PUNCT
ijassa-1405	189	1	if	if	SCONJ
ijassa-1405	189	2	v	v	NOUN
ijassa-1405	189	3	votes	vote	NOUN
ijassa-1405	189	4	“	"	PUNCT
ijassa-1405	189	5	against	against	ADP
ijassa-1405	189	6	”	"	PUNCT
ijassa-1405	189	7	in	in	ADP
ijassa-1405	189	8	hf	hf	PROPN
ijassa-1405	189	9	,	,	PUNCT
ijassa-1405	189	10	then	then	ADV
ijassa-1405	189	11	f	f	PROPN
ijassa-1405	189	12	remains	remain	VERB
ijassa-1405	189	13	a	a	DET
ijassa-1405	189	14	strict	strict	ADJ
ijassa-1405	189	15	majority	majority	NOUN
ijassa-1405	189	16	function	function	NOUN
ijassa-1405	189	17	after	after	ADP
ijassa-1405	189	18	adding	add	VERB
ijassa-1405	189	19	edge	edge	NOUN
ijassa-1405	189	20	uv	uv	NOUN
ijassa-1405	189	21	,	,	PUNCT
ijassa-1405	189	22	since	since	SCONJ
ijassa-1405	189	23	the	the	DET
ijassa-1405	189	24	number	number	NOUN
ijassa-1405	189	25	of	of	ADP
ijassa-1405	189	26	votes	vote	NOUN
ijassa-1405	189	27	“	"	PUNCT
ijassa-1405	189	28	for	for	ADP
ijassa-1405	189	29	”	"	PUNCT
ijassa-1405	189	30	does	do	AUX
ijassa-1405	189	31	not	not	PART
ijassa-1405	189	32	decrease	decrease	VERB
ijassa-1405	189	33	.	.	PUNCT
ijassa-1405	190	1	if	if	SCONJ
ijassa-1405	190	2	v	v	NOUN
ijassa-1405	190	3	votes	vote	NOUN
ijassa-1405	190	4	“	"	PUNCT
ijassa-1405	190	5	for	for	ADP
ijassa-1405	190	6	”	"	PUNCT
ijassa-1405	190	7	,	,	PUNCT
ijassa-1405	190	8	then	then	ADV
ijassa-1405	190	9	obtaining	obtain	VERB
ijassa-1405	190	10	a	a	DET
ijassa-1405	190	11	strict	strict	ADJ
ijassa-1405	190	12	majority	majority	NOUN
ijassa-1405	190	13	function	function	NOUN
ijassa-1405	190	14	f̃	f̃	PROPN
ijassa-1405	190	15	for	for	ADP
ijassa-1405	190	16	g	g	NOUN
ijassa-1405	190	17	reduces	reduce	VERB
ijassa-1405	190	18	to	to	ADP
ijassa-1405	190	19	setting	set	VERB
ijassa-1405	190	20	f̃(u	f̃(u	PROPN
ijassa-1405	190	21	)	)	PUNCT
ijassa-1405	191	1	=	=	SYM
ijassa-1405	191	2	+1	+1	PROPN
ijassa-1405	191	3	,	,	PUNCT
ijassa-1405	191	4	which	which	PRON
ijassa-1405	191	5	implies	imply	VERB
ijassa-1405	191	6	f̃(v	f̃(v	NOUN
ijassa-1405	191	7	)	)	PUNCT
ijassa-1405	191	8	=	=	PUNCT
ijassa-1405	191	9	f(v	f(v	PRON
ijassa-1405	191	10	)	)	PUNCT
ijassa-1405	192	1	+	+	CCONJ
ijassa-1405	192	2	2	2	X
ijassa-1405	192	3	.	.	X
ijassa-1405	192	4	therefore	therefore	ADV
ijassa-1405	192	5	,	,	PUNCT
ijassa-1405	192	6	γ(g	γ(g	PROPN
ijassa-1405	192	7	)	)	PUNCT
ijassa-1405	192	8	≤	≤	PROPN
ijassa-1405	192	9	f̃(v	f̃(v	NOUN
ijassa-1405	192	10	)	)	PUNCT
ijassa-1405	193	1	=	=	SYM
ijassa-1405	193	2	γ(h	γ(h	NOUN
ijassa-1405	193	3	)	)	PUNCT
ijassa-1405	194	1	+	+	NOUN
ijassa-1405	194	2	2	2	X
ijassa-1405	194	3	.	.	PUNCT
ijassa-1405	194	4	now	now	ADV
ijassa-1405	194	5	let	let	VERB
ijassa-1405	194	6	f	f	PRON
ijassa-1405	194	7	be	be	AUX
ijassa-1405	194	8	an	an	DET
ijassa-1405	194	9	optimal	optimal	ADJ
ijassa-1405	194	10	strict	strict	ADJ
ijassa-1405	194	11	majority	majority	NOUN
ijassa-1405	194	12	function	function	NOUN
ijassa-1405	194	13	for	for	ADP
ijassa-1405	194	14	g	g	NOUN
ijassa-1405	194	15	,	,	PUNCT
ijassa-1405	194	16	which	which	PRON
ijassa-1405	194	17	implies	imply	VERB
ijassa-1405	194	18	f(v	f(v	PROPN
ijassa-1405	194	19	)	)	PUNCT
ijassa-1405	195	1	=	=	PUNCT
ijassa-1405	195	2	γ(g	γ(g	PROPN
ijassa-1405	195	3	)	)	PUNCT
ijassa-1405	195	4	.	.	PUNCT
ijassa-1405	196	1	let	let	VERB
ijassa-1405	196	2	us	we	PRON
ijassa-1405	196	3	bound	bind	VERB
ijassa-1405	196	4	γ(h	γ(h	NOUN
ijassa-1405	196	5	)	)	PUNCT
ijassa-1405	196	6	from	from	ADP
ijassa-1405	196	7	above	above	ADV
ijassa-1405	196	8	by	by	ADP
ijassa-1405	196	9	transforming	transform	VERB
ijassa-1405	196	10	f	f	PROPN
ijassa-1405	196	11	into	into	ADP
ijassa-1405	196	12	a	a	DET
ijassa-1405	196	13	strict	strict	ADJ
ijassa-1405	196	14	majority	majority	NOUN
ijassa-1405	196	15	function	function	NOUN
ijassa-1405	196	16	f̃	f̃	PROPN
ijassa-1405	196	17	for	for	ADP
ijassa-1405	196	18	h	h	NOUN
ijassa-1405	196	19	.	.	PUNCT
ijassa-1405	197	1	1	1	X
ijassa-1405	197	2	.	.	X
ijassa-1405	197	3	let	let	VERB
ijassa-1405	197	4	f(u	f(u	PROPN
ijassa-1405	197	5	)	)	PUNCT
ijassa-1405	198	1	=	=	PUNCT
ijassa-1405	198	2	f(v	f(v	NOUN
ijassa-1405	198	3	)	)	PUNCT
ijassa-1405	198	4	=	=	SYM
ijassa-1405	199	1	−1	−1	NOUN
ijassa-1405	199	2	.	.	PUNCT
ijassa-1405	200	1	removing	remove	VERB
ijassa-1405	200	2	edge	edge	NOUN
ijassa-1405	200	3	uv	uv	NOUN
ijassa-1405	200	4	does	do	AUX
ijassa-1405	200	5	not	not	PART
ijassa-1405	200	6	worsen	worsen	VERB
ijassa-1405	200	7	the	the	DET
ijassa-1405	200	8	voting	voting	NOUN
ijassa-1405	200	9	conditions	condition	NOUN
ijassa-1405	200	10	for	for	ADP
ijassa-1405	200	11	u	u	NOUN
ijassa-1405	200	12	or	or	CCONJ
ijassa-1405	200	13	v.	v.	ADP
ijassa-1405	200	14	hence	hence	ADV
ijassa-1405	200	15	f	f	PROPN
ijassa-1405	200	16	remains	remain	VERB
ijassa-1405	200	17	a	a	DET
ijassa-1405	200	18	strict	strict	ADJ
ijassa-1405	200	19	majority	majority	NOUN
ijassa-1405	200	20	function	function	NOUN
ijassa-1405	200	21	for	for	ADP
ijassa-1405	200	22	h	h	NOUN
ijassa-1405	200	23	and	and	CCONJ
ijassa-1405	200	24	γ(h	γ(h	NOUN
ijassa-1405	200	25	)	)	PUNCT
ijassa-1405	200	26	≤	≤	NUM
ijassa-1405	200	27	f(v	f(v	PROPN
ijassa-1405	200	28	)	)	PUNCT
ijassa-1405	201	1	=	=	PUNCT
ijassa-1405	201	2	γ(g	γ(g	PROPN
ijassa-1405	201	3	)	)	PUNCT
ijassa-1405	201	4	.	.	PUNCT
ijassa-1405	202	1	2	2	X
ijassa-1405	202	2	.	.	X
ijassa-1405	202	3	let	let	VERB
ijassa-1405	202	4	f(u	f(u	PROPN
ijassa-1405	202	5	)	)	PUNCT
ijassa-1405	202	6	=	=	PUNCT
ijassa-1405	202	7	f(v	f(v	NOUN
ijassa-1405	202	8	)	)	PUNCT
ijassa-1405	202	9	=	=	SYM
ijassa-1405	203	1	1	1	X
ijassa-1405	203	2	.	.	PUNCT
ijassa-1405	203	3	then	then	ADV
ijassa-1405	203	4	removing	remove	VERB
ijassa-1405	203	5	edge	edge	NOUN
ijassa-1405	203	6	uv	uv	NOUN
ijassa-1405	203	7	worsens	worsen	VERB
ijassa-1405	203	8	the	the	DET
ijassa-1405	203	9	voting	voting	NOUN
ijassa-1405	203	10	conditions	condition	NOUN
ijassa-1405	203	11	for	for	ADP
ijassa-1405	203	12	both	both	CCONJ
ijassa-1405	203	13	u	u	NOUN
ijassa-1405	203	14	and	and	CCONJ
ijassa-1405	203	15	v.	v.	ADP
ijassa-1405	203	16	•	•	NOUN
ijassa-1405	203	17	if	if	SCONJ
ijassa-1405	203	18	u	u	NOUN
ijassa-1405	203	19	or	or	CCONJ
ijassa-1405	203	20	v	v	NUM
ijassa-1405	203	21	votes	vote	NOUN
ijassa-1405	203	22	“	"	PUNCT
ijassa-1405	203	23	for	for	ADP
ijassa-1405	203	24	”	"	PUNCT
ijassa-1405	203	25	in	in	ADP
ijassa-1405	203	26	gf	gf	PROPN
ijassa-1405	203	27	(	(	PUNCT
ijassa-1405	203	28	let	let	VERB
ijassa-1405	203	29	it	it	PRON
ijassa-1405	203	30	be	be	AUX
ijassa-1405	203	31	u	u	NOUN
ijassa-1405	203	32	)	)	PUNCT
ijassa-1405	203	33	,	,	PUNCT
ijassa-1405	203	34	while	while	SCONJ
ijassa-1405	203	35	the	the	DET
ijassa-1405	203	36	other	other	ADJ
ijassa-1405	203	37	vertex	vertex	NOUN
ijassa-1405	203	38	votes	vote	NOUN
ijassa-1405	203	39	“	"	PUNCT
ijassa-1405	203	40	against	against	ADP
ijassa-1405	203	41	”	"	PUNCT
ijassa-1405	203	42	,	,	PUNCT
ijassa-1405	203	43	then	then	ADV
ijassa-1405	203	44	f	f	PROPN
ijassa-1405	203	45	may	may	AUX
ijassa-1405	203	46	cease	cease	VERB
ijassa-1405	203	47	to	to	PART
ijassa-1405	203	48	be	be	AUX
ijassa-1405	203	49	a	a	DET
ijassa-1405	203	50	strict	strict	ADJ
ijassa-1405	203	51	majority	majority	NOUN
ijassa-1405	203	52	function	function	NOUN
ijassa-1405	203	53	for	for	ADP
ijassa-1405	203	54	h	h	NOUN
ijassa-1405	203	55	.	.	PUNCT
ijassa-1405	204	1	this	this	PRON
ijassa-1405	204	2	may	may	AUX
ijassa-1405	204	3	happen	happen	VERB
ijassa-1405	204	4	if	if	SCONJ
ijassa-1405	204	5	f(nu(g	f(nu(g	ADJ
ijassa-1405	204	6	)	)	PUNCT
ijassa-1405	204	7	)	)	PUNCT
ijassa-1405	205	1	=	=	SYM
ijassa-1405	205	2	1	1	NUM
ijassa-1405	205	3	,	,	PUNCT
ijassa-1405	205	4	in	in	ADP
ijassa-1405	205	5	which	which	DET
ijassa-1405	205	6	case	case	NOUN
ijassa-1405	205	7	f(nu(h	f(nu(h	NUM
ijassa-1405	205	8	)	)	PUNCT
ijassa-1405	205	9	)	)	PUNCT
ijassa-1405	206	1	=	=	PUNCT
ijassa-1405	206	2	0	0	X
ijassa-1405	206	3	.	.	PUNCT
ijassa-1405	206	4	to	to	PART
ijassa-1405	206	5	obtain	obtain	VERB
ijassa-1405	206	6	a	a	DET
ijassa-1405	206	7	strict	strict	ADJ
ijassa-1405	206	8	majority	majority	NOUN
ijassa-1405	206	9	function	function	NOUN
ijassa-1405	206	10	f̃	f̃	PROPN
ijassa-1405	206	11	for	for	ADP
ijassa-1405	206	12	h	h	NOUN
ijassa-1405	206	13	,	,	PUNCT
ijassa-1405	206	14	it	it	PRON
ijassa-1405	206	15	suffices	suffice	VERB
ijassa-1405	206	16	to	to	PART
ijassa-1405	206	17	change	change	VERB
ijassa-1405	206	18	the	the	DET
ijassa-1405	206	19	opinion	opinion	NOUN
ijassa-1405	206	20	of	of	ADP
ijassa-1405	206	21	one	one	NUM
ijassa-1405	206	22	of	of	ADP
ijassa-1405	206	23	the	the	DET
ijassa-1405	206	24	neighbors	neighbor	NOUN
ijassa-1405	206	25	of	of	ADP
ijassa-1405	206	26	u	u	NOUN
ijassa-1405	206	27	from	from	ADP
ijassa-1405	206	28	−1	−1	NOUN
ijassa-1405	206	29	to	to	ADP
ijassa-1405	206	30	1	1	NUM
ijassa-1405	206	31	.	.	PUNCT
ijassa-1405	207	1	this	this	PRON
ijassa-1405	207	2	can	can	AUX
ijassa-1405	207	3	always	always	ADV
ijassa-1405	207	4	be	be	AUX
ijassa-1405	207	5	done	do	VERB
ijassa-1405	207	6	,	,	PUNCT
ijassa-1405	207	7	since	since	SCONJ
ijassa-1405	207	8	f(nu(h	f(nu(h	NUM
ijassa-1405	207	9	)	)	PUNCT
ijassa-1405	207	10	)	)	PUNCT
ijassa-1405	208	1	=	=	SYM
ijassa-1405	208	2	0	0	NUM
ijassa-1405	208	3	and	and	CCONJ
ijassa-1405	208	4	f(u	f(u	PROPN
ijassa-1405	208	5	)	)	PUNCT
ijassa-1405	209	1	=	=	SYM
ijassa-1405	210	1	+1	+1	PRON
ijassa-1405	210	2	imply	imply	VERB
ijassa-1405	210	3	the	the	DET
ijassa-1405	210	4	existence	existence	NOUN
ijassa-1405	210	5	of	of	ADP
ijassa-1405	210	6	a	a	DET
ijassa-1405	210	7	neighbor	neighbor	NOUN
ijassa-1405	210	8	of	of	ADP
ijassa-1405	210	9	u	u	NOUN
ijassa-1405	210	10	with	with	ADP
ijassa-1405	210	11	opinion	opinion	NOUN
ijassa-1405	210	12	−1	−1	NOUN
ijassa-1405	210	13	.	.	PUNCT
ijassa-1405	211	1	therefore	therefore	ADV
ijassa-1405	211	2	,	,	PUNCT
ijassa-1405	211	3	f̃(v	f̃(v	NOUN
ijassa-1405	211	4	)	)	PUNCT
ijassa-1405	211	5	=	=	PUNCT
ijassa-1405	211	6	f(v	f(v	PRON
ijassa-1405	211	7	)	)	PUNCT
ijassa-1405	211	8	+	+	CCONJ
ijassa-1405	211	9	2	2	X
ijassa-1405	211	10	.	.	NUM
ijassa-1405	211	11	•	•	NOUN
ijassa-1405	211	12	if	if	SCONJ
ijassa-1405	211	13	both	both	PRON
ijassa-1405	211	14	u	u	NOUN
ijassa-1405	211	15	and	and	CCONJ
ijassa-1405	211	16	v	v	ADP
ijassa-1405	211	17	vote	vote	NOUN
ijassa-1405	211	18	“	"	PUNCT
ijassa-1405	211	19	for	for	ADP
ijassa-1405	211	20	”	"	PUNCT
ijassa-1405	211	21	in	in	ADP
ijassa-1405	211	22	gf	gf	PROPN
ijassa-1405	211	23	,	,	PUNCT
ijassa-1405	211	24	then	then	ADV
ijassa-1405	211	25	f	f	PROPN
ijassa-1405	211	26	may	may	AUX
ijassa-1405	211	27	cease	cease	VERB
ijassa-1405	211	28	to	to	PART
ijassa-1405	211	29	be	be	AUX
ijassa-1405	211	30	a	a	DET
ijassa-1405	211	31	strict	strict	ADJ
ijassa-1405	211	32	majority	majority	NOUN
ijassa-1405	211	33	function	function	NOUN
ijassa-1405	211	34	for	for	ADP
ijassa-1405	211	35	h	h	NOUN
ijassa-1405	211	36	if	if	SCONJ
ijassa-1405	211	37	f(nu(g	f(nu(g	ADJ
ijassa-1405	211	38	)	)	PUNCT
ijassa-1405	211	39	)	)	PUNCT
ijassa-1405	212	1	=	=	SYM
ijassa-1405	212	2	1	1	NUM
ijassa-1405	212	3	or	or	CCONJ
ijassa-1405	212	4	f(nv(g	f(nv(g	NOUN
ijassa-1405	212	5	)	)	PUNCT
ijassa-1405	212	6	)	)	PUNCT
ijassa-1405	213	1	=	=	SYM
ijassa-1405	213	2	1	1	NUM
ijassa-1405	213	3	(	(	PUNCT
ijassa-1405	213	4	or	or	CCONJ
ijassa-1405	213	5	both	both	PRON
ijassa-1405	213	6	)	)	PUNCT
ijassa-1405	213	7	.	.	PUNCT
ijassa-1405	214	1	then	then	ADV
ijassa-1405	214	2	a	a	DET
ijassa-1405	214	3	strict	strict	ADJ
ijassa-1405	214	4	majority	majority	NOUN
ijassa-1405	214	5	function	function	NOUN
ijassa-1405	214	6	f̃	f̃	PROPN
ijassa-1405	214	7	for	for	ADP
ijassa-1405	214	8	h	h	NOUN
ijassa-1405	214	9	can	can	AUX
ijassa-1405	214	10	be	be	AUX
ijassa-1405	214	11	obtained	obtain	VERB
ijassa-1405	214	12	by	by	ADP
ijassa-1405	214	13	changing	change	VERB
ijassa-1405	214	14	the	the	DET
ijassa-1405	214	15	opinion	opinion	NOUN
ijassa-1405	214	16	of	of	ADP
ijassa-1405	214	17	one	one	NUM
ijassa-1405	214	18	neighbor	neighbor	NOUN
ijassa-1405	214	19	of	of	ADP
ijassa-1405	214	20	u	u	NOUN
ijassa-1405	214	21	or	or	CCONJ
ijassa-1405	214	22	/	/	SYM
ijassa-1405	214	23	and	and	CCONJ
ijassa-1405	214	24	one	one	NUM
ijassa-1405	214	25	neighbor	neighbor	NOUN
ijassa-1405	214	26	of	of	ADP
ijassa-1405	214	27	v	v	NOUN
ijassa-1405	214	28	from	from	ADP
ijassa-1405	214	29	−1	−1	NOUN
ijassa-1405	214	30	to	to	ADP
ijassa-1405	214	31	+1	+1	PROPN
ijassa-1405	214	32	,	,	PUNCT
ijassa-1405	214	33	as	as	ADP
ijassa-1405	214	34	in	in	ADP
ijassa-1405	214	35	the	the	DET
ijassa-1405	214	36	previous	previous	ADJ
ijassa-1405	214	37	case	case	NOUN
ijassa-1405	214	38	.	.	PUNCT
ijassa-1405	215	1	then	then	ADV
ijassa-1405	215	2	f̃(v	f̃(v	NOUN
ijassa-1405	215	3	)	)	PUNCT
ijassa-1405	215	4	≤	≤	NUM
ijassa-1405	215	5	f(v	f(v	PROPN
ijassa-1405	215	6	)	)	PUNCT
ijassa-1405	216	1	+	+	CCONJ
ijassa-1405	216	2	4	4	X
ijassa-1405	216	3	.	.	PUNCT
ijassa-1405	216	4	thus	thus	ADV
ijassa-1405	216	5	,	,	PUNCT
ijassa-1405	216	6	γ(h	γ(h	NOUN
ijassa-1405	216	7	)	)	PUNCT
ijassa-1405	216	8	≤	≤	NUM
ijassa-1405	216	9	f̃(v	f̃(v	NOUN
ijassa-1405	216	10	)	)	PUNCT
ijassa-1405	216	11	≤	≤	PROPN
ijassa-1405	216	12	γ(g	γ(g	PROPN
ijassa-1405	216	13	)	)	PUNCT
ijassa-1405	217	1	+	+	CCONJ
ijassa-1405	217	2	4	4	NUM
ijassa-1405	217	3	.	.	NOUN
ijassa-1405	218	1	3	3	X
ijassa-1405	218	2	.	.	X
ijassa-1405	218	3	let	let	VERB
ijassa-1405	218	4	f(u	f(u	PROPN
ijassa-1405	218	5	)	)	PUNCT
ijassa-1405	218	6	=	=	SYM
ijassa-1405	218	7	1	1	NUM
ijassa-1405	218	8	,	,	PUNCT
ijassa-1405	218	9	f(v	f(v	NOUN
ijassa-1405	218	10	)	)	PUNCT
ijassa-1405	219	1	=	=	SYM
ijassa-1405	219	2	−1	−1	NOUN
ijassa-1405	219	3	.	.	PUNCT
ijassa-1405	220	1	removing	remove	VERB
ijassa-1405	220	2	edge	edge	NOUN
ijassa-1405	220	3	uv	uv	NOUN
ijassa-1405	220	4	improves	improve	VERB
ijassa-1405	220	5	the	the	DET
ijassa-1405	220	6	voting	voting	NOUN
ijassa-1405	220	7	conditions	condition	NOUN
ijassa-1405	220	8	for	for	ADP
ijassa-1405	220	9	u	u	NOUN
ijassa-1405	220	10	and	and	CCONJ
ijassa-1405	220	11	worsens	worsen	VERB
ijassa-1405	220	12	them	they	PRON
ijassa-1405	220	13	for	for	ADP
ijassa-1405	220	14	v.	v.	ADP
ijassa-1405	220	15	if	if	SCONJ
ijassa-1405	220	16	v	v	NOUN
ijassa-1405	220	17	votes	vote	NOUN
ijassa-1405	220	18	“	"	PUNCT
ijassa-1405	220	19	for	for	ADP
ijassa-1405	220	20	”	"	PUNCT
ijassa-1405	220	21	in	in	ADP
ijassa-1405	220	22	gf	gf	PROPN
ijassa-1405	220	23	,	,	PUNCT
ijassa-1405	220	24	then	then	ADV
ijassa-1405	220	25	this	this	PRON
ijassa-1405	220	26	may	may	AUX
ijassa-1405	220	27	lead	lead	VERB
ijassa-1405	220	28	to	to	ADP
ijassa-1405	220	29	its	its	PRON
ijassa-1405	220	30	vote	vote	NOUN
ijassa-1405	220	31	“	"	PUNCT
ijassa-1405	220	32	against	against	ADP
ijassa-1405	220	33	”	"	PUNCT
ijassa-1405	220	34	in	in	ADP
ijassa-1405	220	35	hf	hf	PROPN
ijassa-1405	220	36	.	.	PUNCT
ijassa-1405	221	1	as	as	ADP
ijassa-1405	221	2	a	a	DET
ijassa-1405	221	3	result	result	NOUN
ijassa-1405	221	4	,	,	PUNCT
ijassa-1405	221	5	f	f	PROPN
ijassa-1405	221	6	may	may	AUX
ijassa-1405	221	7	cease	cease	VERB
ijassa-1405	221	8	to	to	PART
ijassa-1405	221	9	be	be	AUX
ijassa-1405	221	10	a	a	DET
ijassa-1405	221	11	strict	strict	ADJ
ijassa-1405	221	12	majority	majority	NOUN
ijassa-1405	221	13	function	function	NOUN
ijassa-1405	221	14	for	for	ADP
ijassa-1405	221	15	h	h	NOUN
ijassa-1405	221	16	.	.	PUNCT
ijassa-1405	222	1	to	to	PART
ijassa-1405	222	2	obtain	obtain	VERB
ijassa-1405	222	3	a	a	DET
ijassa-1405	222	4	strict	strict	ADJ
ijassa-1405	222	5	majority	majority	NOUN
ijassa-1405	222	6	function	function	NOUN
ijassa-1405	222	7	f̃	f̃	PROPN
ijassa-1405	222	8	for	for	ADP
ijassa-1405	222	9	h	h	NOUN
ijassa-1405	222	10	,	,	PUNCT
ijassa-1405	222	11	it	it	PRON
ijassa-1405	222	12	suffices	suffice	VERB
ijassa-1405	222	13	to	to	PART
ijassa-1405	222	14	set	set	VERB
ijassa-1405	222	15	f̃(v	f̃(v	NOUN
ijassa-1405	222	16	)	)	PUNCT
ijassa-1405	223	1	=	=	SYM
ijassa-1405	223	2	+1	+1	PROPN
ijassa-1405	223	3	,	,	PUNCT
ijassa-1405	223	4	which	which	PRON
ijassa-1405	223	5	yields	yield	VERB
ijassa-1405	223	6	f̃(nv(h	f̃(nv(h	NOUN
ijassa-1405	223	7	)	)	PUNCT
ijassa-1405	223	8	)	)	PUNCT
ijassa-1405	224	1	=	=	PUNCT
ijassa-1405	224	2	f(nv(g	f(nv(g	X
ijassa-1405	224	3	)	)	PUNCT
ijassa-1405	224	4	)	)	PUNCT
ijassa-1405	225	1	+	+	CCONJ
ijassa-1405	225	2	1	1	NUM
ijassa-1405	225	3	and	and	CCONJ
ijassa-1405	225	4	f̃(nu(h	f̃(nu(h	NUM
ijassa-1405	225	5	)	)	PUNCT
ijassa-1405	225	6	)	)	PUNCT
ijassa-1405	226	1	=	=	PUNCT
ijassa-1405	226	2	f(nu(g	f(nu(g	X
ijassa-1405	226	3	)	)	PUNCT
ijassa-1405	226	4	)	)	PUNCT
ijassa-1405	227	1	+	+	CCONJ
ijassa-1405	227	2	1	1	X
ijassa-1405	227	3	.	.	X
ijassa-1405	227	4	then	then	ADV
ijassa-1405	227	5	γ(h	γ(h	NOUN
ijassa-1405	227	6	)	)	PUNCT
ijassa-1405	227	7	≤	≤	NUM
ijassa-1405	227	8	f̃(v	f̃(v	NOUN
ijassa-1405	227	9	)	)	PUNCT
ijassa-1405	228	1	=	=	PUNCT
ijassa-1405	228	2	f(v	f(v	PRON
ijassa-1405	228	3	)	)	PUNCT
ijassa-1405	229	1	+	+	CCONJ
ijassa-1405	229	2	2	2	NUM
ijassa-1405	229	3	=	=	SYM
ijassa-1405	229	4	γ(g	γ(g	PROPN
ijassa-1405	229	5	)	)	PUNCT
ijassa-1405	230	1	+	+	CCONJ
ijassa-1405	230	2	2	2	NUM
ijassa-1405	230	3	,	,	PUNCT
ijassa-1405	230	4	since	since	SCONJ
ijassa-1405	230	5	f(v	f(v	PRON
ijassa-1405	230	6	)	)	PUNCT
ijassa-1405	231	1	=	=	PUNCT
ijassa-1405	231	2	γ(g	γ(g	PROPN
ijassa-1405	231	3	)	)	PUNCT
ijassa-1405	231	4	.	.	PUNCT
ijassa-1405	232	1	collecting	collect	VERB
ijassa-1405	232	2	the	the	DET
ijassa-1405	232	3	obtained	obtain	VERB
ijassa-1405	232	4	inequalities	inequality	NOUN
ijassa-1405	232	5	,	,	PUNCT
ijassa-1405	232	6	we	we	PRON
ijassa-1405	232	7	get	get	VERB
ijassa-1405	232	8	(	(	PUNCT
ijassa-1405	232	9	3.1	3.1	NUM
ijassa-1405	232	10	)	)	PUNCT
ijassa-1405	232	11	.	.	PUNCT
ijassa-1405	233	1	g	g	PROPN
ijassa-1405	233	2	h	h	PROPN
ijassa-1405	233	3	fig	fig	NOUN
ijassa-1405	233	4	.	.	PUNCT
ijassa-1405	234	1	3.1	3.1	NUM
ijassa-1405	234	2	.	.	PUNCT
ijassa-1405	234	3	graph	graph	NOUN
ijassa-1405	234	4	g	g	NOUN
ijassa-1405	234	5	and	and	CCONJ
ijassa-1405	234	6	graph	graph	NOUN
ijassa-1405	234	7	h	h	PROPN
ijassa-1405	234	8	obtained	obtain	VERB
ijassa-1405	234	9	from	from	ADP
ijassa-1405	234	10	g	g	NOUN
ijassa-1405	234	11	by	by	ADP
ijassa-1405	234	12	removing	remove	VERB
ijassa-1405	234	13	one	one	NUM
ijassa-1405	234	14	edge	edge	NOUN
ijassa-1405	234	15	such	such	ADJ
ijassa-1405	234	16	that	that	DET
ijassa-1405	234	17	γ(g)−	γ(g)−	ADJ
ijassa-1405	234	18	γ(h	γ(h	NOUN
ijassa-1405	234	19	)	)	PUNCT
ijassa-1405	234	20	=	=	PUNCT
ijassa-1405	235	1	−4	−4	PROPN
ijassa-1405	235	2	,	,	PUNCT
ijassa-1405	235	3	since	since	SCONJ
ijassa-1405	235	4	γ(g	γ(g	PROPN
ijassa-1405	235	5	)	)	PUNCT
ijassa-1405	236	1	=	=	PRON
ijassa-1405	236	2	−7	−7	NOUN
ijassa-1405	236	3	and	and	CCONJ
ijassa-1405	236	4	γ(h	γ(h	NOUN
ijassa-1405	236	5	)	)	PUNCT
ijassa-1405	236	6	=	=	PUNCT
ijassa-1405	237	1	−3	−3	X
ijassa-1405	237	2	.	.	PUNCT
ijassa-1405	238	1	inequality	inequality	NOUN
ijassa-1405	238	2	(	(	PUNCT
ijassa-1405	238	3	3.1	3.1	NUM
ijassa-1405	238	4	)	)	PUNCT
ijassa-1405	238	5	is	be	AUX
ijassa-1405	238	6	sharp	sharp	ADJ
ijassa-1405	238	7	.	.	PUNCT
ijassa-1405	239	1	examples	example	NOUN
ijassa-1405	239	2	of	of	ADP
ijassa-1405	239	3	graph	graph	NOUN
ijassa-1405	239	4	g	g	NOUN
ijassa-1405	239	5	and	and	CCONJ
ijassa-1405	239	6	graph	graph	NOUN
ijassa-1405	239	7	h	h	PROPN
ijassa-1405	239	8	obtained	obtain	VERB
ijassa-1405	239	9	from	from	ADP
ijassa-1405	239	10	g	g	NOUN
ijassa-1405	239	11	by	by	ADP
ijassa-1405	239	12	removing	remove	VERB
ijassa-1405	239	13	one	one	NUM
ijassa-1405	239	14	that	that	PRON
ijassa-1405	239	15	satisfy	satisfy	VERB
ijassa-1405	239	16	that	that	SCONJ
ijassa-1405	239	17	γ(g)−	γ(g)−	ADJ
ijassa-1405	239	18	γ(h	γ(h	NOUN
ijassa-1405	239	19	)	)	PUNCT
ijassa-1405	239	20	=	=	SYM
ijassa-1405	240	1	−4	−4	X
ijassa-1405	240	2	and	and	CCONJ
ijassa-1405	240	3	γ(g)−	γ(g)−	PROPN
ijassa-1405	240	4	γ(h	γ(h	NOUN
ijassa-1405	240	5	)	)	PUNCT
ijassa-1405	240	6	=	=	SYM
ijassa-1405	240	7	2	2	NUM
ijassa-1405	240	8	are	be	AUX
ijassa-1405	240	9	shown	show	VERB
ijassa-1405	240	10	in	in	ADP
ijassa-1405	240	11	fig	fig	NOUN
ijassa-1405	240	12	.	.	PUNCT
ijassa-1405	241	1	3.1	3.1	NUM
ijassa-1405	241	2	and	and	CCONJ
ijassa-1405	241	3	fig	fig	NOUN
ijassa-1405	241	4	.	.	PUNCT
ijassa-1405	242	1	3.1	3.1	NUM
ijassa-1405	242	2	,	,	PUNCT
ijassa-1405	242	3	respectively	respectively	ADV
ijassa-1405	242	4	.	.	PUNCT
ijassa-1405	243	1	copyright	copyright	NOUN
ijassa-1405	243	2	©	©	PROPN
ijassa-1405	243	3	2023	2023	NUM
ijassa-1405	243	4	assa	assa	NOUN
ijassa-1405	243	5	.	.	PUNCT
ijassa-1405	244	1	adv	adv	PROPN
ijassa-1405	244	2	syst	syst	PROPN
ijassa-1405	244	3	sci	sci	PROPN
ijassa-1405	244	4	appl	appl	PROPN
ijassa-1405	244	5	(	(	PUNCT
ijassa-1405	244	6	2023	2023	NUM
ijassa-1405	244	7	)	)	PUNCT
ijassa-1405	244	8	pairwise	pairwise	NOUN
ijassa-1405	244	9	similarity	similarity	NOUN
ijassa-1405	244	10	estimation	estimation	NOUN
ijassa-1405	244	11	for	for	ADP
ijassa-1405	244	12	discrete	discrete	ADJ
ijassa-1405	244	13	optimization	optimization	NOUN
ijassa-1405	244	14	problems	problem	NOUN
ijassa-1405	244	15	171	171	NUM
ijassa-1405	244	16	g	g	PROPN
ijassa-1405	244	17	h	h	NOUN
ijassa-1405	244	18	fig	fig	NOUN
ijassa-1405	244	19	.	.	PUNCT
ijassa-1405	245	1	3.2	3.2	NUM
ijassa-1405	245	2	.	.	PUNCT
ijassa-1405	246	1	graph	graph	NOUN
ijassa-1405	246	2	g	g	NOUN
ijassa-1405	246	3	and	and	CCONJ
ijassa-1405	246	4	graph	graph	NOUN
ijassa-1405	246	5	h	h	PROPN
ijassa-1405	246	6	obtained	obtain	VERB
ijassa-1405	246	7	from	from	ADP
ijassa-1405	246	8	g	g	NOUN
ijassa-1405	246	9	by	by	ADP
ijassa-1405	246	10	removing	remove	VERB
ijassa-1405	246	11	one	one	NUM
ijassa-1405	246	12	edge	edge	NOUN
ijassa-1405	246	13	such	such	ADJ
ijassa-1405	246	14	that	that	DET
ijassa-1405	246	15	γ(g)−	γ(g)−	ADJ
ijassa-1405	246	16	γ(h	γ(h	NOUN
ijassa-1405	246	17	)	)	PUNCT
ijassa-1405	246	18	=	=	SYM
ijassa-1405	247	1	2	2	NUM
ijassa-1405	247	2	,	,	PUNCT
ijassa-1405	247	3	since	since	SCONJ
ijassa-1405	247	4	γ(g	γ(g	PROPN
ijassa-1405	247	5	)	)	PUNCT
ijassa-1405	247	6	=	=	SYM
ijassa-1405	247	7	1	1	NUM
ijassa-1405	247	8	and	and	CCONJ
ijassa-1405	247	9	γ(h	γ(h	NOUN
ijassa-1405	247	10	)	)	PUNCT
ijassa-1405	247	11	=	=	SYM
ijassa-1405	247	12	−1	−1	NOUN
ijassa-1405	247	13	.	.	PUNCT
ijassa-1405	248	1	theorem	theorem	VERB
ijassa-1405	248	2	3.1	3.1	NUM
ijassa-1405	248	3	:	:	PUNCT
ijassa-1405	248	4	let	let	VERB
ijassa-1405	248	5	a	a	DET
ijassa-1405	248	6	connected	connected	ADJ
ijassa-1405	248	7	graph	graph	NOUN
ijassa-1405	248	8	g	g	NOUN
ijassa-1405	248	9	have	have	VERB
ijassa-1405	248	10	cyclomatic	cyclomatic	ADJ
ijassa-1405	248	11	number	number	NOUN
ijassa-1405	248	12	k	k	PROPN
ijassa-1405	248	13	,	,	PUNCT
ijassa-1405	248	14	and	and	CCONJ
ijassa-1405	248	15	let	let	VERB
ijassa-1405	248	16	t	t	PROPN
ijassa-1405	248	17	be	be	AUX
ijassa-1405	248	18	its	its	PRON
ijassa-1405	248	19	arbitrary	arbitrary	ADJ
ijassa-1405	248	20	spanning	span	VERB
ijassa-1405	248	21	tree	tree	NOUN
ijassa-1405	248	22	.	.	PUNCT
ijassa-1405	249	1	then	then	ADV
ijassa-1405	249	2	γ(t	γ(t	NOUN
ijassa-1405	249	3	)	)	PUNCT
ijassa-1405	249	4	−	−	PROPN
ijassa-1405	249	5	4k	4k	PROPN
ijassa-1405	249	6	≤	≤	PROPN
ijassa-1405	249	7	γ(g	γ(g	PROPN
ijassa-1405	249	8	)	)	PUNCT
ijassa-1405	249	9	≤	≤	NOUN
ijassa-1405	249	10	γ(t	γ(t	PUNCT
ijassa-1405	249	11	)	)	PUNCT
ijassa-1405	250	1	+	+	CCONJ
ijassa-1405	250	2	2k	2k	NUM
ijassa-1405	250	3	.	.	PUNCT
ijassa-1405	251	1	proof	proof	NOUN
ijassa-1405	251	2	by	by	ADP
ijassa-1405	251	3	the	the	DET
ijassa-1405	251	4	definition	definition	NOUN
ijassa-1405	251	5	of	of	ADP
ijassa-1405	251	6	cyclomatic	cyclomatic	ADJ
ijassa-1405	251	7	number	number	NOUN
ijassa-1405	251	8	,	,	PUNCT
ijassa-1405	251	9	tree	tree	NOUN
ijassa-1405	251	10	t	t	PROPN
ijassa-1405	251	11	is	be	AUX
ijassa-1405	251	12	obtained	obtain	VERB
ijassa-1405	251	13	from	from	ADP
ijassa-1405	251	14	g	g	NOUN
ijassa-1405	251	15	by	by	ADP
ijassa-1405	251	16	removing	remove	VERB
ijassa-1405	251	17	k	k	PROPN
ijassa-1405	251	18	edges	edge	NOUN
ijassa-1405	251	19	.	.	PUNCT
ijassa-1405	252	1	deleting	delete	VERB
ijassa-1405	252	2	these	these	DET
ijassa-1405	252	3	edges	edge	NOUN
ijassa-1405	252	4	one	one	NUM
ijassa-1405	252	5	by	by	ADP
ijassa-1405	252	6	one	one	NUM
ijassa-1405	252	7	generates	generate	VERB
ijassa-1405	252	8	a	a	DET
ijassa-1405	252	9	sequence	sequence	NOUN
ijassa-1405	252	10	of	of	ADP
ijassa-1405	252	11	graphs	graph	NOUN
ijassa-1405	252	12	g	g	NOUN
ijassa-1405	252	13	:	:	PUNCT
ijassa-1405	252	14	=	=	NOUN
ijassa-1405	252	15	h0	h0	PROPN
ijassa-1405	252	16	,	,	PUNCT
ijassa-1405	252	17	h1	h1	PROPN
ijassa-1405	252	18	,	,	PUNCT
ijassa-1405	252	19	...	...	PUNCT
ijassa-1405	252	20	,	,	PUNCT
ijassa-1405	252	21	hk=:t	hk=:t	X
ijassa-1405	252	22	.	.	PUNCT
ijassa-1405	253	1	the	the	DET
ijassa-1405	253	2	proof	proof	NOUN
ijassa-1405	253	3	of	of	ADP
ijassa-1405	253	4	the	the	DET
ijassa-1405	253	5	theorem	theorem	NOUN
ijassa-1405	253	6	reduces	reduce	VERB
ijassa-1405	253	7	to	to	ADP
ijassa-1405	253	8	applying	apply	VERB
ijassa-1405	253	9	lemma	lemma	PROPN
ijassa-1405	253	10	3.1	3.1	NUM
ijassa-1405	253	11	to	to	ADP
ijassa-1405	253	12	pairs	pair	NOUN
ijassa-1405	253	13	of	of	ADP
ijassa-1405	253	14	graphs	graph	NOUN
ijassa-1405	253	15	hi−1	hi−1	PROPN
ijassa-1405	253	16	,	,	PUNCT
ijassa-1405	253	17	hi	hi	INTJ
ijassa-1405	253	18	,	,	PUNCT
ijassa-1405	253	19	i	i	PRON
ijassa-1405	253	20	=	=	NOUN
ijassa-1405	253	21	1	1	NUM
ijassa-1405	253	22	,	,	PUNCT
ijassa-1405	253	23	...	...	PUNCT
ijassa-1405	253	24	,	,	PUNCT
ijassa-1405	253	25	k	k	PROPN
ijassa-1405	253	26	and	and	CCONJ
ijassa-1405	253	27	summing	sum	VERB
ijassa-1405	253	28	the	the	DET
ijassa-1405	253	29	resulting	result	VERB
ijassa-1405	253	30	inequalities	inequality	NOUN
ijassa-1405	253	31	(	(	PUNCT
ijassa-1405	253	32	3.1	3.1	NUM
ijassa-1405	253	33	)	)	PUNCT
ijassa-1405	253	34	for	for	ADP
ijassa-1405	253	35	them	they	PRON
ijassa-1405	253	36	.	.	PUNCT
ijassa-1405	254	1	theorem	theorem	VERB
ijassa-1405	254	2	3.1	3.1	NUM
ijassa-1405	254	3	defines	define	NOUN
ijassa-1405	254	4	a	a	DET
ijassa-1405	254	5	pairwise	pairwise	NOUN
ijassa-1405	254	6	dissimilarity	dissimilarity	NOUN
ijassa-1405	254	7	function	function	NOUN
ijassa-1405	254	8	,	,	PUNCT
ijassa-1405	254	9	according	accord	VERB
ijassa-1405	254	10	to	to	ADP
ijassa-1405	254	11	which	which	PRON
ijassa-1405	254	12	each	each	DET
ijassa-1405	254	13	spanning	span	VERB
ijassa-1405	254	14	tree	tree	NOUN
ijassa-1405	254	15	of	of	ADP
ijassa-1405	254	16	a	a	DET
ijassa-1405	254	17	graph	graph	NOUN
ijassa-1405	254	18	g	g	NOUN
ijassa-1405	254	19	with	with	ADP
ijassa-1405	254	20	cyclomatic	cyclomatic	ADJ
ijassa-1405	254	21	number	number	NOUN
ijassa-1405	254	22	k	k	PROPN
ijassa-1405	254	23	is	be	AUX
ijassa-1405	254	24	at	at	ADP
ijassa-1405	254	25	distance	distance	NOUN
ijassa-1405	254	26	k	k	PROPN
ijassa-1405	254	27	from	from	ADP
ijassa-1405	254	28	g.	g.	PROPN
ijassa-1405	254	29	a	a	DET
ijassa-1405	254	30	spanning	span	VERB
ijassa-1405	254	31	tree	tree	NOUN
ijassa-1405	254	32	of	of	ADP
ijassa-1405	254	33	g	g	NOUN
ijassa-1405	254	34	can	can	AUX
ijassa-1405	254	35	be	be	AUX
ijassa-1405	254	36	found	find	VERB
ijassa-1405	254	37	via	via	ADP
ijassa-1405	254	38	breadth	breadth	NOUN
ijassa-1405	254	39	-	-	PUNCT
ijassa-1405	254	40	first	first	ADJ
ijassa-1405	254	41	search	search	NOUN
ijassa-1405	254	42	or	or	CCONJ
ijassa-1405	254	43	depth	depth	NOUN
ijassa-1405	254	44	-	-	PUNCT
ijassa-1405	254	45	first	first	ADJ
ijassa-1405	254	46	search	search	NOUN
ijassa-1405	254	47	algorithms	algorithm	NOUN
ijassa-1405	254	48	,	,	PUNCT
ijassa-1405	254	49	which	which	PRON
ijassa-1405	254	50	have	have	VERB
ijassa-1405	254	51	linear	linear	ADJ
ijassa-1405	254	52	time	time	NOUN
ijassa-1405	254	53	complexity	complexity	NOUN
ijassa-1405	254	54	.	.	PUNCT
ijassa-1405	255	1	on	on	ADP
ijassa-1405	255	2	the	the	DET
ijassa-1405	255	3	other	other	ADJ
ijassa-1405	255	4	hand	hand	NOUN
ijassa-1405	255	5	,	,	PUNCT
ijassa-1405	255	6	spanning	span	VERB
ijassa-1405	255	7	trees	tree	NOUN
ijassa-1405	255	8	refer	refer	VERB
ijassa-1405	255	9	to	to	ADP
ijassa-1405	255	10	a	a	DET
ijassa-1405	255	11	simple	simple	ADJ
ijassa-1405	255	12	special	special	ADJ
ijassa-1405	255	13	case	case	NOUN
ijassa-1405	255	14	of	of	ADP
ijassa-1405	255	15	the	the	DET
ijassa-1405	255	16	strict	strict	ADJ
ijassa-1405	255	17	majority	majority	NOUN
ijassa-1405	255	18	domination	domination	NOUN
ijassa-1405	255	19	number	number	NOUN
ijassa-1405	255	20	problem	problem	NOUN
ijassa-1405	255	21	,	,	PUNCT
ijassa-1405	255	22	which	which	PRON
ijassa-1405	255	23	allows	allow	VERB
ijassa-1405	255	24	one	one	PRON
ijassa-1405	255	25	to	to	PART
ijassa-1405	255	26	find	find	VERB
ijassa-1405	255	27	the	the	DET
ijassa-1405	255	28	strict	strict	ADJ
ijassa-1405	255	29	majority	majority	NOUN
ijassa-1405	255	30	domination	domination	NOUN
ijassa-1405	255	31	number	number	NOUN
ijassa-1405	255	32	for	for	ADP
ijassa-1405	255	33	any	any	PRON
ijassa-1405	255	34	of	of	ADP
ijassa-1405	255	35	them	they	PRON
ijassa-1405	255	36	in	in	ADP
ijassa-1405	255	37	polynomial	polynomial	ADJ
ijassa-1405	255	38	time	time	NOUN
ijassa-1405	255	39	o(n2	o(n2	ADV
ijassa-1405	255	40	)	)	PUNCT
ijassa-1405	255	41	and	and	CCONJ
ijassa-1405	255	42	use	use	VERB
ijassa-1405	255	43	the	the	DET
ijassa-1405	255	44	tree	tree	NOUN
ijassa-1405	255	45	’s	’s	PART
ijassa-1405	255	46	optimal	optimal	ADJ
ijassa-1405	255	47	strict	strict	ADJ
ijassa-1405	255	48	majority	majority	NOUN
ijassa-1405	255	49	function	function	NOUN
ijassa-1405	255	50	to	to	PART
ijassa-1405	255	51	construct	construct	VERB
ijassa-1405	255	52	a	a	DET
ijassa-1405	255	53	strict	strict	ADJ
ijassa-1405	255	54	majority	majority	NOUN
ijassa-1405	255	55	function	function	NOUN
ijassa-1405	255	56	for	for	ADP
ijassa-1405	255	57	the	the	DET
ijassa-1405	255	58	graph	graph	NOUN
ijassa-1405	255	59	g	g	NOUN
ijassa-1405	255	60	,	,	PUNCT
ijassa-1405	255	61	which	which	PRON
ijassa-1405	255	62	gives	give	VERB
ijassa-1405	255	63	an	an	DET
ijassa-1405	255	64	approximate	approximate	ADJ
ijassa-1405	255	65	solution	solution	NOUN
ijassa-1405	255	66	to	to	ADP
ijassa-1405	255	67	the	the	DET
ijassa-1405	255	68	original	original	ADJ
ijassa-1405	255	69	problem	problem	NOUN
ijassa-1405	255	70	.	.	PUNCT
ijassa-1405	256	1	a	a	DET
ijassa-1405	256	2	strict	strict	ADJ
ijassa-1405	256	3	majority	majority	NOUN
ijassa-1405	256	4	function	function	NOUN
ijassa-1405	256	5	for	for	ADP
ijassa-1405	256	6	a	a	DET
ijassa-1405	256	7	graph	graph	NOUN
ijassa-1405	256	8	g	g	NOUN
ijassa-1405	256	9	with	with	ADP
ijassa-1405	256	10	cyclomatic	cyclomatic	ADJ
ijassa-1405	256	11	number	number	NOUN
ijassa-1405	256	12	k	k	PROPN
ijassa-1405	256	13	can	can	AUX
ijassa-1405	256	14	be	be	AUX
ijassa-1405	256	15	found	find	VERB
ijassa-1405	256	16	as	as	SCONJ
ijassa-1405	256	17	follows	follow	VERB
ijassa-1405	256	18	:	:	PUNCT
ijassa-1405	256	19	1	1	X
ijassa-1405	256	20	.	.	X
ijassa-1405	256	21	find	find	VERB
ijassa-1405	256	22	a	a	DET
ijassa-1405	256	23	spanning	span	VERB
ijassa-1405	256	24	tree	tree	NOUN
ijassa-1405	256	25	t	t	PROPN
ijassa-1405	256	26	of	of	ADP
ijassa-1405	256	27	g.	g.	PROPN
ijassa-1405	256	28	determine	determine	VERB
ijassa-1405	256	29	an	an	DET
ijassa-1405	256	30	optimal	optimal	ADJ
ijassa-1405	256	31	strict	strict	ADJ
ijassa-1405	256	32	majority	majority	NOUN
ijassa-1405	256	33	function	function	NOUN
ijassa-1405	256	34	for	for	ADP
ijassa-1405	256	35	t	t	NOUN
ijassa-1405	256	36	using	use	VERB
ijassa-1405	256	37	the	the	DET
ijassa-1405	256	38	polynomial	polynomial	ADJ
ijassa-1405	256	39	algorithm	algorithm	NOUN
ijassa-1405	257	1	[	[	X
ijassa-1405	257	2	9	9	NUM
ijassa-1405	257	3	]	]	SYM
ijassa-1405	257	4	.	.	PUNCT
ijassa-1405	258	1	2	2	X
ijassa-1405	258	2	.	.	X
ijassa-1405	258	3	sequentially	sequentially	ADV
ijassa-1405	258	4	add	add	VERB
ijassa-1405	258	5	k	k	PROPN
ijassa-1405	258	6	edges	edge	NOUN
ijassa-1405	258	7	to	to	ADP
ijassa-1405	258	8	t	t	NOUN
ijassa-1405	258	9	until	until	SCONJ
ijassa-1405	258	10	g	g	PROPN
ijassa-1405	258	11	is	be	AUX
ijassa-1405	258	12	obtained	obtain	VERB
ijassa-1405	258	13	:	:	PUNCT
ijassa-1405	258	14	•	•	ADP
ijassa-1405	258	15	add	add	VERB
ijassa-1405	258	16	an	an	DET
ijassa-1405	258	17	edge	edge	NOUN
ijassa-1405	258	18	that	that	PRON
ijassa-1405	258	19	belongs	belong	VERB
ijassa-1405	258	20	to	to	ADP
ijassa-1405	258	21	e(g)∖e(t	e(g)∖e(t	PROPN
ijassa-1405	258	22	)	)	PUNCT
ijassa-1405	258	23	.	.	PUNCT
ijassa-1405	259	1	with	with	ADP
ijassa-1405	259	2	the	the	DET
ijassa-1405	259	3	current	current	ADJ
ijassa-1405	259	4	opinion	opinion	NOUN
ijassa-1405	259	5	function	function	NOUN
ijassa-1405	259	6	,	,	PUNCT
ijassa-1405	259	7	check	check	VERB
ijassa-1405	259	8	if	if	SCONJ
ijassa-1405	259	9	|v	|v	ADJ
ijassa-1405	259	10	+	+	ADV
ijassa-1405	259	11	|	|	ADV
ijassa-1405	259	12	>	>	X
ijassa-1405	259	13	|v	|v	PROPN
ijassa-1405	259	14	|/2	|/2	PROPN
ijassa-1405	259	15	.	.	PUNCT
ijassa-1405	260	1	if	if	SCONJ
ijassa-1405	260	2	this	this	PRON
ijassa-1405	260	3	is	be	AUX
ijassa-1405	260	4	true	true	ADJ
ijassa-1405	260	5	,	,	PUNCT
ijassa-1405	260	6	proceed	procee	VERB
ijassa-1405	260	7	by	by	ADP
ijassa-1405	260	8	adding	add	VERB
ijassa-1405	260	9	the	the	DET
ijassa-1405	260	10	next	next	ADJ
ijassa-1405	260	11	edge	edge	NOUN
ijassa-1405	260	12	.	.	PUNCT
ijassa-1405	261	1	•	•	NUM
ijassa-1405	261	2	otherwise	otherwise	ADV
ijassa-1405	261	3	,	,	PUNCT
ijassa-1405	261	4	change	change	VERB
ijassa-1405	261	5	the	the	DET
ijassa-1405	261	6	opinion	opinion	NOUN
ijassa-1405	261	7	−1	−1	NOUN
ijassa-1405	261	8	of	of	ADP
ijassa-1405	261	9	a	a	DET
ijassa-1405	261	10	vertex	vertex	NOUN
ijassa-1405	261	11	incident	incident	NOUN
ijassa-1405	261	12	to	to	ADP
ijassa-1405	261	13	the	the	DET
ijassa-1405	261	14	new	new	ADJ
ijassa-1405	261	15	edge	edge	NOUN
ijassa-1405	261	16	to	to	ADP
ijassa-1405	261	17	+1	+1	PROPN
ijassa-1405	261	18	.	.	PUNCT
ijassa-1405	262	1	in	in	ADP
ijassa-1405	262	2	accordance	accordance	NOUN
ijassa-1405	262	3	with	with	ADP
ijassa-1405	262	4	the	the	DET
ijassa-1405	262	5	general	general	ADJ
ijassa-1405	262	6	scheme	scheme	NOUN
ijassa-1405	262	7	of	of	ADP
ijassa-1405	262	8	the	the	DET
ijassa-1405	262	9	pairwise	pairwise	NOUN
ijassa-1405	262	10	similarity	similarity	NOUN
ijassa-1405	262	11	method	method	NOUN
ijassa-1405	262	12	,	,	PUNCT
ijassa-1405	262	13	as	as	ADP
ijassa-1405	262	14	an	an	DET
ijassa-1405	262	15	approximate	approximate	ADJ
ijassa-1405	262	16	strict	strict	ADJ
ijassa-1405	262	17	majority	majority	NOUN
ijassa-1405	262	18	domination	domination	NOUN
ijassa-1405	262	19	number	number	NOUN
ijassa-1405	262	20	of	of	ADP
ijassa-1405	262	21	g	g	NOUN
ijassa-1405	262	22	,	,	PUNCT
ijassa-1405	262	23	the	the	DET
ijassa-1405	262	24	best	good	ADJ
ijassa-1405	262	25	solution	solution	NOUN
ijassa-1405	262	26	constructed	construct	VERB
ijassa-1405	262	27	on	on	ADP
ijassa-1405	262	28	the	the	DET
ijassa-1405	262	29	basis	basis	NOUN
ijassa-1405	262	30	of	of	ADP
ijassa-1405	262	31	the	the	DET
ijassa-1405	262	32	optimal	optimal	ADJ
ijassa-1405	262	33	strict	strict	ADJ
ijassa-1405	262	34	majority	majority	NOUN
ijassa-1405	262	35	functions	function	NOUN
ijassa-1405	262	36	of	of	ADP
ijassa-1405	262	37	the	the	DET
ijassa-1405	262	38	spanning	span	VERB
ijassa-1405	262	39	trees	tree	NOUN
ijassa-1405	262	40	of	of	ADP
ijassa-1405	262	41	g	g	NOUN
ijassa-1405	262	42	should	should	AUX
ijassa-1405	262	43	be	be	AUX
ijassa-1405	262	44	taken	take	VERB
ijassa-1405	262	45	.	.	PUNCT
ijassa-1405	263	1	in	in	ADP
ijassa-1405	263	2	practice	practice	NOUN
ijassa-1405	263	3	,	,	PUNCT
ijassa-1405	263	4	one	one	PRON
ijassa-1405	263	5	can	can	AUX
ijassa-1405	263	6	limit	limit	VERB
ijassa-1405	263	7	oneself	oneself	PRON
ijassa-1405	263	8	to	to	ADP
ijassa-1405	263	9	constructing	construct	VERB
ijassa-1405	263	10	several	several	ADJ
ijassa-1405	263	11	randomly	randomly	ADV
ijassa-1405	263	12	selected	select	VERB
ijassa-1405	263	13	spanning	span	VERB
ijassa-1405	263	14	trees	tree	NOUN
ijassa-1405	263	15	.	.	PUNCT
ijassa-1405	264	1	3.2	3.2	NUM
ijassa-1405	264	2	.	.	PUNCT
ijassa-1405	265	1	maximum	maximum	ADJ
ijassa-1405	265	2	cut	cut	VERB
ijassa-1405	265	3	problem	problem	NOUN
ijassa-1405	265	4	in	in	ADP
ijassa-1405	265	5	this	this	DET
ijassa-1405	265	6	section	section	NOUN
ijassa-1405	266	1	,	,	PUNCT
ijassa-1405	266	2	the	the	DET
ijassa-1405	266	3	pairwise	pairwise	NOUN
ijassa-1405	266	4	dissimilarity	dissimilarity	NOUN
ijassa-1405	266	5	function	function	NOUN
ijassa-1405	266	6	based	base	VERB
ijassa-1405	266	7	on	on	ADP
ijassa-1405	266	8	the	the	DET
ijassa-1405	266	9	relative	relative	ADJ
ijassa-1405	266	10	error	error	NOUN
ijassa-1405	266	11	is	be	AUX
ijassa-1405	266	12	estimated	estimate	VERB
ijassa-1405	266	13	numerically	numerically	ADV
ijassa-1405	266	14	.	.	PUNCT
ijassa-1405	267	1	for	for	ADP
ijassa-1405	267	2	this	this	PRON
ijassa-1405	267	3	,	,	PUNCT
ijassa-1405	267	4	an	an	DET
ijassa-1405	267	5	estimate	estimate	NOUN
ijassa-1405	267	6	of	of	ADP
ijassa-1405	267	7	the	the	DET
ijassa-1405	267	8	error	error	NOUN
ijassa-1405	267	9	is	be	AUX
ijassa-1405	267	10	constructed	construct	VERB
ijassa-1405	267	11	,	,	PUNCT
ijassa-1405	267	12	based	base	VERB
ijassa-1405	267	13	on	on	ADP
ijassa-1405	267	14	the	the	DET
ijassa-1405	267	15	reduction	reduction	NOUN
ijassa-1405	267	16	of	of	ADP
ijassa-1405	267	17	problem	problem	NOUN
ijassa-1405	267	18	instances	instance	NOUN
ijassa-1405	267	19	to	to	ADP
ijassa-1405	267	20	a	a	DET
ijassa-1405	267	21	simple	simple	ADJ
ijassa-1405	267	22	special	special	ADJ
ijassa-1405	267	23	case	case	NOUN
ijassa-1405	267	24	.	.	PUNCT
ijassa-1405	268	1	we	we	PRON
ijassa-1405	268	2	use	use	VERB
ijassa-1405	268	3	bipartite	bipartite	NOUN
ijassa-1405	268	4	graphs	graph	NOUN
ijassa-1405	268	5	as	as	ADP
ijassa-1405	268	6	a	a	DET
ijassa-1405	268	7	simple	simple	ADJ
ijassa-1405	268	8	special	special	ADJ
ijassa-1405	268	9	case	case	NOUN
ijassa-1405	268	10	for	for	ADP
ijassa-1405	268	11	the	the	DET
ijassa-1405	268	12	maximum	maximum	ADJ
ijassa-1405	268	13	cut	cut	NOUN
ijassa-1405	268	14	problem	problem	NOUN
ijassa-1405	268	15	.	.	PUNCT
ijassa-1405	269	1	first	first	ADV
ijassa-1405	269	2	,	,	PUNCT
ijassa-1405	269	3	we	we	PRON
ijassa-1405	269	4	introduce	introduce	VERB
ijassa-1405	269	5	the	the	DET
ijassa-1405	269	6	main	main	ADJ
ijassa-1405	269	7	definitions	definition	NOUN
ijassa-1405	269	8	related	relate	VERB
ijassa-1405	269	9	to	to	ADP
ijassa-1405	269	10	this	this	DET
ijassa-1405	269	11	problem	problem	NOUN
ijassa-1405	269	12	.	.	PUNCT
ijassa-1405	270	1	copyright	copyright	NOUN
ijassa-1405	270	2	©	©	PROPN
ijassa-1405	270	3	2023	2023	NUM
ijassa-1405	270	4	assa	assa	NOUN
ijassa-1405	270	5	.	.	PUNCT
ijassa-1405	271	1	adv	adv	PROPN
ijassa-1405	271	2	syst	syst	PROPN
ijassa-1405	271	3	sci	sci	PROPN
ijassa-1405	271	4	appl	appl	PROPN
ijassa-1405	271	5	(	(	PUNCT
ijassa-1405	271	6	2023	2023	NUM
ijassa-1405	271	7	)	)	PUNCT
ijassa-1405	271	8	172	172	NUM
ijassa-1405	271	9	d.	d.	PROPN
ijassa-1405	271	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	271	11	,	,	PUNCT
ijassa-1405	271	12	p.	p.	PROPN
ijassa-1405	271	13	chebotarev	chebotarev	PROPN
ijassa-1405	271	14	,	,	PUNCT
ijassa-1405	271	15	m.	m.	NOUN
ijassa-1405	271	16	goubko	goubko	NOUN
ijassa-1405	271	17	,	,	PUNCT
ijassa-1405	271	18	m.	m.	NOUN
ijassa-1405	271	19	somov	somov	PROPN
ijassa-1405	271	20	,	,	PUNCT
ijassa-1405	271	21	n.	n.	PROPN
ijassa-1405	271	22	shushko	shushko	PROPN
ijassa-1405	271	23	definition	definition	NOUN
ijassa-1405	271	24	3.4	3.4	NUM
ijassa-1405	271	25	.	.	PUNCT
ijassa-1405	272	1	a	a	DET
ijassa-1405	272	2	bipartite	bipartite	ADJ
ijassa-1405	272	3	graph	graph	NOUN
ijassa-1405	272	4	is	be	AUX
ijassa-1405	272	5	a	a	DET
ijassa-1405	272	6	graph	graph	NOUN
ijassa-1405	272	7	whose	whose	DET
ijassa-1405	272	8	set	set	NOUN
ijassa-1405	272	9	of	of	ADP
ijassa-1405	272	10	vertices	vertex	NOUN
ijassa-1405	272	11	can	can	AUX
ijassa-1405	272	12	be	be	AUX
ijassa-1405	272	13	divided	divide	VERB
ijassa-1405	272	14	into	into	ADP
ijassa-1405	272	15	two	two	NUM
ijassa-1405	272	16	parts	part	NOUN
ijassa-1405	272	17	in	in	ADP
ijassa-1405	272	18	such	such	DET
ijassa-1405	272	19	a	a	DET
ijassa-1405	272	20	way	way	NOUN
ijassa-1405	272	21	that	that	PRON
ijassa-1405	272	22	each	each	DET
ijassa-1405	272	23	edge	edge	NOUN
ijassa-1405	272	24	of	of	ADP
ijassa-1405	272	25	the	the	DET
ijassa-1405	272	26	graph	graph	NOUN
ijassa-1405	272	27	connects	connect	VERB
ijassa-1405	272	28	a	a	DET
ijassa-1405	272	29	vertex	vertex	NOUN
ijassa-1405	272	30	of	of	ADP
ijassa-1405	272	31	one	one	NUM
ijassa-1405	272	32	part	part	NOUN
ijassa-1405	272	33	with	with	ADP
ijassa-1405	272	34	a	a	DET
ijassa-1405	272	35	vertex	vertex	NOUN
ijassa-1405	272	36	of	of	ADP
ijassa-1405	272	37	the	the	DET
ijassa-1405	272	38	other	other	ADJ
ijassa-1405	272	39	part	part	NOUN
ijassa-1405	272	40	.	.	PUNCT
ijassa-1405	273	1	definition	definition	NOUN
ijassa-1405	273	2	3.5	3.5	NUM
ijassa-1405	273	3	.	.	PUNCT
ijassa-1405	274	1	a	a	DET
ijassa-1405	274	2	cut	cut	NOUN
ijassa-1405	274	3	is	be	AUX
ijassa-1405	274	4	a	a	DET
ijassa-1405	274	5	partition	partition	NOUN
ijassa-1405	274	6	of	of	ADP
ijassa-1405	274	7	the	the	DET
ijassa-1405	274	8	vertices	vertex	NOUN
ijassa-1405	274	9	of	of	ADP
ijassa-1405	274	10	a	a	DET
ijassa-1405	274	11	graph	graph	NOUN
ijassa-1405	274	12	into	into	ADP
ijassa-1405	274	13	two	two	NUM
ijassa-1405	274	14	subsets	subset	NOUN
ijassa-1405	274	15	.	.	PUNCT
ijassa-1405	275	1	any	any	DET
ijassa-1405	275	2	cut	cut	NOUN
ijassa-1405	275	3	determines	determine	VERB
ijassa-1405	275	4	a	a	DET
ijassa-1405	275	5	cut	cut	NOUN
ijassa-1405	275	6	-	-	PUNCT
ijassa-1405	275	7	set	set	NOUN
ijassa-1405	275	8	,	,	PUNCT
ijassa-1405	275	9	the	the	DET
ijassa-1405	275	10	set	set	NOUN
ijassa-1405	275	11	of	of	ADP
ijassa-1405	275	12	edges	edge	NOUN
ijassa-1405	275	13	that	that	PRON
ijassa-1405	275	14	have	have	VERB
ijassa-1405	275	15	one	one	NUM
ijassa-1405	275	16	endpoint	endpoint	NOUN
ijassa-1405	275	17	in	in	ADP
ijassa-1405	275	18	each	each	DET
ijassa-1405	275	19	subset	subset	NOUN
ijassa-1405	275	20	of	of	ADP
ijassa-1405	275	21	the	the	DET
ijassa-1405	275	22	partition	partition	NOUN
ijassa-1405	275	23	.	.	PUNCT
ijassa-1405	276	1	these	these	DET
ijassa-1405	276	2	edges	edge	NOUN
ijassa-1405	276	3	are	be	AUX
ijassa-1405	276	4	said	say	VERB
ijassa-1405	276	5	to	to	PART
ijassa-1405	276	6	cross	cross	VERB
ijassa-1405	276	7	the	the	DET
ijassa-1405	276	8	cut	cut	NOUN
ijassa-1405	276	9	.	.	PUNCT
ijassa-1405	277	1	definition	definition	NOUN
ijassa-1405	277	2	3.6	3.6	NUM
ijassa-1405	277	3	.	.	PUNCT
ijassa-1405	278	1	in	in	ADP
ijassa-1405	278	2	the	the	DET
ijassa-1405	278	3	case	case	NOUN
ijassa-1405	278	4	of	of	ADP
ijassa-1405	278	5	an	an	DET
ijassa-1405	278	6	unweighted	unweighted	ADJ
ijassa-1405	278	7	graph	graph	NOUN
ijassa-1405	278	8	,	,	PUNCT
ijassa-1405	278	9	the	the	DET
ijassa-1405	278	10	size	size	NOUN
ijassa-1405	278	11	or	or	CCONJ
ijassa-1405	278	12	weight	weight	NOUN
ijassa-1405	278	13	of	of	ADP
ijassa-1405	278	14	a	a	DET
ijassa-1405	278	15	cut	cut	NOUN
ijassa-1405	278	16	is	be	AUX
ijassa-1405	278	17	the	the	DET
ijassa-1405	278	18	number	number	NOUN
ijassa-1405	278	19	of	of	ADP
ijassa-1405	278	20	edges	edge	NOUN
ijassa-1405	278	21	crossing	cross	VERB
ijassa-1405	278	22	the	the	DET
ijassa-1405	278	23	cut	cut	NOUN
ijassa-1405	278	24	;	;	PUNCT
ijassa-1405	278	25	in	in	ADP
ijassa-1405	278	26	the	the	DET
ijassa-1405	278	27	case	case	NOUN
ijassa-1405	278	28	of	of	ADP
ijassa-1405	278	29	a	a	DET
ijassa-1405	278	30	weighted	weight	VERB
ijassa-1405	278	31	graph	graph	NOUN
ijassa-1405	278	32	,	,	PUNCT
ijassa-1405	278	33	the	the	DET
ijassa-1405	278	34	weight	weight	NOUN
ijassa-1405	278	35	of	of	ADP
ijassa-1405	278	36	a	a	DET
ijassa-1405	278	37	cut	cut	NOUN
ijassa-1405	278	38	is	be	AUX
ijassa-1405	278	39	the	the	DET
ijassa-1405	278	40	sum	sum	NOUN
ijassa-1405	278	41	of	of	ADP
ijassa-1405	278	42	the	the	DET
ijassa-1405	278	43	weights	weight	NOUN
ijassa-1405	278	44	of	of	ADP
ijassa-1405	278	45	the	the	DET
ijassa-1405	278	46	crossing	crossing	NOUN
ijassa-1405	278	47	edges	edge	NOUN
ijassa-1405	278	48	.	.	PUNCT
ijassa-1405	279	1	definition	definition	NOUN
ijassa-1405	279	2	3.7	3.7	NUM
ijassa-1405	279	3	.	.	PUNCT
ijassa-1405	280	1	a	a	DET
ijassa-1405	280	2	maximum	maximum	ADJ
ijassa-1405	280	3	cut	cut	NOUN
ijassa-1405	280	4	of	of	ADP
ijassa-1405	280	5	a	a	DET
ijassa-1405	280	6	graph	graph	NOUN
ijassa-1405	280	7	is	be	AUX
ijassa-1405	280	8	a	a	DET
ijassa-1405	280	9	cut	cut	NOUN
ijassa-1405	280	10	whose	whose	DET
ijassa-1405	280	11	size	size	NOUN
ijassa-1405	280	12	is	be	AUX
ijassa-1405	280	13	at	at	ADP
ijassa-1405	280	14	least	least	ADJ
ijassa-1405	280	15	the	the	DET
ijassa-1405	280	16	size	size	NOUN
ijassa-1405	280	17	of	of	ADP
ijassa-1405	280	18	any	any	DET
ijassa-1405	280	19	other	other	ADJ
ijassa-1405	280	20	cut	cut	NOUN
ijassa-1405	280	21	(	(	PUNCT
ijassa-1405	280	22	an	an	DET
ijassa-1405	280	23	example	example	NOUN
ijassa-1405	280	24	is	be	AUX
ijassa-1405	280	25	shown	show	VERB
ijassa-1405	280	26	in	in	ADP
ijassa-1405	280	27	fig	fig	NOUN
ijassa-1405	280	28	.	.	PUNCT
ijassa-1405	281	1	3.3	3.3	NUM
ijassa-1405	281	2	)	)	PUNCT
ijassa-1405	281	3	.	.	PUNCT
ijassa-1405	282	1	the	the	DET
ijassa-1405	282	2	maximum	maximum	ADJ
ijassa-1405	282	3	cut	cut	NOUN
ijassa-1405	282	4	problem	problem	NOUN
ijassa-1405	282	5	for	for	ADP
ijassa-1405	282	6	unweighted	unweighted	ADJ
ijassa-1405	282	7	undirected	undirected	ADJ
ijassa-1405	282	8	graphs	graph	NOUN
ijassa-1405	282	9	can	can	AUX
ijassa-1405	282	10	be	be	AUX
ijassa-1405	282	11	formulated	formulate	VERB
ijassa-1405	282	12	as	as	SCONJ
ijassa-1405	282	13	follows	follow	VERB
ijassa-1405	282	14	.	.	PUNCT
ijassa-1405	283	1	given	give	VERB
ijassa-1405	283	2	a	a	DET
ijassa-1405	283	3	connected	connected	ADJ
ijassa-1405	283	4	graph	graph	NOUN
ijassa-1405	283	5	g	g	NOUN
ijassa-1405	283	6	,	,	PUNCT
ijassa-1405	283	7	find	find	VERB
ijassa-1405	283	8	a	a	DET
ijassa-1405	283	9	subset	subset	NOUN
ijassa-1405	283	10	s	s	NOUN
ijassa-1405	283	11	of	of	ADP
ijassa-1405	283	12	its	its	PRON
ijassa-1405	283	13	vertices	vertex	NOUN
ijassa-1405	283	14	such	such	ADJ
ijassa-1405	283	15	that	that	SCONJ
ijassa-1405	283	16	the	the	DET
ijassa-1405	283	17	number	number	NOUN
ijassa-1405	283	18	of	of	ADP
ijassa-1405	283	19	edges	edge	NOUN
ijassa-1405	283	20	connecting	connect	VERB
ijassa-1405	283	21	s	s	NOUN
ijassa-1405	283	22	with	with	ADP
ijassa-1405	283	23	v	v	NOUN
ijassa-1405	283	24	(	(	PUNCT
ijassa-1405	283	25	g)∖s	g)∖	NOUN
ijassa-1405	283	26	is	be	AUX
ijassa-1405	283	27	maximum	maximum	ADJ
ijassa-1405	283	28	.	.	PUNCT
ijassa-1405	284	1	fig	fig	NOUN
ijassa-1405	284	2	.	.	PUNCT
ijassa-1405	285	1	3.3	3.3	NUM
ijassa-1405	285	2	.	.	PUNCT
ijassa-1405	286	1	maximum	maximum	ADJ
ijassa-1405	286	2	cut	cut	NOUN
ijassa-1405	286	3	of	of	ADP
ijassa-1405	286	4	a	a	DET
ijassa-1405	286	5	graph	graph	NOUN
ijassa-1405	286	6	this	this	DET
ijassa-1405	286	7	problem	problem	NOUN
ijassa-1405	286	8	is	be	AUX
ijassa-1405	286	9	np	np	INTJ
ijassa-1405	286	10	-	-	ADJ
ijassa-1405	286	11	hard	hard	ADJ
ijassa-1405	286	12	[	[	X
ijassa-1405	286	13	5	5	NUM
ijassa-1405	286	14	]	]	PUNCT
ijassa-1405	286	15	.	.	PUNCT
ijassa-1405	287	1	consider	consider	VERB
ijassa-1405	287	2	the	the	DET
ijassa-1405	287	3	maximum	maximum	ADJ
ijassa-1405	287	4	cut	cut	NOUN
ijassa-1405	287	5	problems	problem	NOUN
ijassa-1405	287	6	on	on	ADP
ijassa-1405	287	7	bipartite	bipartite	NOUN
ijassa-1405	287	8	graphs	graph	NOUN
ijassa-1405	287	9	(	(	PUNCT
ijassa-1405	287	10	definition	definition	NOUN
ijassa-1405	287	11	3.4	3.4	NUM
ijassa-1405	287	12	)	)	PUNCT
ijassa-1405	287	13	as	as	ADP
ijassa-1405	287	14	a	a	DET
ijassa-1405	287	15	special	special	ADJ
ijassa-1405	287	16	case	case	NOUN
ijassa-1405	287	17	.	.	PUNCT
ijassa-1405	288	1	for	for	ADP
ijassa-1405	288	2	them	they	PRON
ijassa-1405	288	3	,	,	PUNCT
ijassa-1405	288	4	the	the	DET
ijassa-1405	288	5	solution	solution	NOUN
ijassa-1405	288	6	is	be	AUX
ijassa-1405	288	7	trivial	trivial	ADJ
ijassa-1405	288	8	:	:	PUNCT
ijassa-1405	288	9	the	the	DET
ijassa-1405	288	10	maximum	maximum	ADJ
ijassa-1405	288	11	cut	cut	NOUN
ijassa-1405	288	12	includes	include	VERB
ijassa-1405	288	13	all	all	DET
ijassa-1405	288	14	edges	edge	NOUN
ijassa-1405	288	15	.	.	PUNCT
ijassa-1405	289	1	it	it	PRON
ijassa-1405	289	2	can	can	AUX
ijassa-1405	289	3	be	be	AUX
ijassa-1405	289	4	easily	easily	ADV
ijassa-1405	289	5	checked	check	VERB
ijassa-1405	289	6	in	in	ADP
ijassa-1405	289	7	linear	linear	ADJ
ijassa-1405	289	8	time	time	NOUN
ijassa-1405	289	9	in	in	ADP
ijassa-1405	289	10	the	the	DET
ijassa-1405	289	11	number	number	NOUN
ijassa-1405	289	12	of	of	ADP
ijassa-1405	289	13	edges	edge	NOUN
ijassa-1405	289	14	whether	whether	SCONJ
ijassa-1405	289	15	a	a	DET
ijassa-1405	289	16	graph	graph	NOUN
ijassa-1405	289	17	is	be	AUX
ijassa-1405	289	18	bipartite	bipartite	ADJ
ijassa-1405	289	19	,	,	PUNCT
ijassa-1405	289	20	therefore	therefore	ADV
ijassa-1405	289	21	,	,	PUNCT
ijassa-1405	289	22	by	by	ADP
ijassa-1405	289	23	definition	definition	NOUN
ijassa-1405	289	24	2.2	2.2	NUM
ijassa-1405	289	25	,	,	PUNCT
ijassa-1405	289	26	bipartite	bipartite	NOUN
ijassa-1405	289	27	graphs	graph	NOUN
ijassa-1405	289	28	determine	determine	VERB
ijassa-1405	289	29	a	a	DET
ijassa-1405	289	30	simple	simple	ADJ
ijassa-1405	289	31	special	special	ADJ
ijassa-1405	289	32	case	case	NOUN
ijassa-1405	289	33	for	for	ADP
ijassa-1405	289	34	the	the	DET
ijassa-1405	289	35	maximum	maximum	ADJ
ijassa-1405	289	36	cut	cut	NOUN
ijassa-1405	289	37	problem	problem	NOUN
ijassa-1405	289	38	.	.	PUNCT
ijassa-1405	290	1	the	the	DET
ijassa-1405	290	2	following	follow	VERB
ijassa-1405	290	3	simple	simple	ADJ
ijassa-1405	290	4	depth	depth	NOUN
ijassa-1405	290	5	-	-	PUNCT
ijassa-1405	290	6	first	first	ADJ
ijassa-1405	290	7	search	search	NOUN
ijassa-1405	290	8	algorithm	algorithm	NOUN
ijassa-1405	290	9	finds	find	VERB
ijassa-1405	290	10	an	an	DET
ijassa-1405	290	11	approximate	approximate	ADJ
ijassa-1405	290	12	solution	solution	NOUN
ijassa-1405	290	13	to	to	ADP
ijassa-1405	290	14	the	the	DET
ijassa-1405	290	15	maximum	maximum	ADJ
ijassa-1405	290	16	cut	cut	NOUN
ijassa-1405	290	17	problem	problem	NOUN
ijassa-1405	290	18	;	;	PUNCT
ijassa-1405	290	19	this	this	DET
ijassa-1405	290	20	solution	solution	NOUN
ijassa-1405	290	21	is	be	AUX
ijassa-1405	290	22	exact	exact	ADJ
ijassa-1405	290	23	for	for	ADP
ijassa-1405	290	24	bipartite	bipartite	NOUN
ijassa-1405	290	25	graphs	graph	NOUN
ijassa-1405	290	26	.	.	PUNCT
ijassa-1405	291	1	the	the	DET
ijassa-1405	291	2	error	error	NOUN
ijassa-1405	291	3	of	of	ADP
ijassa-1405	291	4	this	this	DET
ijassa-1405	291	5	algorithm	algorithm	NOUN
ijassa-1405	291	6	gives	give	VERB
ijassa-1405	291	7	rise	rise	NOUN
ijassa-1405	291	8	to	to	ADP
ijassa-1405	291	9	a	a	DET
ijassa-1405	291	10	dissimilarity	dissimilarity	NOUN
ijassa-1405	291	11	function	function	NOUN
ijassa-1405	291	12	,	,	PUNCT
ijassa-1405	291	13	which	which	PRON
ijassa-1405	291	14	is	be	AUX
ijassa-1405	291	15	an	an	DET
ijassa-1405	291	16	upper	upper	ADV
ijassa-1405	291	17	-	-	PUNCT
ijassa-1405	291	18	bound	bind	VERB
ijassa-1405	291	19	estimate	estimate	NOUN
ijassa-1405	291	20	of	of	ADP
ijassa-1405	291	21	the	the	DET
ijassa-1405	291	22	error	error	NOUN
ijassa-1405	291	23	.	.	PUNCT
ijassa-1405	292	1	the	the	DET
ijassa-1405	292	2	input	input	NOUN
ijassa-1405	292	3	of	of	ADP
ijassa-1405	292	4	algorithm	algorithm	NOUN
ijassa-1405	292	5	1	1	NUM
ijassa-1405	292	6	is	be	AUX
ijassa-1405	292	7	an	an	DET
ijassa-1405	292	8	arbitrary	arbitrary	ADJ
ijassa-1405	292	9	undirected	undirected	ADJ
ijassa-1405	292	10	connected	connected	ADJ
ijassa-1405	292	11	graph	graph	NOUN
ijassa-1405	292	12	g	g	PROPN
ijassa-1405	292	13	=	=	PUNCT
ijassa-1405	292	14	(	(	PUNCT
ijassa-1405	292	15	v	v	NOUN
ijassa-1405	292	16	,	,	PUNCT
ijassa-1405	292	17	e	e	NOUN
ijassa-1405	292	18	)	)	PUNCT
ijassa-1405	292	19	.	.	PUNCT
ijassa-1405	293	1	by	by	ADP
ijassa-1405	293	2	removing	remove	VERB
ijassa-1405	293	3	edges	edge	NOUN
ijassa-1405	293	4	,	,	PUNCT
ijassa-1405	293	5	the	the	DET
ijassa-1405	293	6	algorithm	algorithm	NOUN
ijassa-1405	293	7	selects	select	VERB
ijassa-1405	293	8	a	a	DET
ijassa-1405	293	9	bipartite	bipartite	NOUN
ijassa-1405	293	10	graph	graph	NOUN
ijassa-1405	293	11	gb	gb	ADP
ijassa-1405	293	12	=	=	PUNCT
ijassa-1405	293	13	(	(	PUNCT
ijassa-1405	293	14	v	v	PROPN
ijassa-1405	293	15	,	,	PUNCT
ijassa-1405	293	16	eb	eb	PROPN
ijassa-1405	293	17	)	)	PUNCT
ijassa-1405	293	18	.	.	PUNCT
ijassa-1405	294	1	it	it	PRON
ijassa-1405	294	2	works	work	VERB
ijassa-1405	294	3	recursively	recursively	ADV
ijassa-1405	294	4	and	and	CCONJ
ijassa-1405	294	5	paints	paint	VERB
ijassa-1405	294	6	the	the	DET
ijassa-1405	294	7	vertices	vertex	NOUN
ijassa-1405	294	8	in	in	ADP
ijassa-1405	294	9	two	two	NUM
ijassa-1405	294	10	colors	color	NOUN
ijassa-1405	294	11	,	,	PUNCT
ijassa-1405	294	12	red	red	ADJ
ijassa-1405	294	13	and	and	CCONJ
ijassa-1405	294	14	blue	blue	NOUN
ijassa-1405	294	15	for	for	ADP
ijassa-1405	294	16	definiteness	definiteness	NOUN
ijassa-1405	294	17	.	.	PUNCT
ijassa-1405	295	1	first	first	ADV
ijassa-1405	295	2	,	,	PUNCT
ijassa-1405	295	3	we	we	PRON
ijassa-1405	295	4	color	color	VERB
ijassa-1405	295	5	an	an	DET
ijassa-1405	295	6	arbitrary	arbitrary	ADJ
ijassa-1405	295	7	vertex	vertex	NOUN
ijassa-1405	295	8	blue	blue	NOUN
ijassa-1405	295	9	and	and	CCONJ
ijassa-1405	295	10	the	the	DET
ijassa-1405	295	11	adjacent	adjacent	ADJ
ijassa-1405	295	12	vertices	vertice	VERB
ijassa-1405	295	13	a	a	DET
ijassa-1405	295	14	different	different	ADJ
ijassa-1405	295	15	color	color	NOUN
ijassa-1405	295	16	(	(	PUNCT
ijassa-1405	295	17	in	in	ADP
ijassa-1405	295	18	this	this	DET
ijassa-1405	295	19	case	case	NOUN
ijassa-1405	295	20	,	,	PUNCT
ijassa-1405	295	21	red	red	NOUN
ijassa-1405	295	22	)	)	PUNCT
ijassa-1405	295	23	.	.	PUNCT
ijassa-1405	296	1	further	far	ADV
ijassa-1405	296	2	,	,	PUNCT
ijassa-1405	296	3	the	the	DET
ijassa-1405	296	4	algorithm	algorithm	NOUN
ijassa-1405	296	5	recursively	recursively	ADV
ijassa-1405	296	6	repeats	repeat	VERB
ijassa-1405	296	7	this	this	DET
ijassa-1405	296	8	procedure	procedure	NOUN
ijassa-1405	296	9	on	on	ADP
ijassa-1405	296	10	all	all	DET
ijassa-1405	296	11	adjacent	adjacent	ADJ
ijassa-1405	296	12	vertices	vertex	NOUN
ijassa-1405	296	13	that	that	PRON
ijassa-1405	296	14	were	be	AUX
ijassa-1405	296	15	painted	paint	VERB
ijassa-1405	296	16	at	at	ADP
ijassa-1405	296	17	the	the	DET
ijassa-1405	296	18	current	current	ADJ
ijassa-1405	296	19	iteration	iteration	NOUN
ijassa-1405	296	20	.	.	PUNCT
ijassa-1405	297	1	if	if	SCONJ
ijassa-1405	297	2	the	the	DET
ijassa-1405	297	3	current	current	NOUN
ijassa-1405	297	4	and	and	CCONJ
ijassa-1405	297	5	an	an	DET
ijassa-1405	297	6	adjacent	adjacent	ADJ
ijassa-1405	297	7	vertices	vertex	NOUN
ijassa-1405	297	8	have	have	VERB
ijassa-1405	297	9	the	the	DET
ijassa-1405	297	10	same	same	ADJ
ijassa-1405	297	11	color	color	NOUN
ijassa-1405	297	12	,	,	PUNCT
ijassa-1405	297	13	then	then	ADV
ijassa-1405	297	14	instead	instead	ADV
ijassa-1405	297	15	of	of	ADP
ijassa-1405	297	16	repainting	repaint	VERB
ijassa-1405	297	17	the	the	DET
ijassa-1405	297	18	latter	latter	ADJ
ijassa-1405	297	19	one	one	NOUN
ijassa-1405	297	20	,	,	PUNCT
ijassa-1405	297	21	we	we	PRON
ijassa-1405	297	22	remove	remove	VERB
ijassa-1405	297	23	the	the	DET
ijassa-1405	297	24	edge	edge	NOUN
ijassa-1405	297	25	between	between	ADP
ijassa-1405	297	26	them	they	PRON
ijassa-1405	297	27	.	.	PUNCT
ijassa-1405	298	1	as	as	ADP
ijassa-1405	298	2	a	a	DET
ijassa-1405	298	3	result	result	NOUN
ijassa-1405	298	4	,	,	PUNCT
ijassa-1405	298	5	the	the	DET
ijassa-1405	298	6	algorithm	algorithm	NOUN
ijassa-1405	298	7	returns	return	VERB
ijassa-1405	298	8	a	a	DET
ijassa-1405	298	9	bipartite	bipartite	ADJ
ijassa-1405	298	10	graph	graph	NOUN
ijassa-1405	298	11	with	with	ADP
ijassa-1405	298	12	blue	blue	ADJ
ijassa-1405	298	13	and	and	CCONJ
ijassa-1405	298	14	red	red	ADJ
ijassa-1405	298	15	vertices	vertex	NOUN
ijassa-1405	298	16	,	,	PUNCT
ijassa-1405	298	17	the	the	DET
ijassa-1405	298	18	colors	color	NOUN
ijassa-1405	298	19	of	of	ADP
ijassa-1405	298	20	adjacent	adjacent	ADJ
ijassa-1405	298	21	vertices	vertex	NOUN
ijassa-1405	298	22	of	of	ADP
ijassa-1405	298	23	which	which	PRON
ijassa-1405	298	24	differ	differ	VERB
ijassa-1405	298	25	.	.	PUNCT
ijassa-1405	299	1	the	the	DET
ijassa-1405	299	2	complexity	complexity	NOUN
ijassa-1405	299	3	of	of	ADP
ijassa-1405	299	4	the	the	DET
ijassa-1405	299	5	algorithm	algorithm	NOUN
ijassa-1405	299	6	is	be	AUX
ijassa-1405	299	7	o(|v	o(|v	X
ijassa-1405	299	8	|2	|2	NUM
ijassa-1405	299	9	)	)	PUNCT
ijassa-1405	299	10	,	,	PUNCT
ijassa-1405	299	11	since	since	SCONJ
ijassa-1405	299	12	the	the	DET
ijassa-1405	299	13	algorithm	algorithm	NOUN
ijassa-1405	299	14	passes	pass	VERB
ijassa-1405	299	15	through	through	ADP
ijassa-1405	299	16	all	all	DET
ijassa-1405	299	17	the	the	DET
ijassa-1405	299	18	vertices	vertex	NOUN
ijassa-1405	299	19	of	of	ADP
ijassa-1405	299	20	the	the	DET
ijassa-1405	299	21	graph	graph	NOUN
ijassa-1405	299	22	,	,	PUNCT
ijassa-1405	299	23	and	and	CCONJ
ijassa-1405	299	24	for	for	ADP
ijassa-1405	299	25	each	each	DET
ijassa-1405	299	26	vertex	vertex	NOUN
ijassa-1405	299	27	,	,	PUNCT
ijassa-1405	299	28	its	its	PRON
ijassa-1405	299	29	adjacent	adjacent	ADJ
ijassa-1405	299	30	vertices	vertex	NOUN
ijassa-1405	299	31	are	be	AUX
ijassa-1405	299	32	checked	check	VERB
ijassa-1405	299	33	.	.	PUNCT
ijassa-1405	300	1	according	accord	VERB
ijassa-1405	300	2	to	to	ADP
ijassa-1405	300	3	the	the	DET
ijassa-1405	300	4	general	general	ADJ
ijassa-1405	300	5	concept	concept	NOUN
ijassa-1405	300	6	of	of	ADP
ijassa-1405	300	7	dissimilarity	dissimilarity	NOUN
ijassa-1405	300	8	function	function	NOUN
ijassa-1405	300	9	(	(	PUNCT
ijassa-1405	300	10	section	section	NOUN
ijassa-1405	300	11	2	2	NUM
ijassa-1405	300	12	)	)	PUNCT
ijassa-1405	300	13	,	,	PUNCT
ijassa-1405	300	14	the	the	DET
ijassa-1405	300	15	dissimilarity	dissimilarity	NOUN
ijassa-1405	300	16	based	base	VERB
ijassa-1405	300	17	on	on	ADP
ijassa-1405	300	18	the	the	DET
ijassa-1405	300	19	relative	relative	ADJ
ijassa-1405	300	20	error	error	NOUN
ijassa-1405	300	21	between	between	ADP
ijassa-1405	300	22	the	the	DET
ijassa-1405	300	23	maximum	maximum	ADJ
ijassa-1405	300	24	cut	cut	NOUN
ijassa-1405	300	25	problems	problem	NOUN
ijassa-1405	300	26	ag	ag	PROPN
ijassa-1405	300	27	with	with	ADP
ijassa-1405	300	28	graph	graph	NOUN
ijassa-1405	300	29	g	g	PROPN
ijassa-1405	300	30	and	and	CCONJ
ijassa-1405	300	31	ah	ah	INTJ
ijassa-1405	300	32	copyright	copyright	NOUN
ijassa-1405	300	33	©	©	PROPN
ijassa-1405	300	34	2023	2023	NUM
ijassa-1405	300	35	assa	assa	NOUN
ijassa-1405	300	36	.	.	PUNCT
ijassa-1405	301	1	adv	adv	PROPN
ijassa-1405	301	2	syst	syst	PROPN
ijassa-1405	301	3	sci	sci	PROPN
ijassa-1405	301	4	appl	appl	PROPN
ijassa-1405	301	5	(	(	PUNCT
ijassa-1405	301	6	2023	2023	NUM
ijassa-1405	301	7	)	)	PUNCT
ijassa-1405	301	8	pairwise	pairwise	NOUN
ijassa-1405	301	9	similarity	similarity	NOUN
ijassa-1405	301	10	estimation	estimation	NOUN
ijassa-1405	301	11	for	for	ADP
ijassa-1405	301	12	discrete	discrete	ADJ
ijassa-1405	301	13	optimization	optimization	NOUN
ijassa-1405	301	14	problems	problem	NOUN
ijassa-1405	301	15	173	173	NUM
ijassa-1405	301	16	algorithm	algorithm	NOUN
ijassa-1405	301	17	1	1	NUM
ijassa-1405	301	18	max	max	NOUN
ijassa-1405	301	19	-	-	PUNCT
ijassa-1405	301	20	cut	cut	VERB
ijassa-1405	301	21	heuristic	heuristic	ADJ
ijassa-1405	301	22	algorithm	algorithm	NOUN
ijassa-1405	301	23	function	function	NOUN
ijassa-1405	301	24	max	max	PROPN
ijassa-1405	301	25	-	-	PUNCT
ijassa-1405	301	26	cut	cut	VERB
ijassa-1405	301	27	heuristics(v	heuristics(v	NOUN
ijassa-1405	301	28	)	)	PUNCT
ijassa-1405	301	29	a	a	DET
ijassa-1405	301	30	–	–	PUNCT
ijassa-1405	301	31	adjacency	adjacency	NOUN
ijassa-1405	301	32	matrix	matrix	NOUN
ijassa-1405	301	33	of	of	ADP
ijassa-1405	301	34	the	the	DET
ijassa-1405	301	35	connected	connected	ADJ
ijassa-1405	301	36	graph	graph	NOUN
ijassa-1405	301	37	color	color	NOUN
ijassa-1405	301	38	=	=	PUNCT
ijassa-1405	302	1	[	[	X
ijassa-1405	302	2	0	0	NUM
ijassa-1405	302	3	for	for	ADP
ijassa-1405	302	4	v	v	NOUN
ijassa-1405	302	5	in	in	ADP
ijassa-1405	302	6	v	v	NOUN
ijassa-1405	302	7	]	]	PUNCT
ijassa-1405	302	8	#	#	NOUN
ijassa-1405	302	9	0	0	NUM
ijassa-1405	302	10	–	–	PUNCT
ijassa-1405	302	11	not	not	PART
ijassa-1405	302	12	colored	color	VERB
ijassa-1405	302	13	,	,	PUNCT
ijassa-1405	302	14	−1	−1	NOUN
ijassa-1405	302	15	–	–	PUNCT
ijassa-1405	302	16	first	first	ADJ
ijassa-1405	302	17	color	color	NOUN
ijassa-1405	302	18	,	,	PUNCT
ijassa-1405	302	19	1	1	NUM
ijassa-1405	302	20	–	–	PUNCT
ijassa-1405	302	21	second	second	ADJ
ijassa-1405	302	22	color	color	NOUN
ijassa-1405	302	23	v	v	NOUN
ijassa-1405	302	24	:	:	PUNCT
ijassa-1405	302	25	=	=	SYM
ijassa-1405	302	26	random(v	random(v	ADJ
ijassa-1405	302	27	)	)	PUNCT
ijassa-1405	302	28	#	#	NOUN
ijassa-1405	302	29	choose	choose	VERB
ijassa-1405	302	30	an	an	DET
ijassa-1405	302	31	arbitrary	arbitrary	ADJ
ijassa-1405	302	32	vertex	vertex	NOUN
ijassa-1405	302	33	color[v	color[v	NOUN
ijassa-1405	302	34	]	]	PUNCT
ijassa-1405	302	35	=	=	SYM
ijassa-1405	302	36	1	1	NUM
ijassa-1405	302	37	#	#	NOUN
ijassa-1405	302	38	paint	paint	NOUN
ijassa-1405	302	39	first	first	ADJ
ijassa-1405	302	40	vertex	vertex	NOUN
ijassa-1405	302	41	color	color	NOUN
ijassa-1405	302	42	adjacent	adjacent	ADJ
ijassa-1405	302	43	vertices(v	vertices(v	PROPN
ijassa-1405	302	44	)	)	PUNCT
ijassa-1405	302	45	return	return	VERB
ijassa-1405	302	46	∑	∑	PROPN
ijassa-1405	302	47	u	u	PROPN
ijassa-1405	302	48	,	,	PUNCT
ijassa-1405	302	49	v	v	PROPN
ijassa-1405	302	50	a[u	a[u	PROPN
ijassa-1405	302	51	,	,	PUNCT
ijassa-1405	302	52	v	v	NOUN
ijassa-1405	302	53	]	]	PUNCT
ijassa-1405	302	54	2	2	NUM
ijassa-1405	302	55	end	end	NOUN
ijassa-1405	302	56	function	function	NOUN
ijassa-1405	302	57	procedure	procedure	NOUN
ijassa-1405	302	58	color	color	NOUN
ijassa-1405	302	59	adjacent	adjacent	ADJ
ijassa-1405	302	60	vertices(v	vertices(v	PROPN
ijassa-1405	302	61	)	)	PUNCT
ijassa-1405	302	62	for	for	SCONJ
ijassa-1405	302	63	u	u	NOUN
ijassa-1405	302	64	in	in	ADP
ijassa-1405	302	65	v	v	NUM
ijassa-1405	302	66	do	do	VERB
ijassa-1405	302	67	if	if	SCONJ
ijassa-1405	302	68	a[u	a[u	PROPN
ijassa-1405	302	69	,	,	PUNCT
ijassa-1405	302	70	v	v	NOUN
ijassa-1405	302	71	]	]	X
ijassa-1405	302	72	=	=	SYM
ijassa-1405	302	73	1	1	NUM
ijassa-1405	302	74	and	and	CCONJ
ijassa-1405	302	75	color[u	color[u	NOUN
ijassa-1405	302	76	]	]	X
ijassa-1405	302	77	=	=	PUNCT
ijassa-1405	302	78	color[v	color[v	NOUN
ijassa-1405	302	79	]	]	PUNCT
ijassa-1405	302	80	then	then	ADV
ijassa-1405	302	81	a[u	a[u	PROPN
ijassa-1405	302	82	,	,	PUNCT
ijassa-1405	302	83	v	v	NOUN
ijassa-1405	302	84	]	]	X
ijassa-1405	302	85	:	:	PUNCT
ijassa-1405	302	86	=	=	SYM
ijassa-1405	302	87	0	0	NUM
ijassa-1405	302	88	#	#	VERB
ijassa-1405	302	89	remove	remove	VERB
ijassa-1405	302	90	the	the	DET
ijassa-1405	302	91	edge	edge	NOUN
ijassa-1405	302	92	else	else	ADV
ijassa-1405	302	93	if	if	SCONJ
ijassa-1405	302	94	a[u	a[u	PROPN
ijassa-1405	302	95	,	,	PUNCT
ijassa-1405	302	96	v	v	NOUN
ijassa-1405	302	97	]	]	X
ijassa-1405	302	98	=	=	SYM
ijassa-1405	302	99	1	1	NUM
ijassa-1405	302	100	and	and	CCONJ
ijassa-1405	302	101	color[u	color[u	NOUN
ijassa-1405	302	102	]	]	X
ijassa-1405	303	1	=	=	SYM
ijassa-1405	303	2	0	0	PUNCT
ijassa-1405	303	3	then	then	ADV
ijassa-1405	303	4	color[u	color[u	PROPN
ijassa-1405	303	5	]	]	X
ijassa-1405	303	6	:	:	PUNCT
ijassa-1405	303	7	=	=	SYM
ijassa-1405	303	8	−color[v	−color[v	X
ijassa-1405	303	9	]	]	X
ijassa-1405	303	10	#	#	PART
ijassa-1405	303	11	paint	paint	VERB
ijassa-1405	303	12	the	the	DET
ijassa-1405	303	13	vertex	vertex	NOUN
ijassa-1405	303	14	in	in	ADP
ijassa-1405	303	15	the	the	DET
ijassa-1405	303	16	opposite	opposite	ADJ
ijassa-1405	303	17	color	color	NOUN
ijassa-1405	303	18	color	color	NOUN
ijassa-1405	303	19	adjacent	adjacent	ADJ
ijassa-1405	303	20	vertices(u	vertices(u	NOUN
ijassa-1405	303	21	)	)	PUNCT
ijassa-1405	303	22	end	end	NOUN
ijassa-1405	303	23	if	if	SCONJ
ijassa-1405	303	24	end	end	NOUN
ijassa-1405	303	25	for	for	ADP
ijassa-1405	303	26	end	end	NOUN
ijassa-1405	303	27	procedure	procedure	NOUN
ijassa-1405	303	28	with	with	ADP
ijassa-1405	303	29	a	a	DET
ijassa-1405	303	30	bipartite	bipartite	NOUN
ijassa-1405	303	31	graph	graph	NOUN
ijassa-1405	303	32	h	h	NOUN
ijassa-1405	303	33	such	such	ADJ
ijassa-1405	303	34	that	that	SCONJ
ijassa-1405	303	35	e(h	e(h	PROPN
ijassa-1405	303	36	)	)	PUNCT
ijassa-1405	303	37	⊆	⊆	NUM
ijassa-1405	303	38	e(g	e(g	PROPN
ijassa-1405	303	39	)	)	PUNCT
ijassa-1405	303	40	can	can	AUX
ijassa-1405	303	41	be	be	AUX
ijassa-1405	303	42	defined	define	VERB
ijassa-1405	303	43	as	as	ADP
ijassa-1405	303	44	τ(ag	τ(ag	PROPN
ijassa-1405	303	45	,	,	PUNCT
ijassa-1405	303	46	ah	ah	INTJ
ijassa-1405	303	47	)	)	PUNCT
ijassa-1405	303	48	=	=	SYM
ijassa-1405	303	49	f(ag)−	f(ag)−	X
ijassa-1405	303	50	f(ah	f(ah	NUM
ijassa-1405	303	51	)	)	PUNCT
ijassa-1405	303	52	f(ag	f(ag	PROPN
ijassa-1405	303	53	)	)	PUNCT
ijassa-1405	303	54	,	,	PUNCT
ijassa-1405	303	55	where	where	SCONJ
ijassa-1405	303	56	f(ag	f(ag	PROPN
ijassa-1405	303	57	)	)	PUNCT
ijassa-1405	303	58	is	be	AUX
ijassa-1405	303	59	the	the	DET
ijassa-1405	303	60	optimal	optimal	ADJ
ijassa-1405	303	61	value	value	NOUN
ijassa-1405	303	62	of	of	ADP
ijassa-1405	303	63	the	the	DET
ijassa-1405	303	64	objective	objective	ADJ
ijassa-1405	303	65	function	function	NOUN
ijassa-1405	303	66	for	for	ADP
ijassa-1405	303	67	ag	ag	PROPN
ijassa-1405	303	68	.	.	PUNCT
ijassa-1405	304	1	in	in	ADP
ijassa-1405	304	2	what	what	PRON
ijassa-1405	304	3	follows	follow	VERB
ijassa-1405	304	4	,	,	PUNCT
ijassa-1405	304	5	for	for	ADP
ijassa-1405	304	6	simplicity	simplicity	NOUN
ijassa-1405	304	7	,	,	PUNCT
ijassa-1405	304	8	we	we	PRON
ijassa-1405	304	9	will	will	AUX
ijassa-1405	304	10	use	use	VERB
ijassa-1405	304	11	f(g	f(g	NOUN
ijassa-1405	304	12	)	)	PUNCT
ijassa-1405	304	13	as	as	ADP
ijassa-1405	304	14	an	an	DET
ijassa-1405	304	15	abbreviation	abbreviation	NOUN
ijassa-1405	304	16	for	for	ADP
ijassa-1405	304	17	f(ag	f(ag	PROPN
ijassa-1405	304	18	)	)	PUNCT
ijassa-1405	304	19	.	.	PUNCT
ijassa-1405	305	1	for	for	ADP
ijassa-1405	305	2	the	the	DET
ijassa-1405	305	3	above	above	ADJ
ijassa-1405	305	4	algorithm	algorithm	NOUN
ijassa-1405	305	5	,	,	PUNCT
ijassa-1405	305	6	it	it	PRON
ijassa-1405	305	7	is	be	AUX
ijassa-1405	305	8	not	not	PART
ijassa-1405	305	9	easy	easy	ADJ
ijassa-1405	305	10	to	to	PART
ijassa-1405	305	11	obtain	obtain	VERB
ijassa-1405	305	12	the	the	DET
ijassa-1405	305	13	upper	upper	ADJ
ijassa-1405	305	14	bound	bind	VERB
ijassa-1405	305	15	for	for	ADP
ijassa-1405	305	16	the	the	DET
ijassa-1405	305	17	dissimilarity	dissimilarity	NOUN
ijassa-1405	305	18	between	between	ADP
ijassa-1405	305	19	ag	ag	PROPN
ijassa-1405	305	20	and	and	CCONJ
ijassa-1405	305	21	ah	ah	INTJ
ijassa-1405	305	22	,	,	PUNCT
ijassa-1405	305	23	where	where	SCONJ
ijassa-1405	305	24	h	h	NOUN
ijassa-1405	305	25	is	be	AUX
ijassa-1405	305	26	the	the	DET
ijassa-1405	305	27	bipartite	bipartite	PROPN
ijassa-1405	305	28	graph	graph	NOUN
ijassa-1405	305	29	provided	provide	VERB
ijassa-1405	305	30	by	by	ADP
ijassa-1405	305	31	the	the	DET
ijassa-1405	305	32	algorithm	algorithm	NOUN
ijassa-1405	305	33	,	,	PUNCT
ijassa-1405	305	34	analytically	analytically	ADV
ijassa-1405	305	35	.	.	PUNCT
ijassa-1405	306	1	however	however	ADV
ijassa-1405	306	2	,	,	PUNCT
ijassa-1405	306	3	this	this	PRON
ijassa-1405	306	4	bound	bind	VERB
ijassa-1405	306	5	can	can	AUX
ijassa-1405	306	6	be	be	AUX
ijassa-1405	306	7	approximated	approximate	VERB
ijassa-1405	306	8	by	by	ADP
ijassa-1405	306	9	numerical	numerical	ADJ
ijassa-1405	306	10	experiments	experiment	NOUN
ijassa-1405	306	11	.	.	PUNCT
ijassa-1405	307	1	in	in	ADP
ijassa-1405	307	2	such	such	ADJ
ijassa-1405	307	3	experiments	experiment	NOUN
ijassa-1405	307	4	,	,	PUNCT
ijassa-1405	307	5	graphs	graph	NOUN
ijassa-1405	307	6	gi(n	gi(n	NOUN
ijassa-1405	307	7	,	,	PUNCT
ijassa-1405	307	8	p	p	NOUN
ijassa-1405	307	9	)	)	PUNCT
ijassa-1405	307	10	are	be	AUX
ijassa-1405	307	11	randomly	randomly	ADV
ijassa-1405	307	12	generated	generate	VERB
ijassa-1405	307	13	with	with	ADP
ijassa-1405	307	14	two	two	NUM
ijassa-1405	307	15	parameters	parameter	NOUN
ijassa-1405	307	16	:	:	PUNCT
ijassa-1405	307	17	the	the	DET
ijassa-1405	307	18	number	number	NOUN
ijassa-1405	307	19	of	of	ADP
ijassa-1405	307	20	vertices	vertex	NOUN
ijassa-1405	307	21	n	n	CCONJ
ijassa-1405	307	22	and	and	CCONJ
ijassa-1405	307	23	the	the	DET
ijassa-1405	307	24	density	density	NOUN
ijassa-1405	307	25	p	p	X
ijassa-1405	307	26	(	(	PUNCT
ijassa-1405	307	27	the	the	DET
ijassa-1405	307	28	ratio	ratio	NOUN
ijassa-1405	307	29	of	of	ADP
ijassa-1405	307	30	the	the	DET
ijassa-1405	307	31	number	number	NOUN
ijassa-1405	307	32	of	of	ADP
ijassa-1405	307	33	edges	edge	NOUN
ijassa-1405	307	34	in	in	ADP
ijassa-1405	307	35	the	the	DET
ijassa-1405	307	36	graph	graph	NOUN
ijassa-1405	307	37	to	to	ADP
ijassa-1405	307	38	the	the	DET
ijassa-1405	307	39	maximum	maximum	ADJ
ijassa-1405	307	40	possible	possible	ADJ
ijassa-1405	307	41	number	number	NOUN
ijassa-1405	307	42	of	of	ADP
ijassa-1405	307	43	edges	edge	NOUN
ijassa-1405	307	44	n(n	n(n	PROPN
ijassa-1405	307	45	−	−	PROPN
ijassa-1405	307	46	1)/2	1)/2	NUM
ijassa-1405	307	47	)	)	PUNCT
ijassa-1405	307	48	.	.	PUNCT
ijassa-1405	308	1	that	that	PRON
ijassa-1405	308	2	is	be	AUX
ijassa-1405	308	3	,	,	PUNCT
ijassa-1405	308	4	the	the	DET
ijassa-1405	308	5	probability	probability	NOUN
ijassa-1405	308	6	that	that	SCONJ
ijassa-1405	308	7	there	there	PRON
ijassa-1405	308	8	is	be	VERB
ijassa-1405	308	9	an	an	DET
ijassa-1405	308	10	edge	edge	NOUN
ijassa-1405	308	11	between	between	ADP
ijassa-1405	308	12	any	any	DET
ijassa-1405	308	13	two	two	NUM
ijassa-1405	308	14	vertices	vertex	NOUN
ijassa-1405	308	15	is	be	AUX
ijassa-1405	308	16	p.	p.	NOUN
ijassa-1405	308	17	all	all	DET
ijassa-1405	308	18	edge	edge	NOUN
ijassa-1405	308	19	weights	weight	NOUN
ijassa-1405	308	20	are	be	AUX
ijassa-1405	308	21	equal	equal	ADJ
ijassa-1405	308	22	to	to	ADP
ijassa-1405	308	23	1	1	NUM
ijassa-1405	308	24	.	.	PUNCT
ijassa-1405	309	1	each	each	DET
ijassa-1405	309	2	point	point	NOUN
ijassa-1405	309	3	in	in	ADP
ijassa-1405	309	4	the	the	DET
ijassa-1405	309	5	figures	figure	NOUN
ijassa-1405	309	6	below	below	ADV
ijassa-1405	309	7	is	be	AUX
ijassa-1405	309	8	the	the	DET
ijassa-1405	309	9	average	average	ADJ
ijassa-1405	309	10	over	over	ADP
ijassa-1405	309	11	100	100	NUM
ijassa-1405	309	12	random	random	ADJ
ijassa-1405	309	13	instances	instance	NOUN
ijassa-1405	309	14	.	.	PUNCT
ijassa-1405	310	1	to	to	PART
ijassa-1405	310	2	estimate	estimate	VERB
ijassa-1405	310	3	the	the	DET
ijassa-1405	310	4	upper	upper	ADJ
ijassa-1405	310	5	bound	bound	NOUN
ijassa-1405	310	6	of	of	ADP
ijassa-1405	310	7	the	the	DET
ijassa-1405	310	8	pairwise	pairwise	NOUN
ijassa-1405	310	9	dissimilarity	dissimilarity	NOUN
ijassa-1405	310	10	function	function	NOUN
ijassa-1405	310	11	,	,	PUNCT
ijassa-1405	310	12	the	the	DET
ijassa-1405	310	13	average	average	ADJ
ijassa-1405	310	14	relative	relative	ADJ
ijassa-1405	310	15	error	error	NOUN
ijassa-1405	310	16	and	and	CCONJ
ijassa-1405	310	17	the	the	DET
ijassa-1405	310	18	maximum	maximum	ADJ
ijassa-1405	310	19	relative	relative	ADJ
ijassa-1405	310	20	error	error	NOUN
ijassa-1405	310	21	are	be	AUX
ijassa-1405	310	22	used	use	VERB
ijassa-1405	310	23	:	:	PUNCT
ijassa-1405	310	24	δav(n	δav(n	NOUN
ijassa-1405	310	25	,	,	PUNCT
ijassa-1405	310	26	p	p	NOUN
ijassa-1405	310	27	)	)	PUNCT
ijassa-1405	310	28	=	=	SYM
ijassa-1405	311	1	1	1	NUM
ijassa-1405	311	2	k	k	NOUN
ijassa-1405	311	3	k∑	k∑	PROPN
ijassa-1405	311	4	i=1	i=1	PROPN
ijassa-1405	311	5	f(gi(n	f(gi(n	PROPN
ijassa-1405	311	6	,	,	PUNCT
ijassa-1405	311	7	p))−	p))−	NOUN
ijassa-1405	311	8	f̂(gi(n	f̂(gi(n	ADV
ijassa-1405	311	9	,	,	PUNCT
ijassa-1405	311	10	p	p	NOUN
ijassa-1405	311	11	)	)	PUNCT
ijassa-1405	311	12	)	)	PUNCT
ijassa-1405	312	1	f(gi(n	f(gi(n	PROPN
ijassa-1405	312	2	,	,	PUNCT
ijassa-1405	312	3	p	p	NOUN
ijassa-1405	312	4	)	)	PUNCT
ijassa-1405	312	5	)	)	PUNCT
ijassa-1405	312	6	;	;	PUNCT
ijassa-1405	313	1	δmax(n	δmax(n	NOUN
ijassa-1405	313	2	,	,	PUNCT
ijassa-1405	313	3	p	p	NOUN
ijassa-1405	313	4	)	)	PUNCT
ijassa-1405	313	5	=	=	SYM
ijassa-1405	313	6	max	max	PROPN
ijassa-1405	313	7	i∈{1,	i∈{1,	PROPN
ijassa-1405	313	8	...	...	PUNCT
ijassa-1405	313	9	,k	,k	ADJ
ijassa-1405	313	10	}	}	PUNCT
ijassa-1405	313	11	f(gi(n	f(gi(n	PROPN
ijassa-1405	313	12	,	,	PUNCT
ijassa-1405	313	13	p))−	p))−	NOUN
ijassa-1405	313	14	f̂(gi(n	f̂(gi(n	ADV
ijassa-1405	313	15	,	,	PUNCT
ijassa-1405	313	16	p	p	NOUN
ijassa-1405	313	17	)	)	PUNCT
ijassa-1405	313	18	)	)	PUNCT
ijassa-1405	314	1	f(gi(n	f(gi(n	PROPN
ijassa-1405	314	2	,	,	PUNCT
ijassa-1405	314	3	p	p	NOUN
ijassa-1405	314	4	)	)	PUNCT
ijassa-1405	314	5	)	)	PUNCT
ijassa-1405	314	6	,	,	PUNCT
ijassa-1405	314	7	where	where	SCONJ
ijassa-1405	314	8	k	k	PROPN
ijassa-1405	314	9	is	be	AUX
ijassa-1405	314	10	the	the	DET
ijassa-1405	314	11	number	number	NOUN
ijassa-1405	314	12	of	of	ADP
ijassa-1405	314	13	instances	instance	NOUN
ijassa-1405	314	14	with	with	ADP
ijassa-1405	314	15	given	give	VERB
ijassa-1405	314	16	parameters	parameter	NOUN
ijassa-1405	314	17	,	,	PUNCT
ijassa-1405	314	18	f̂(gi(n	f̂(gi(n	ADP
ijassa-1405	314	19	,	,	PUNCT
ijassa-1405	314	20	p	p	NOUN
ijassa-1405	314	21	)	)	PUNCT
ijassa-1405	314	22	)	)	PUNCT
ijassa-1405	314	23	is	be	AUX
ijassa-1405	314	24	the	the	DET
ijassa-1405	314	25	value	value	NOUN
ijassa-1405	314	26	of	of	ADP
ijassa-1405	314	27	the	the	DET
ijassa-1405	314	28	objective	objective	ADJ
ijassa-1405	314	29	function	function	NOUN
ijassa-1405	314	30	of	of	ADP
ijassa-1405	314	31	the	the	DET
ijassa-1405	314	32	algorithm	algorithm	NOUN
ijassa-1405	314	33	,	,	PUNCT
ijassa-1405	314	34	and	and	CCONJ
ijassa-1405	314	35	f(gi(n	f(gi(n	PROPN
ijassa-1405	314	36	,	,	PUNCT
ijassa-1405	314	37	p	p	NOUN
ijassa-1405	314	38	)	)	PUNCT
ijassa-1405	314	39	)	)	PUNCT
ijassa-1405	314	40	is	be	AUX
ijassa-1405	314	41	the	the	DET
ijassa-1405	314	42	optimal	optimal	ADJ
ijassa-1405	314	43	value	value	NOUN
ijassa-1405	314	44	of	of	ADP
ijassa-1405	314	45	the	the	DET
ijassa-1405	314	46	objective	objective	ADJ
ijassa-1405	314	47	function	function	NOUN
ijassa-1405	314	48	.	.	PUNCT
ijassa-1405	315	1	fig	fig	NOUN
ijassa-1405	315	2	.	.	PUNCT
ijassa-1405	316	1	3.4	3.4	NUM
ijassa-1405	316	2	shows	show	VERB
ijassa-1405	316	3	the	the	DET
ijassa-1405	316	4	dependence	dependence	NOUN
ijassa-1405	316	5	of	of	ADP
ijassa-1405	316	6	the	the	DET
ijassa-1405	316	7	average	average	ADJ
ijassa-1405	316	8	relative	relative	ADJ
ijassa-1405	316	9	error	error	NOUN
ijassa-1405	316	10	δav(n	δav(n	NOUN
ijassa-1405	316	11	,	,	PUNCT
ijassa-1405	316	12	p	p	NOUN
ijassa-1405	316	13	)	)	PUNCT
ijassa-1405	316	14	of	of	ADP
ijassa-1405	316	15	the	the	DET
ijassa-1405	316	16	objective	objective	ADJ
ijassa-1405	316	17	function	function	NOUN
ijassa-1405	316	18	on	on	ADP
ijassa-1405	316	19	the	the	DET
ijassa-1405	316	20	number	number	NOUN
ijassa-1405	316	21	of	of	ADP
ijassa-1405	316	22	vertices	vertex	NOUN
ijassa-1405	316	23	in	in	ADP
ijassa-1405	316	24	a	a	DET
ijassa-1405	316	25	graph	graph	NOUN
ijassa-1405	316	26	with	with	ADP
ijassa-1405	316	27	a	a	DET
ijassa-1405	316	28	density	density	NOUN
ijassa-1405	316	29	p	p	NOUN
ijassa-1405	316	30	=	=	NOUN
ijassa-1405	316	31	0.6	0.6	NUM
ijassa-1405	316	32	.	.	PUNCT
ijassa-1405	317	1	it	it	PRON
ijassa-1405	317	2	can	can	AUX
ijassa-1405	317	3	be	be	AUX
ijassa-1405	317	4	seen	see	VERB
ijassa-1405	317	5	that	that	SCONJ
ijassa-1405	317	6	with	with	ADP
ijassa-1405	317	7	an	an	DET
ijassa-1405	317	8	increase	increase	NOUN
ijassa-1405	317	9	in	in	ADP
ijassa-1405	317	10	the	the	DET
ijassa-1405	317	11	number	number	NOUN
ijassa-1405	317	12	of	of	ADP
ijassa-1405	317	13	vertices	vertex	NOUN
ijassa-1405	317	14	,	,	PUNCT
ijassa-1405	317	15	the	the	DET
ijassa-1405	317	16	relative	relative	ADJ
ijassa-1405	317	17	error	error	NOUN
ijassa-1405	317	18	decreases	decrease	VERB
ijassa-1405	317	19	.	.	PUNCT
ijassa-1405	318	1	copyright	copyright	NOUN
ijassa-1405	318	2	©	©	PROPN
ijassa-1405	318	3	2023	2023	NUM
ijassa-1405	318	4	assa	assa	NOUN
ijassa-1405	318	5	.	.	PUNCT
ijassa-1405	319	1	adv	adv	PROPN
ijassa-1405	319	2	syst	syst	PROPN
ijassa-1405	319	3	sci	sci	PROPN
ijassa-1405	319	4	appl	appl	PROPN
ijassa-1405	319	5	(	(	PUNCT
ijassa-1405	319	6	2023	2023	NUM
ijassa-1405	319	7	)	)	PUNCT
ijassa-1405	319	8	174	174	NUM
ijassa-1405	319	9	d.	d.	PROPN
ijassa-1405	319	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	319	11	,	,	PUNCT
ijassa-1405	319	12	p.	p.	PROPN
ijassa-1405	319	13	chebotarev	chebotarev	PROPN
ijassa-1405	319	14	,	,	PUNCT
ijassa-1405	319	15	m.	m.	NOUN
ijassa-1405	319	16	goubko	goubko	NOUN
ijassa-1405	319	17	,	,	PUNCT
ijassa-1405	319	18	m.	m.	NOUN
ijassa-1405	319	19	somov	somov	PROPN
ijassa-1405	319	20	,	,	PUNCT
ijassa-1405	319	21	n.	n.	PROPN
ijassa-1405	319	22	shushko	shushko	VERB
ijassa-1405	319	23	50	50	NUM
ijassa-1405	319	24	100	100	NUM
ijassa-1405	319	25	150	150	NUM
ijassa-1405	319	26	200	200	NUM
ijassa-1405	319	27	250	250	NUM
ijassa-1405	319	28	300	300	NUM
ijassa-1405	319	29	350	350	NUM
ijassa-1405	319	30	400	400	NUM
ijassa-1405	319	31	n	n	ADV
ijassa-1405	319	32	0.050	0.050	NUM
ijassa-1405	319	33	0.055	0.055	NUM
ijassa-1405	319	34	0.060	0.060	NUM
ijassa-1405	319	35	0.065	0.065	NUM
ijassa-1405	319	36	0.070	0.070	NUM
ijassa-1405	319	37	0.075	0.075	NUM
ijassa-1405	319	38	0.080	0.080	NUM
ijassa-1405	319	39	0.085	0.085	NUM
ijassa-1405	319	40	av	av	PROPN
ijassa-1405	319	41	er	er	INTJ
ijassa-1405	319	42	ag	ag	PROPN
ijassa-1405	319	43	e	e	PROPN
ijassa-1405	319	44	re	re	X
ijassa-1405	319	45	la	la	PROPN
ijassa-1405	319	46	tiv	tiv	PROPN
ijassa-1405	319	47	e	e	PROPN
ijassa-1405	319	48	er	er	INTJ
ijassa-1405	319	49	ro	ro	INTJ
ijassa-1405	319	50	r	r	NOUN
ijassa-1405	319	51	fig	fig	NOUN
ijassa-1405	319	52	.	.	PUNCT
ijassa-1405	320	1	3.4	3.4	NUM
ijassa-1405	320	2	.	.	PUNCT
ijassa-1405	320	3	dependence	dependence	NOUN
ijassa-1405	320	4	of	of	ADP
ijassa-1405	320	5	the	the	DET
ijassa-1405	320	6	relative	relative	ADJ
ijassa-1405	320	7	error	error	NOUN
ijassa-1405	320	8	of	of	ADP
ijassa-1405	320	9	the	the	DET
ijassa-1405	320	10	objective	objective	ADJ
ijassa-1405	320	11	function	function	NOUN
ijassa-1405	320	12	on	on	ADP
ijassa-1405	320	13	the	the	DET
ijassa-1405	320	14	number	number	NOUN
ijassa-1405	320	15	of	of	ADP
ijassa-1405	320	16	vertices	vertex	NOUN
ijassa-1405	320	17	.	.	PUNCT
ijassa-1405	321	1	fig	fig	NOUN
ijassa-1405	321	2	.	.	PUNCT
ijassa-1405	322	1	3.5	3.5	NUM
ijassa-1405	322	2	shows	show	VERB
ijassa-1405	322	3	the	the	DET
ijassa-1405	322	4	dependence	dependence	NOUN
ijassa-1405	322	5	of	of	ADP
ijassa-1405	322	6	the	the	DET
ijassa-1405	322	7	average	average	ADJ
ijassa-1405	322	8	relative	relative	ADJ
ijassa-1405	322	9	error	error	NOUN
ijassa-1405	322	10	δav(n	δav(n	NOUN
ijassa-1405	322	11	,	,	PUNCT
ijassa-1405	322	12	p	p	NOUN
ijassa-1405	322	13	)	)	PUNCT
ijassa-1405	322	14	of	of	ADP
ijassa-1405	322	15	the	the	DET
ijassa-1405	322	16	objective	objective	ADJ
ijassa-1405	322	17	function	function	NOUN
ijassa-1405	322	18	on	on	ADP
ijassa-1405	322	19	the	the	DET
ijassa-1405	322	20	density	density	NOUN
ijassa-1405	322	21	of	of	ADP
ijassa-1405	322	22	a	a	DET
ijassa-1405	322	23	graph	graph	NOUN
ijassa-1405	322	24	with	with	ADP
ijassa-1405	322	25	a	a	DET
ijassa-1405	322	26	constant	constant	ADJ
ijassa-1405	322	27	number	number	NOUN
ijassa-1405	322	28	of	of	ADP
ijassa-1405	322	29	vertices	vertex	NOUN
ijassa-1405	322	30	n	n	X
ijassa-1405	322	31	=	=	SYM
ijassa-1405	322	32	150	150	NUM
ijassa-1405	322	33	.	.	PUNCT
ijassa-1405	323	1	it	it	PRON
ijassa-1405	323	2	can	can	AUX
ijassa-1405	323	3	be	be	AUX
ijassa-1405	323	4	seen	see	VERB
ijassa-1405	323	5	that	that	SCONJ
ijassa-1405	323	6	with	with	ADP
ijassa-1405	323	7	increasing	increase	VERB
ijassa-1405	323	8	density	density	NOUN
ijassa-1405	323	9	the	the	DET
ijassa-1405	323	10	relative	relative	ADJ
ijassa-1405	323	11	error	error	NOUN
ijassa-1405	323	12	decreases	decrease	VERB
ijassa-1405	323	13	.	.	PUNCT
ijassa-1405	324	1	fig	fig	NOUN
ijassa-1405	324	2	.	.	PUNCT
ijassa-1405	325	1	3.6	3.6	NUM
ijassa-1405	325	2	shows	show	VERB
ijassa-1405	325	3	the	the	DET
ijassa-1405	325	4	dependence	dependence	NOUN
ijassa-1405	325	5	of	of	ADP
ijassa-1405	325	6	the	the	DET
ijassa-1405	325	7	average	average	ADJ
ijassa-1405	325	8	relative	relative	ADJ
ijassa-1405	325	9	error	error	NOUN
ijassa-1405	325	10	δav(n	δav(n	NOUN
ijassa-1405	325	11	,	,	PUNCT
ijassa-1405	325	12	p	p	NOUN
ijassa-1405	325	13	)	)	PUNCT
ijassa-1405	325	14	of	of	ADP
ijassa-1405	325	15	the	the	DET
ijassa-1405	325	16	objective	objective	ADJ
ijassa-1405	325	17	function	function	NOUN
ijassa-1405	325	18	on	on	ADP
ijassa-1405	325	19	the	the	DET
ijassa-1405	325	20	density	density	NOUN
ijassa-1405	325	21	of	of	ADP
ijassa-1405	325	22	a	a	DET
ijassa-1405	325	23	graph	graph	NOUN
ijassa-1405	325	24	and	and	CCONJ
ijassa-1405	325	25	on	on	ADP
ijassa-1405	325	26	the	the	DET
ijassa-1405	325	27	number	number	NOUN
ijassa-1405	325	28	of	of	ADP
ijassa-1405	325	29	vertices	vertex	NOUN
ijassa-1405	325	30	.	.	PUNCT
ijassa-1405	326	1	it	it	PRON
ijassa-1405	326	2	can	can	AUX
ijassa-1405	326	3	be	be	AUX
ijassa-1405	326	4	seen	see	VERB
ijassa-1405	326	5	that	that	SCONJ
ijassa-1405	326	6	the	the	DET
ijassa-1405	326	7	density	density	NOUN
ijassa-1405	326	8	of	of	ADP
ijassa-1405	326	9	the	the	DET
ijassa-1405	326	10	graph	graph	NOUN
ijassa-1405	326	11	has	have	VERB
ijassa-1405	326	12	a	a	DET
ijassa-1405	326	13	much	much	ADV
ijassa-1405	326	14	stronger	strong	ADJ
ijassa-1405	326	15	effect	effect	NOUN
ijassa-1405	326	16	on	on	ADP
ijassa-1405	326	17	the	the	DET
ijassa-1405	326	18	relative	relative	ADJ
ijassa-1405	326	19	error	error	NOUN
ijassa-1405	326	20	than	than	ADP
ijassa-1405	326	21	the	the	DET
ijassa-1405	326	22	number	number	NOUN
ijassa-1405	326	23	of	of	ADP
ijassa-1405	326	24	vertices	vertex	NOUN
ijassa-1405	326	25	.	.	PUNCT
ijassa-1405	327	1	fig	fig	NOUN
ijassa-1405	327	2	.	.	PUNCT
ijassa-1405	328	1	3.7	3.7	NUM
ijassa-1405	328	2	shows	show	VERB
ijassa-1405	328	3	the	the	DET
ijassa-1405	328	4	dependence	dependence	NOUN
ijassa-1405	328	5	of	of	ADP
ijassa-1405	328	6	the	the	DET
ijassa-1405	328	7	maximum	maximum	ADJ
ijassa-1405	328	8	relative	relative	ADJ
ijassa-1405	328	9	error	error	NOUN
ijassa-1405	328	10	δmax(n	δmax(n	NOUN
ijassa-1405	328	11	,	,	PUNCT
ijassa-1405	328	12	p	p	NOUN
ijassa-1405	328	13	)	)	PUNCT
ijassa-1405	328	14	of	of	ADP
ijassa-1405	328	15	the	the	DET
ijassa-1405	328	16	objective	objective	ADJ
ijassa-1405	328	17	function	function	NOUN
ijassa-1405	328	18	on	on	ADP
ijassa-1405	328	19	the	the	DET
ijassa-1405	328	20	density	density	NOUN
ijassa-1405	328	21	of	of	ADP
ijassa-1405	328	22	a	a	DET
ijassa-1405	328	23	graph	graph	NOUN
ijassa-1405	328	24	.	.	PUNCT
ijassa-1405	329	1	the	the	DET
ijassa-1405	329	2	shape	shape	NOUN
ijassa-1405	329	3	of	of	ADP
ijassa-1405	329	4	this	this	DET
ijassa-1405	329	5	curve	curve	NOUN
ijassa-1405	329	6	is	be	AUX
ijassa-1405	329	7	very	very	ADV
ijassa-1405	329	8	similar	similar	ADJ
ijassa-1405	329	9	to	to	ADP
ijassa-1405	329	10	that	that	PRON
ijassa-1405	329	11	of	of	ADP
ijassa-1405	329	12	the	the	DET
ijassa-1405	329	13	average	average	ADJ
ijassa-1405	329	14	relative	relative	ADJ
ijassa-1405	329	15	error	error	NOUN
ijassa-1405	329	16	one	one	NUM
ijassa-1405	329	17	.	.	PUNCT
ijassa-1405	330	1	fig	fig	NOUN
ijassa-1405	330	2	.	.	PUNCT
ijassa-1405	331	1	3.8	3.8	NUM
ijassa-1405	331	2	shows	show	VERB
ijassa-1405	331	3	the	the	DET
ijassa-1405	331	4	dependence	dependence	NOUN
ijassa-1405	331	5	of	of	ADP
ijassa-1405	331	6	the	the	DET
ijassa-1405	331	7	maximum	maximum	ADJ
ijassa-1405	331	8	relative	relative	ADJ
ijassa-1405	331	9	error	error	NOUN
ijassa-1405	331	10	δmax(n	δmax(n	NOUN
ijassa-1405	331	11	,	,	PUNCT
ijassa-1405	331	12	p	p	NOUN
ijassa-1405	331	13	)	)	PUNCT
ijassa-1405	331	14	of	of	ADP
ijassa-1405	331	15	the	the	DET
ijassa-1405	331	16	objective	objective	ADJ
ijassa-1405	331	17	function	function	NOUN
ijassa-1405	331	18	on	on	ADP
ijassa-1405	331	19	the	the	DET
ijassa-1405	331	20	number	number	NOUN
ijassa-1405	331	21	of	of	ADP
ijassa-1405	331	22	vertices	vertex	NOUN
ijassa-1405	331	23	.	.	PUNCT
ijassa-1405	332	1	this	this	DET
ijassa-1405	332	2	curve	curve	NOUN
ijassa-1405	332	3	is	be	AUX
ijassa-1405	332	4	also	also	ADV
ijassa-1405	332	5	similar	similar	ADJ
ijassa-1405	332	6	to	to	ADP
ijassa-1405	332	7	the	the	DET
ijassa-1405	332	8	curve	curve	NOUN
ijassa-1405	332	9	of	of	ADP
ijassa-1405	332	10	the	the	DET
ijassa-1405	332	11	average	average	ADJ
ijassa-1405	332	12	relative	relative	ADJ
ijassa-1405	332	13	error	error	NOUN
ijassa-1405	332	14	,	,	PUNCT
ijassa-1405	332	15	but	but	CCONJ
ijassa-1405	332	16	it	it	PRON
ijassa-1405	332	17	is	be	AUX
ijassa-1405	332	18	less	less	ADV
ijassa-1405	332	19	robust	robust	ADJ
ijassa-1405	332	20	.	.	PUNCT
ijassa-1405	333	1	fig	fig	NOUN
ijassa-1405	333	2	.	.	PUNCT
ijassa-1405	334	1	3.9	3.9	NUM
ijassa-1405	334	2	shows	show	VERB
ijassa-1405	334	3	the	the	DET
ijassa-1405	334	4	dependence	dependence	NOUN
ijassa-1405	334	5	of	of	ADP
ijassa-1405	334	6	the	the	DET
ijassa-1405	334	7	maximum	maximum	ADJ
ijassa-1405	334	8	relative	relative	ADJ
ijassa-1405	334	9	error	error	NOUN
ijassa-1405	334	10	δmax(n	δmax(n	NOUN
ijassa-1405	334	11	,	,	PUNCT
ijassa-1405	334	12	p	p	NOUN
ijassa-1405	334	13	)	)	PUNCT
ijassa-1405	334	14	of	of	ADP
ijassa-1405	334	15	the	the	DET
ijassa-1405	334	16	objective	objective	ADJ
ijassa-1405	334	17	function	function	NOUN
ijassa-1405	334	18	on	on	ADP
ijassa-1405	334	19	the	the	DET
ijassa-1405	334	20	density	density	NOUN
ijassa-1405	334	21	and	and	CCONJ
ijassa-1405	334	22	number	number	NOUN
ijassa-1405	334	23	of	of	ADP
ijassa-1405	334	24	vertices	vertex	NOUN
ijassa-1405	334	25	.	.	PUNCT
ijassa-1405	335	1	it	it	PRON
ijassa-1405	335	2	is	be	AUX
ijassa-1405	335	3	not	not	PART
ijassa-1405	335	4	monotonic	monotonic	ADJ
ijassa-1405	335	5	in	in	ADP
ijassa-1405	335	6	the	the	DET
ijassa-1405	335	7	region	region	NOUN
ijassa-1405	335	8	of	of	ADP
ijassa-1405	335	9	small	small	ADJ
ijassa-1405	335	10	numbers	number	NOUN
ijassa-1405	335	11	of	of	ADP
ijassa-1405	335	12	vertices	vertex	NOUN
ijassa-1405	335	13	,	,	PUNCT
ijassa-1405	335	14	since	since	SCONJ
ijassa-1405	335	15	for	for	ADP
ijassa-1405	335	16	such	such	ADJ
ijassa-1405	335	17	numbers	number	NOUN
ijassa-1405	335	18	,	,	PUNCT
ijassa-1405	335	19	the	the	DET
ijassa-1405	335	20	solution	solution	NOUN
ijassa-1405	335	21	is	be	AUX
ijassa-1405	335	22	very	very	ADV
ijassa-1405	335	23	unstable	unstable	ADJ
ijassa-1405	335	24	.	.	PUNCT
ijassa-1405	336	1	since	since	SCONJ
ijassa-1405	336	2	we	we	PRON
ijassa-1405	336	3	choose	choose	VERB
ijassa-1405	336	4	a	a	DET
ijassa-1405	336	5	random	random	ADJ
ijassa-1405	336	6	vertex	vertex	NOUN
ijassa-1405	336	7	to	to	PART
ijassa-1405	336	8	start	start	VERB
ijassa-1405	336	9	the	the	DET
ijassa-1405	336	10	algorithm	algorithm	NOUN
ijassa-1405	336	11	,	,	PUNCT
ijassa-1405	336	12	the	the	DET
ijassa-1405	336	13	algorithm	algorithm	NOUN
ijassa-1405	336	14	works	work	VERB
ijassa-1405	336	15	in	in	ADP
ijassa-1405	336	16	a	a	DET
ijassa-1405	336	17	nondeterministic	nondeterministic	ADJ
ijassa-1405	336	18	way	way	NOUN
ijassa-1405	336	19	.	.	PUNCT
ijassa-1405	337	1	obviously	obviously	ADV
ijassa-1405	337	2	,	,	PUNCT
ijassa-1405	337	3	it	it	PRON
ijassa-1405	337	4	is	be	AUX
ijassa-1405	337	5	necessary	necessary	ADJ
ijassa-1405	337	6	to	to	PART
ijassa-1405	337	7	remove	remove	VERB
ijassa-1405	337	8	as	as	ADV
ijassa-1405	337	9	few	few	ADJ
ijassa-1405	337	10	edges	edge	NOUN
ijassa-1405	337	11	as	as	ADP
ijassa-1405	337	12	possible	possible	ADJ
ijassa-1405	337	13	from	from	ADP
ijassa-1405	337	14	the	the	DET
ijassa-1405	337	15	initial	initial	ADJ
ijassa-1405	337	16	graph	graph	NOUN
ijassa-1405	337	17	,	,	PUNCT
ijassa-1405	337	18	since	since	SCONJ
ijassa-1405	337	19	the	the	DET
ijassa-1405	337	20	number	number	NOUN
ijassa-1405	337	21	of	of	ADP
ijassa-1405	337	22	remaining	remain	VERB
ijassa-1405	337	23	edges	edge	NOUN
ijassa-1405	337	24	determines	determine	VERB
ijassa-1405	337	25	the	the	DET
ijassa-1405	337	26	value	value	NOUN
ijassa-1405	337	27	of	of	ADP
ijassa-1405	337	28	the	the	DET
ijassa-1405	337	29	objective	objective	ADJ
ijassa-1405	337	30	function	function	NOUN
ijassa-1405	337	31	.	.	PUNCT
ijassa-1405	338	1	therefore	therefore	ADV
ijassa-1405	338	2	,	,	PUNCT
ijassa-1405	338	3	in	in	ADP
ijassa-1405	338	4	the	the	DET
ijassa-1405	338	5	general	general	ADJ
ijassa-1405	338	6	case	case	NOUN
ijassa-1405	338	7	,	,	PUNCT
ijassa-1405	338	8	appropriate	appropriate	ADJ
ijassa-1405	338	9	heuristics	heuristic	NOUN
ijassa-1405	338	10	can	can	AUX
ijassa-1405	338	11	be	be	AUX
ijassa-1405	338	12	used	use	VERB
ijassa-1405	338	13	to	to	PART
ijassa-1405	338	14	select	select	VERB
ijassa-1405	338	15	the	the	DET
ijassa-1405	338	16	first	first	ADJ
ijassa-1405	338	17	vertex	vertex	NOUN
ijassa-1405	338	18	and	and	CCONJ
ijassa-1405	338	19	study	study	VERB
ijassa-1405	338	20	the	the	DET
ijassa-1405	338	21	influence	influence	NOUN
ijassa-1405	338	22	of	of	ADP
ijassa-1405	338	23	this	this	DET
ijassa-1405	338	24	choice	choice	NOUN
ijassa-1405	338	25	on	on	ADP
ijassa-1405	338	26	the	the	DET
ijassa-1405	338	27	size	size	NOUN
ijassa-1405	338	28	of	of	ADP
ijassa-1405	338	29	the	the	DET
ijassa-1405	338	30	resulting	result	VERB
ijassa-1405	338	31	bipartite	bipartite	NOUN
ijassa-1405	338	32	graph	graph	NOUN
ijassa-1405	338	33	.	.	PUNCT
ijassa-1405	339	1	copyright	copyright	NOUN
ijassa-1405	339	2	©	©	PROPN
ijassa-1405	339	3	2023	2023	NUM
ijassa-1405	339	4	assa	assa	NOUN
ijassa-1405	339	5	.	.	PUNCT
ijassa-1405	340	1	adv	adv	PROPN
ijassa-1405	340	2	syst	syst	PROPN
ijassa-1405	340	3	sci	sci	PROPN
ijassa-1405	340	4	appl	appl	PROPN
ijassa-1405	340	5	(	(	PUNCT
ijassa-1405	340	6	2023	2023	NUM
ijassa-1405	340	7	)	)	PUNCT
ijassa-1405	340	8	pairwise	pairwise	NOUN
ijassa-1405	340	9	similarity	similarity	NOUN
ijassa-1405	340	10	estimation	estimation	NOUN
ijassa-1405	340	11	for	for	ADP
ijassa-1405	340	12	discrete	discrete	ADJ
ijassa-1405	340	13	optimization	optimization	NOUN
ijassa-1405	340	14	problems	problem	NOUN
ijassa-1405	340	15	175	175	NUM
ijassa-1405	340	16	0.1	0.1	NUM
ijassa-1405	340	17	0.2	0.2	NUM
ijassa-1405	340	18	0.3	0.3	NUM
ijassa-1405	340	19	0.4	0.4	NUM
ijassa-1405	340	20	0.5	0.5	NUM
ijassa-1405	340	21	0.6	0.6	NUM
ijassa-1405	340	22	0.7	0.7	NUM
ijassa-1405	340	23	0.8	0.8	NUM
ijassa-1405	340	24	0.9	0.9	NUM
ijassa-1405	340	25	p	p	NOUN
ijassa-1405	340	26	0.04	0.04	NUM
ijassa-1405	340	27	0.06	0.06	NUM
ijassa-1405	340	28	0.08	0.08	NUM
ijassa-1405	340	29	0.10	0.10	NUM
ijassa-1405	340	30	0.12	0.12	NUM
ijassa-1405	340	31	0.14	0.14	NUM
ijassa-1405	340	32	av	av	PROPN
ijassa-1405	340	33	er	er	INTJ
ijassa-1405	340	34	ag	ag	PROPN
ijassa-1405	340	35	e	e	PROPN
ijassa-1405	340	36	re	re	X
ijassa-1405	340	37	la	la	PROPN
ijassa-1405	340	38	tiv	tiv	PROPN
ijassa-1405	340	39	e	e	PROPN
ijassa-1405	340	40	er	er	INTJ
ijassa-1405	340	41	ro	ro	INTJ
ijassa-1405	340	42	r	r	NOUN
ijassa-1405	340	43	fig	fig	NOUN
ijassa-1405	340	44	.	.	PUNCT
ijassa-1405	341	1	3.5	3.5	NUM
ijassa-1405	341	2	.	.	PUNCT
ijassa-1405	342	1	the	the	DET
ijassa-1405	342	2	dependence	dependence	NOUN
ijassa-1405	342	3	of	of	ADP
ijassa-1405	342	4	the	the	DET
ijassa-1405	342	5	relative	relative	ADJ
ijassa-1405	342	6	error	error	NOUN
ijassa-1405	342	7	of	of	ADP
ijassa-1405	342	8	the	the	DET
ijassa-1405	342	9	objective	objective	ADJ
ijassa-1405	342	10	function	function	NOUN
ijassa-1405	342	11	on	on	ADP
ijassa-1405	342	12	the	the	DET
ijassa-1405	342	13	density	density	NOUN
ijassa-1405	342	14	.	.	PUNCT
ijassa-1405	343	1	according	accord	VERB
ijassa-1405	343	2	to	to	ADP
ijassa-1405	343	3	the	the	DET
ijassa-1405	343	4	general	general	ADJ
ijassa-1405	343	5	scheme	scheme	NOUN
ijassa-1405	343	6	of	of	ADP
ijassa-1405	343	7	pairwise	pairwise	NOUN
ijassa-1405	343	8	similarity	similarity	NOUN
ijassa-1405	343	9	method	method	NOUN
ijassa-1405	343	10	,	,	PUNCT
ijassa-1405	343	11	it	it	PRON
ijassa-1405	343	12	is	be	AUX
ijassa-1405	343	13	suggested	suggest	VERB
ijassa-1405	343	14	to	to	PART
ijassa-1405	343	15	run	run	VERB
ijassa-1405	343	16	the	the	DET
ijassa-1405	343	17	heuristic	heuristic	ADJ
ijassa-1405	343	18	algorithm	algorithm	NOUN
ijassa-1405	343	19	1	1	NUM
ijassa-1405	343	20	several	several	ADJ
ijassa-1405	343	21	times	time	NOUN
ijassa-1405	343	22	and	and	CCONJ
ijassa-1405	343	23	choose	choose	VERB
ijassa-1405	343	24	the	the	DET
ijassa-1405	343	25	graph	graph	NOUN
ijassa-1405	343	26	with	with	ADP
ijassa-1405	343	27	the	the	DET
ijassa-1405	343	28	least	least	ADJ
ijassa-1405	343	29	number	number	NOUN
ijassa-1405	343	30	of	of	ADP
ijassa-1405	343	31	removed	removed	ADJ
ijassa-1405	343	32	edges	edge	NOUN
ijassa-1405	343	33	.	.	PUNCT
ijassa-1405	344	1	in	in	ADP
ijassa-1405	344	2	this	this	DET
ijassa-1405	344	3	case	case	NOUN
ijassa-1405	344	4	δav(n	δav(n	NOUN
ijassa-1405	344	5	,	,	PUNCT
ijassa-1405	344	6	p	p	NOUN
ijassa-1405	344	7	)	)	PUNCT
ijassa-1405	344	8	can	can	AUX
ijassa-1405	344	9	be	be	AUX
ijassa-1405	344	10	used	use	VERB
ijassa-1405	344	11	as	as	ADP
ijassa-1405	344	12	an	an	DET
ijassa-1405	344	13	estimate	estimate	NOUN
ijassa-1405	344	14	for	for	ADP
ijassa-1405	344	15	the	the	DET
ijassa-1405	344	16	upper	upper	ADJ
ijassa-1405	344	17	bound	bind	VERB
ijassa-1405	344	18	for	for	ADP
ijassa-1405	344	19	the	the	DET
ijassa-1405	344	20	dissimilarity	dissimilarity	NOUN
ijassa-1405	344	21	,	,	PUNCT
ijassa-1405	344	22	while	while	SCONJ
ijassa-1405	344	23	δmax(n	δmax(n	NOUN
ijassa-1405	344	24	,	,	PUNCT
ijassa-1405	344	25	p	p	NOUN
ijassa-1405	344	26	)	)	PUNCT
ijassa-1405	344	27	is	be	AUX
ijassa-1405	344	28	more	more	ADV
ijassa-1405	344	29	appropriate	appropriate	ADJ
ijassa-1405	344	30	if	if	SCONJ
ijassa-1405	344	31	the	the	DET
ijassa-1405	344	32	algorithm	algorithm	NOUN
ijassa-1405	344	33	was	be	AUX
ijassa-1405	344	34	run	run	VERB
ijassa-1405	344	35	once	once	ADV
ijassa-1405	344	36	.	.	PUNCT
ijassa-1405	345	1	4	4	X
ijassa-1405	345	2	.	.	X
ijassa-1405	345	3	conclusion	conclusion	NOUN
ijassa-1405	345	4	in	in	ADP
ijassa-1405	345	5	this	this	DET
ijassa-1405	345	6	paper	paper	NOUN
ijassa-1405	345	7	,	,	PUNCT
ijassa-1405	345	8	a	a	DET
ijassa-1405	345	9	new	new	ADJ
ijassa-1405	345	10	pairwise	pairwise	NOUN
ijassa-1405	345	11	similarity	similarity	NOUN
ijassa-1405	345	12	method	method	NOUN
ijassa-1405	345	13	is	be	AUX
ijassa-1405	345	14	proposed	propose	VERB
ijassa-1405	345	15	for	for	ADP
ijassa-1405	345	16	measuring	measure	VERB
ijassa-1405	345	17	the	the	DET
ijassa-1405	345	18	quantitative	quantitative	ADJ
ijassa-1405	345	19	complexity	complexity	NOUN
ijassa-1405	345	20	of	of	ADP
ijassa-1405	345	21	np	np	NOUN
ijassa-1405	345	22	-	-	PUNCT
ijassa-1405	345	23	hard	hard	ADJ
ijassa-1405	345	24	problems	problem	NOUN
ijassa-1405	345	25	.	.	PUNCT
ijassa-1405	346	1	this	this	DET
ijassa-1405	346	2	method	method	NOUN
ijassa-1405	346	3	,	,	PUNCT
ijassa-1405	346	4	which	which	PRON
ijassa-1405	346	5	generalizes	generalize	VERB
ijassa-1405	346	6	the	the	DET
ijassa-1405	346	7	metric	metric	ADJ
ijassa-1405	346	8	approach	approach	NOUN
ijassa-1405	346	9	,	,	PUNCT
ijassa-1405	346	10	allows	allow	VERB
ijassa-1405	346	11	one	one	PRON
ijassa-1405	346	12	to	to	PART
ijassa-1405	346	13	compare	compare	VERB
ijassa-1405	346	14	problem	problem	NOUN
ijassa-1405	346	15	instances	instance	NOUN
ijassa-1405	346	16	of	of	ADP
ijassa-1405	346	17	different	different	ADJ
ijassa-1405	346	18	dimensions	dimension	NOUN
ijassa-1405	346	19	and	and	CCONJ
ijassa-1405	346	20	with	with	ADP
ijassa-1405	346	21	different	different	ADJ
ijassa-1405	346	22	constraint	constraint	NOUN
ijassa-1405	346	23	structures	structure	NOUN
ijassa-1405	346	24	.	.	PUNCT
ijassa-1405	347	1	this	this	PRON
ijassa-1405	347	2	,	,	PUNCT
ijassa-1405	347	3	in	in	ADP
ijassa-1405	347	4	turn	turn	NOUN
ijassa-1405	347	5	,	,	PUNCT
ijassa-1405	347	6	makes	make	VERB
ijassa-1405	347	7	it	it	PRON
ijassa-1405	347	8	possible	possible	ADJ
ijassa-1405	347	9	to	to	PART
ijassa-1405	347	10	use	use	VERB
ijassa-1405	347	11	algorithms	algorithm	NOUN
ijassa-1405	347	12	developed	develop	VERB
ijassa-1405	347	13	for	for	ADP
ijassa-1405	347	14	some	some	DET
ijassa-1405	347	15	special	special	ADJ
ijassa-1405	347	16	cases	case	NOUN
ijassa-1405	347	17	of	of	ADP
ijassa-1405	347	18	problems	problem	NOUN
ijassa-1405	347	19	as	as	ADP
ijassa-1405	347	20	heuristic	heuristic	ADJ
ijassa-1405	347	21	algorithms	algorithm	NOUN
ijassa-1405	347	22	for	for	ADP
ijassa-1405	347	23	a	a	DET
ijassa-1405	347	24	wider	wide	ADJ
ijassa-1405	347	25	class	class	NOUN
ijassa-1405	347	26	of	of	ADP
ijassa-1405	347	27	problems	problem	NOUN
ijassa-1405	347	28	.	.	PUNCT
ijassa-1405	348	1	using	use	VERB
ijassa-1405	348	2	the	the	DET
ijassa-1405	348	3	pairwise	pairwise	NOUN
ijassa-1405	348	4	dissimilarity	dissimilarity	NOUN
ijassa-1405	348	5	function	function	NOUN
ijassa-1405	348	6	,	,	PUNCT
ijassa-1405	348	7	one	one	PRON
ijassa-1405	348	8	can	can	AUX
ijassa-1405	348	9	estimate	estimate	VERB
ijassa-1405	348	10	the	the	DET
ijassa-1405	348	11	error	error	NOUN
ijassa-1405	348	12	of	of	ADP
ijassa-1405	348	13	the	the	DET
ijassa-1405	348	14	obtained	obtain	VERB
ijassa-1405	348	15	solutions	solution	NOUN
ijassa-1405	348	16	.	.	PUNCT
ijassa-1405	349	1	since	since	SCONJ
ijassa-1405	349	2	the	the	DET
ijassa-1405	349	3	pairwise	pairwise	NOUN
ijassa-1405	349	4	similarity	similarity	NOUN
ijassa-1405	349	5	method	method	NOUN
ijassa-1405	349	6	includes	include	VERB
ijassa-1405	349	7	two	two	NUM
ijassa-1405	349	8	non	non	ADJ
ijassa-1405	349	9	-	-	ADJ
ijassa-1405	349	10	trivial	trivial	ADJ
ijassa-1405	349	11	tasks	task	NOUN
ijassa-1405	349	12	,	,	PUNCT
ijassa-1405	349	13	namely	namely	ADV
ijassa-1405	349	14	,	,	PUNCT
ijassa-1405	349	15	searching	search	VERB
ijassa-1405	349	16	for	for	ADP
ijassa-1405	349	17	new	new	ADJ
ijassa-1405	349	18	special	special	ADJ
ijassa-1405	349	19	cases	case	NOUN
ijassa-1405	349	20	and	and	CCONJ
ijassa-1405	349	21	defining	define	VERB
ijassa-1405	349	22	the	the	DET
ijassa-1405	349	23	pairwise	pairwise	NOUN
ijassa-1405	349	24	dissimilarity	dissimilarity	NOUN
ijassa-1405	349	25	function	function	NOUN
ijassa-1405	349	26	,	,	PUNCT
ijassa-1405	349	27	the	the	DET
ijassa-1405	349	28	paper	paper	NOUN
ijassa-1405	349	29	provides	provide	VERB
ijassa-1405	349	30	recommendations	recommendation	NOUN
ijassa-1405	349	31	for	for	ADP
ijassa-1405	349	32	solving	solve	VERB
ijassa-1405	349	33	these	these	DET
ijassa-1405	349	34	problems	problem	NOUN
ijassa-1405	349	35	.	.	PUNCT
ijassa-1405	350	1	the	the	DET
ijassa-1405	350	2	proposed	propose	VERB
ijassa-1405	350	3	method	method	NOUN
ijassa-1405	350	4	is	be	AUX
ijassa-1405	350	5	illustrated	illustrate	VERB
ijassa-1405	350	6	for	for	ADP
ijassa-1405	350	7	two	two	NUM
ijassa-1405	350	8	optimization	optimization	NOUN
ijassa-1405	350	9	problems	problem	NOUN
ijassa-1405	350	10	.	.	PUNCT
ijassa-1405	351	1	for	for	ADP
ijassa-1405	351	2	the	the	DET
ijassa-1405	351	3	problem	problem	NOUN
ijassa-1405	351	4	of	of	ADP
ijassa-1405	351	5	finding	find	VERB
ijassa-1405	351	6	the	the	DET
ijassa-1405	351	7	strict	strict	ADJ
ijassa-1405	351	8	majority	majority	NOUN
ijassa-1405	351	9	domination	domination	NOUN
ijassa-1405	351	10	number	number	NOUN
ijassa-1405	351	11	of	of	ADP
ijassa-1405	351	12	a	a	DET
ijassa-1405	351	13	graph	graph	NOUN
ijassa-1405	351	14	with	with	ADP
ijassa-1405	351	15	cycles	cycle	NOUN
ijassa-1405	351	16	in	in	ADP
ijassa-1405	351	17	the	the	DET
ijassa-1405	351	18	framework	framework	NOUN
ijassa-1405	351	19	of	of	ADP
ijassa-1405	351	20	a	a	DET
ijassa-1405	351	21	two	two	NUM
ijassa-1405	351	22	-	-	PUNCT
ijassa-1405	351	23	level	level	NOUN
ijassa-1405	351	24	voting	voting	NOUN
ijassa-1405	351	25	model	model	NOUN
ijassa-1405	351	26	,	,	PUNCT
ijassa-1405	351	27	the	the	DET
ijassa-1405	351	28	pairwise	pairwise	NOUN
ijassa-1405	351	29	similarity	similarity	NOUN
ijassa-1405	351	30	method	method	NOUN
ijassa-1405	351	31	is	be	AUX
ijassa-1405	351	32	applied	apply	VERB
ijassa-1405	351	33	in	in	ADP
ijassa-1405	351	34	the	the	DET
ijassa-1405	351	35	case	case	NOUN
ijassa-1405	351	36	where	where	SCONJ
ijassa-1405	351	37	it	it	PRON
ijassa-1405	351	38	is	be	AUX
ijassa-1405	351	39	possible	possible	ADJ
ijassa-1405	351	40	to	to	PART
ijassa-1405	351	41	analytically	analytically	ADV
ijassa-1405	351	42	estimate	estimate	VERB
ijassa-1405	351	43	the	the	DET
ijassa-1405	351	44	absolute	absolute	ADJ
ijassa-1405	351	45	error	error	NOUN
ijassa-1405	351	46	as	as	SCONJ
ijassa-1405	351	47	specified	specify	VERB
ijassa-1405	351	48	in	in	ADP
ijassa-1405	351	49	section	section	NOUN
ijassa-1405	351	50	2	2	NUM
ijassa-1405	351	51	.	.	PUNCT
ijassa-1405	352	1	for	for	ADP
ijassa-1405	352	2	the	the	DET
ijassa-1405	352	3	maximum	maximum	ADJ
ijassa-1405	352	4	copyright	copyright	NOUN
ijassa-1405	352	5	©	©	PROPN
ijassa-1405	352	6	2023	2023	NUM
ijassa-1405	352	7	assa	assa	NOUN
ijassa-1405	352	8	.	.	PUNCT
ijassa-1405	353	1	adv	adv	PROPN
ijassa-1405	353	2	syst	syst	PROPN
ijassa-1405	353	3	sci	sci	PROPN
ijassa-1405	353	4	appl	appl	PROPN
ijassa-1405	353	5	(	(	PUNCT
ijassa-1405	353	6	2023	2023	NUM
ijassa-1405	353	7	)	)	PUNCT
ijassa-1405	353	8	176	176	NUM
ijassa-1405	353	9	d.	d.	PROPN
ijassa-1405	353	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	353	11	,	,	PUNCT
ijassa-1405	353	12	p.	p.	PROPN
ijassa-1405	353	13	chebotarev	chebotarev	PROPN
ijassa-1405	353	14	,	,	PUNCT
ijassa-1405	353	15	m.	m.	NOUN
ijassa-1405	353	16	goubko	goubko	NOUN
ijassa-1405	353	17	,	,	PUNCT
ijassa-1405	353	18	m.	m.	NOUN
ijassa-1405	353	19	somov	somov	PROPN
ijassa-1405	353	20	,	,	PUNCT
ijassa-1405	353	21	n.	n.	PROPN
ijassa-1405	353	22	shushko	shushko	PROPN
ijassa-1405	353	23	density	density	NOUN
ijassa-1405	353	24	0.2	0.2	NUM
ijassa-1405	353	25	0.4	0.4	NUM
ijassa-1405	353	26	0.6	0.6	NUM
ijassa-1405	353	27	0.8	0.8	NUM
ijassa-1405	353	28	num	num	NOUN
ijassa-1405	353	29	be	be	AUX
ijassa-1405	354	1	r	r	NOUN
ijassa-1405	354	2	o	o	X
ijassa-1405	354	3	f	f	X
ijassa-1405	354	4	v	v	NUM
ijassa-1405	354	5	ert	ert	NOUN
ijassa-1405	354	6	ixe	ixe	PROPN
ijassa-1405	354	7	s	s	PROPN
ijassa-1405	354	8	50	50	NUM
ijassa-1405	354	9	100	100	NUM
ijassa-1405	354	10	150	150	NUM
ijassa-1405	354	11	200	200	NUM
ijassa-1405	354	12	250	250	NUM
ijassa-1405	354	13	300	300	NUM
ijassa-1405	354	14	350	350	NUM
ijassa-1405	354	15	400	400	NUM
ijassa-1405	354	16	av	av	PROPN
ijassa-1405	354	17	er	er	INTJ
ijassa-1405	354	18	ag	ag	PROPN
ijassa-1405	354	19	e	e	PROPN
ijassa-1405	354	20	re	re	X
ijassa-1405	354	21	la	la	PROPN
ijassa-1405	354	22	tiv	tiv	PROPN
ijassa-1405	354	23	e	e	PROPN
ijassa-1405	354	24	er	er	INTJ
ijassa-1405	354	25	ro	ro	X
ijassa-1405	354	26	r	r	NOUN
ijassa-1405	354	27	0.04	0.04	NUM
ijassa-1405	354	28	0.06	0.06	NUM
ijassa-1405	354	29	0.08	0.08	NUM
ijassa-1405	354	30	0.10	0.10	NUM
ijassa-1405	354	31	0.12	0.12	NUM
ijassa-1405	354	32	0.14	0.14	NUM
ijassa-1405	354	33	fig	fig	NOUN
ijassa-1405	354	34	.	.	PUNCT
ijassa-1405	355	1	3.6	3.6	NUM
ijassa-1405	355	2	.	.	PUNCT
ijassa-1405	356	1	the	the	DET
ijassa-1405	356	2	dependence	dependence	NOUN
ijassa-1405	356	3	of	of	ADP
ijassa-1405	356	4	the	the	DET
ijassa-1405	356	5	relative	relative	ADJ
ijassa-1405	356	6	error	error	NOUN
ijassa-1405	356	7	of	of	ADP
ijassa-1405	356	8	the	the	DET
ijassa-1405	356	9	objective	objective	ADJ
ijassa-1405	356	10	function	function	NOUN
ijassa-1405	356	11	on	on	ADP
ijassa-1405	356	12	the	the	DET
ijassa-1405	356	13	density	density	NOUN
ijassa-1405	356	14	and	and	CCONJ
ijassa-1405	356	15	number	number	NOUN
ijassa-1405	356	16	of	of	ADP
ijassa-1405	356	17	vertices	vertex	NOUN
ijassa-1405	356	18	.	.	PUNCT
ijassa-1405	357	1	cut	cut	NOUN
ijassa-1405	357	2	problem	problem	NOUN
ijassa-1405	358	1	,	,	PUNCT
ijassa-1405	358	2	the	the	DET
ijassa-1405	358	3	pairwise	pairwise	NOUN
ijassa-1405	358	4	similarity	similarity	NOUN
ijassa-1405	358	5	method	method	NOUN
ijassa-1405	358	6	is	be	AUX
ijassa-1405	358	7	applied	apply	VERB
ijassa-1405	358	8	in	in	ADP
ijassa-1405	358	9	the	the	DET
ijassa-1405	358	10	case	case	NOUN
ijassa-1405	358	11	where	where	SCONJ
ijassa-1405	358	12	it	it	PRON
ijassa-1405	358	13	is	be	AUX
ijassa-1405	358	14	not	not	PART
ijassa-1405	358	15	possible	possible	ADJ
ijassa-1405	358	16	to	to	PART
ijassa-1405	358	17	estimate	estimate	VERB
ijassa-1405	358	18	the	the	DET
ijassa-1405	358	19	error	error	NOUN
ijassa-1405	358	20	analytically	analytically	ADV
ijassa-1405	358	21	and	and	CCONJ
ijassa-1405	358	22	the	the	DET
ijassa-1405	358	23	estimates	estimate	NOUN
ijassa-1405	358	24	are	be	AUX
ijassa-1405	358	25	based	base	VERB
ijassa-1405	358	26	on	on	ADP
ijassa-1405	358	27	numerical	numerical	ADJ
ijassa-1405	358	28	experiments	experiment	NOUN
ijassa-1405	358	29	.	.	PUNCT
ijassa-1405	359	1	in	in	ADP
ijassa-1405	359	2	the	the	DET
ijassa-1405	359	3	future	future	NOUN
ijassa-1405	359	4	,	,	PUNCT
ijassa-1405	359	5	it	it	PRON
ijassa-1405	359	6	is	be	AUX
ijassa-1405	359	7	planned	plan	VERB
ijassa-1405	359	8	to	to	PART
ijassa-1405	359	9	apply	apply	VERB
ijassa-1405	359	10	the	the	DET
ijassa-1405	359	11	pairwise	pairwise	NOUN
ijassa-1405	359	12	similarity	similarity	NOUN
ijassa-1405	359	13	method	method	NOUN
ijassa-1405	359	14	to	to	ADP
ijassa-1405	359	15	other	other	ADJ
ijassa-1405	359	16	well	well	ADV
ijassa-1405	359	17	-	-	PUNCT
ijassa-1405	359	18	known	know	VERB
ijassa-1405	359	19	optimization	optimization	NOUN
ijassa-1405	359	20	problems	problem	NOUN
ijassa-1405	359	21	on	on	ADP
ijassa-1405	359	22	graphs	graph	NOUN
ijassa-1405	359	23	and	and	CCONJ
ijassa-1405	359	24	to	to	PART
ijassa-1405	359	25	study	study	VERB
ijassa-1405	359	26	a	a	DET
ijassa-1405	359	27	number	number	NOUN
ijassa-1405	359	28	of	of	ADP
ijassa-1405	359	29	variations	variation	NOUN
ijassa-1405	359	30	of	of	ADP
ijassa-1405	359	31	similarity	similarity	NOUN
ijassa-1405	359	32	criteria	criterion	NOUN
ijassa-1405	359	33	.	.	PUNCT
ijassa-1405	360	1	it	it	PRON
ijassa-1405	360	2	is	be	AUX
ijassa-1405	360	3	also	also	ADV
ijassa-1405	360	4	planned	plan	VERB
ijassa-1405	360	5	to	to	PART
ijassa-1405	360	6	develop	develop	VERB
ijassa-1405	360	7	a	a	DET
ijassa-1405	360	8	system	system	NOUN
ijassa-1405	360	9	of	of	ADP
ijassa-1405	360	10	complexity	complexity	NOUN
ijassa-1405	360	11	maps	map	NOUN
ijassa-1405	360	12	for	for	ADP
ijassa-1405	360	13	the	the	DET
ijassa-1405	360	14	most	most	ADV
ijassa-1405	360	15	important	important	ADJ
ijassa-1405	360	16	similarity	similarity	NOUN
ijassa-1405	360	17	criteria	criterion	NOUN
ijassa-1405	360	18	.	.	PUNCT
ijassa-1405	361	1	acknowledgements	acknowledgement	VERB
ijassa-1405	361	2	the	the	DET
ijassa-1405	361	3	research	research	NOUN
ijassa-1405	361	4	was	be	AUX
ijassa-1405	361	5	supported	support	VERB
ijassa-1405	361	6	by	by	ADP
ijassa-1405	361	7	rsf	rsf	PROPN
ijassa-1405	361	8	(	(	PUNCT
ijassa-1405	361	9	project	project	NOUN
ijassa-1405	361	10	no	no	NOUN
ijassa-1405	361	11	.	.	NOUN
ijassa-1405	362	1	22	22	NUM
ijassa-1405	362	2	-	-	SYM
ijassa-1405	362	3	71	71	NUM
ijassa-1405	362	4	-	-	PUNCT
ijassa-1405	362	5	10131	10131	NUM
ijassa-1405	362	6	)	)	PUNCT
ijassa-1405	362	7	.	.	PUNCT
ijassa-1405	363	1	pavel	pavel	PROPN
ijassa-1405	363	2	chebotarev	chebotarev	PROPN
ijassa-1405	363	3	is	be	AUX
ijassa-1405	363	4	supported	support	VERB
ijassa-1405	363	5	by	by	ADP
ijassa-1405	363	6	the	the	DET
ijassa-1405	363	7	european	european	PROPN
ijassa-1405	363	8	union	union	PROPN
ijassa-1405	363	9	(	(	PUNCT
ijassa-1405	363	10	erc	erc	PROPN
ijassa-1405	363	11	,	,	PUNCT
ijassa-1405	363	12	generalization	generalization	NOUN
ijassa-1405	363	13	,	,	PUNCT
ijassa-1405	363	14	101039692	101039692	NUM
ijassa-1405	363	15	)	)	PUNCT
ijassa-1405	363	16	.	.	PUNCT
ijassa-1405	364	1	the	the	DET
ijassa-1405	364	2	results	result	NOUN
ijassa-1405	364	3	of	of	ADP
ijassa-1405	364	4	sections	section	NOUN
ijassa-1405	364	5	1	1	NUM
ijassa-1405	364	6	,	,	PUNCT
ijassa-1405	364	7	2	2	NUM
ijassa-1405	364	8	,	,	PUNCT
ijassa-1405	364	9	subsection	subsection	NOUN
ijassa-1405	364	10	3.2	3.2	NUM
ijassa-1405	364	11	and	and	CCONJ
ijassa-1405	364	12	theorem	theorem	VERB
ijassa-1405	364	13	3.1	3.1	NUM
ijassa-1405	364	14	were	be	AUX
ijassa-1405	364	15	obtained	obtain	VERB
ijassa-1405	364	16	within	within	ADP
ijassa-1405	364	17	the	the	DET
ijassa-1405	364	18	rsf	rsf	PROPN
ijassa-1405	364	19	grant	grant	NOUN
ijassa-1405	364	20	.	.	PUNCT
ijassa-1405	365	1	views	view	NOUN
ijassa-1405	365	2	and	and	CCONJ
ijassa-1405	365	3	opinions	opinion	NOUN
ijassa-1405	365	4	expressed	express	VERB
ijassa-1405	365	5	are	be	AUX
ijassa-1405	365	6	those	those	PRON
ijassa-1405	365	7	of	of	ADP
ijassa-1405	365	8	the	the	DET
ijassa-1405	365	9	authors	author	NOUN
ijassa-1405	365	10	only	only	ADV
ijassa-1405	365	11	and	and	CCONJ
ijassa-1405	365	12	do	do	AUX
ijassa-1405	365	13	not	not	PART
ijassa-1405	365	14	necessarily	necessarily	ADV
ijassa-1405	365	15	reflect	reflect	VERB
ijassa-1405	365	16	those	those	PRON
ijassa-1405	365	17	of	of	ADP
ijassa-1405	365	18	the	the	DET
ijassa-1405	365	19	european	european	PROPN
ijassa-1405	365	20	union	union	PROPN
ijassa-1405	365	21	or	or	CCONJ
ijassa-1405	365	22	the	the	DET
ijassa-1405	365	23	european	european	PROPN
ijassa-1405	365	24	research	research	PROPN
ijassa-1405	365	25	council	council	PROPN
ijassa-1405	365	26	executive	executive	PROPN
ijassa-1405	365	27	agency	agency	NOUN
ijassa-1405	365	28	.	.	PUNCT
ijassa-1405	366	1	neither	neither	CCONJ
ijassa-1405	366	2	the	the	DET
ijassa-1405	366	3	european	european	PROPN
ijassa-1405	366	4	union	union	PROPN
ijassa-1405	366	5	nor	nor	CCONJ
ijassa-1405	366	6	the	the	DET
ijassa-1405	366	7	granting	grant	VERB
ijassa-1405	366	8	authority	authority	NOUN
ijassa-1405	366	9	can	can	AUX
ijassa-1405	366	10	be	be	AUX
ijassa-1405	366	11	held	hold	VERB
ijassa-1405	366	12	responsible	responsible	ADJ
ijassa-1405	366	13	for	for	ADP
ijassa-1405	366	14	them	they	PRON
ijassa-1405	366	15	.	.	PUNCT
ijassa-1405	367	1	references	reference	NOUN
ijassa-1405	367	2	[	[	X
ijassa-1405	367	3	1	1	NUM
ijassa-1405	367	4	]	]	PUNCT
ijassa-1405	367	5	i.	i.	PROPN
ijassa-1405	367	6	broere	broere	PROPN
ijassa-1405	367	7	,	,	PUNCT
ijassa-1405	367	8	j.	j.	PROPN
ijassa-1405	367	9	h.	h.	PROPN
ijassa-1405	367	10	hattingh	hattingh	PROPN
ijassa-1405	367	11	,	,	PUNCT
ijassa-1405	367	12	m.	m.	NOUN
ijassa-1405	367	13	a.	a.	PROPN
ijassa-1405	367	14	henning	henning	PROPN
ijassa-1405	367	15	,	,	PUNCT
ijassa-1405	367	16	and	and	CCONJ
ijassa-1405	367	17	a.	a.	NOUN
ijassa-1405	367	18	a.	a.	PROPN
ijassa-1405	367	19	mcrae	mcrae	PROPN
ijassa-1405	367	20	.	.	PUNCT
ijassa-1405	368	1	majority	majority	NOUN
ijassa-1405	368	2	domination	domination	NOUN
ijassa-1405	368	3	in	in	ADP
ijassa-1405	368	4	graphs	graph	NOUN
ijassa-1405	368	5	.	.	PUNCT
ijassa-1405	369	1	discrete	discrete	ADJ
ijassa-1405	369	2	mathematics	mathematic	NOUN
ijassa-1405	369	3	,	,	PUNCT
ijassa-1405	369	4	138(1–3):125–135	138(1–3):125–135	NUM
ijassa-1405	369	5	,	,	PUNCT
ijassa-1405	369	6	1995	1995	NUM
ijassa-1405	369	7	.	.	PUNCT
ijassa-1405	370	1	copyright	copyright	NOUN
ijassa-1405	370	2	©	©	PROPN
ijassa-1405	370	3	2023	2023	NUM
ijassa-1405	370	4	assa	assa	NOUN
ijassa-1405	370	5	.	.	PUNCT
ijassa-1405	371	1	adv	adv	PROPN
ijassa-1405	371	2	syst	syst	PROPN
ijassa-1405	371	3	sci	sci	PROPN
ijassa-1405	371	4	appl	appl	PROPN
ijassa-1405	371	5	(	(	PUNCT
ijassa-1405	371	6	2023	2023	NUM
ijassa-1405	371	7	)	)	PUNCT
ijassa-1405	371	8	pairwise	pairwise	NOUN
ijassa-1405	371	9	similarity	similarity	NOUN
ijassa-1405	371	10	estimation	estimation	NOUN
ijassa-1405	371	11	for	for	ADP
ijassa-1405	371	12	discrete	discrete	ADJ
ijassa-1405	371	13	optimization	optimization	NOUN
ijassa-1405	371	14	problems	problem	NOUN
ijassa-1405	371	15	177	177	NUM
ijassa-1405	371	16	0.1	0.1	NUM
ijassa-1405	371	17	0.2	0.2	NUM
ijassa-1405	371	18	0.3	0.3	NUM
ijassa-1405	371	19	0.4	0.4	NUM
ijassa-1405	371	20	0.5	0.5	NUM
ijassa-1405	371	21	0.6	0.6	NUM
ijassa-1405	371	22	0.7	0.7	NUM
ijassa-1405	371	23	0.8	0.8	NUM
ijassa-1405	371	24	0.9	0.9	NUM
ijassa-1405	371	25	p	p	NOUN
ijassa-1405	371	26	0.04	0.04	NUM
ijassa-1405	371	27	0.06	0.06	NUM
ijassa-1405	371	28	0.08	0.08	NUM
ijassa-1405	371	29	0.10	0.10	NUM
ijassa-1405	371	30	0.12	0.12	NUM
ijassa-1405	371	31	0.14	0.14	NUM
ijassa-1405	371	32	m	m	NOUN
ijassa-1405	371	33	ax	ax	NOUN
ijassa-1405	371	34	i	i	PRON
ijassa-1405	371	35	m	m	VERB
ijassa-1405	371	36	um	um	INTJ
ijassa-1405	371	37	re	re	X
ijassa-1405	371	38	la	la	X
ijassa-1405	371	39	tiv	tiv	PROPN
ijassa-1405	371	40	e	e	PROPN
ijassa-1405	371	41	er	er	INTJ
ijassa-1405	371	42	ro	ro	INTJ
ijassa-1405	371	43	r	r	NOUN
ijassa-1405	371	44	n	n	NOUN
ijassa-1405	371	45	=	=	SYM
ijassa-1405	371	46	150	150	NUM
ijassa-1405	371	47	fig	fig	NOUN
ijassa-1405	371	48	.	.	PUNCT
ijassa-1405	372	1	3.7	3.7	NUM
ijassa-1405	372	2	.	.	PUNCT
ijassa-1405	373	1	the	the	DET
ijassa-1405	373	2	dependence	dependence	NOUN
ijassa-1405	373	3	of	of	ADP
ijassa-1405	373	4	the	the	DET
ijassa-1405	373	5	maximum	maximum	ADJ
ijassa-1405	373	6	relative	relative	ADJ
ijassa-1405	373	7	error	error	NOUN
ijassa-1405	373	8	of	of	ADP
ijassa-1405	373	9	the	the	DET
ijassa-1405	373	10	objective	objective	ADJ
ijassa-1405	373	11	function	function	NOUN
ijassa-1405	373	12	on	on	ADP
ijassa-1405	373	13	the	the	DET
ijassa-1405	373	14	density	density	NOUN
ijassa-1405	373	15	.	.	PUNCT
ijassa-1405	374	1	[	[	X
ijassa-1405	374	2	2	2	X
ijassa-1405	374	3	]	]	X
ijassa-1405	374	4	e.	e.	PROPN
ijassa-1405	374	5	bukueva	bukueva	PROPN
ijassa-1405	374	6	,	,	PUNCT
ijassa-1405	374	7	i.	i.	PROPN
ijassa-1405	374	8	kudinov	kudinov	PROPN
ijassa-1405	374	9	,	,	PUNCT
ijassa-1405	374	10	and	and	CCONJ
ijassa-1405	374	11	d.	d.	PROPN
ijassa-1405	374	12	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	374	13	.	.	PUNCT
ijassa-1405	375	1	analysis	analysis	NOUN
ijassa-1405	375	2	of	of	ADP
ijassa-1405	375	3	the	the	DET
ijassa-1405	375	4	feasibility	feasibility	NOUN
ijassa-1405	375	5	to	to	PART
ijassa-1405	375	6	use	use	VERB
ijassa-1405	375	7	metric	metric	ADJ
ijassa-1405	375	8	approach	approach	NOUN
ijassa-1405	375	9	for	for	ADP
ijassa-1405	375	10	np	np	NOUN
ijassa-1405	375	11	-	-	PUNCT
ijassa-1405	375	12	hard	hard	ADJ
ijassa-1405	375	13	makespan	makespan	PROPN
ijassa-1405	375	14	minimization	minimization	NOUN
ijassa-1405	375	15	problem	problem	NOUN
ijassa-1405	375	16	.	.	PUNCT
ijassa-1405	376	1	ifac	ifac	NOUN
ijassa-1405	376	2	-	-	PUNCT
ijassa-1405	376	3	papersonline	papersonline	NOUN
ijassa-1405	376	4	,	,	PUNCT
ijassa-1405	376	5	55(10):2898–2901	55(10):2898–2901	NUM
ijassa-1405	376	6	,	,	PUNCT
ijassa-1405	376	7	2022	2022	NUM
ijassa-1405	376	8	.	.	PUNCT
ijassa-1405	377	1	[	[	X
ijassa-1405	377	2	3	3	X
ijassa-1405	377	3	]	]	X
ijassa-1405	377	4	p.	p.	NOUN
ijassa-1405	377	5	chebotarev	chebotarev	PROPN
ijassa-1405	377	6	and	and	CCONJ
ijassa-1405	377	7	d.	d.	PROPN
ijassa-1405	377	8	peleg	peleg	PROPN
ijassa-1405	377	9	.	.	PUNCT
ijassa-1405	378	1	the	the	DET
ijassa-1405	378	2	power	power	NOUN
ijassa-1405	378	3	of	of	ADP
ijassa-1405	378	4	small	small	ADJ
ijassa-1405	378	5	coalitions	coalition	NOUN
ijassa-1405	378	6	under	under	ADP
ijassa-1405	378	7	two	two	NUM
ijassa-1405	378	8	-	-	PUNCT
ijassa-1405	378	9	tier	tier	NOUN
ijassa-1405	378	10	majority	majority	NOUN
ijassa-1405	378	11	on	on	ADP
ijassa-1405	378	12	regular	regular	ADJ
ijassa-1405	378	13	graphs	graph	NOUN
ijassa-1405	378	14	.	.	PUNCT
ijassa-1405	379	1	preprint	preprint	NOUN
ijassa-1405	380	1	[	[	X
ijassa-1405	380	2	math.oc	math.oc	X
ijassa-1405	380	3	]	]	X
ijassa-1405	380	4	2212.03394	2212.03394	NUM
ijassa-1405	380	5	,	,	PUNCT
ijassa-1405	380	6	arxiv	arxiv	NOUN
ijassa-1405	380	7	,	,	PUNCT
ijassa-1405	380	8	2022	2022	NUM
ijassa-1405	380	9	.	.	PUNCT
ijassa-1405	381	1	https://doi.org/10.48550/arxiv.2212.03394	https://doi.org/10.48550/arxiv.2212.03394	X
ijassa-1405	381	2	.	.	PUNCT
ijassa-1405	382	1	[	[	X
ijassa-1405	382	2	4	4	X
ijassa-1405	382	3	]	]	PUNCT
ijassa-1405	382	4	t.	t.	PROPN
ijassa-1405	382	5	e.	e.	PROPN
ijassa-1405	382	6	cheng	cheng	PROPN
ijassa-1405	382	7	,	,	PUNCT
ijassa-1405	382	8	a.	a.	PROPN
ijassa-1405	382	9	lazarev	lazarev	PROPN
ijassa-1405	382	10	,	,	PUNCT
ijassa-1405	382	11	and	and	CCONJ
ijassa-1405	382	12	d.	d.	PROPN
ijassa-1405	382	13	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	382	14	.	.	PUNCT
ijassa-1405	383	1	a	a	DET
ijassa-1405	383	2	metric	metric	ADJ
ijassa-1405	383	3	approach	approach	NOUN
ijassa-1405	383	4	for	for	ADP
ijassa-1405	383	5	the	the	DET
ijassa-1405	383	6	two	two	NUM
ijassa-1405	383	7	-	-	PUNCT
ijassa-1405	383	8	station	station	NOUN
ijassa-1405	383	9	single	single	ADJ
ijassa-1405	383	10	-	-	PUNCT
ijassa-1405	383	11	track	track	NOUN
ijassa-1405	383	12	railway	railway	NOUN
ijassa-1405	383	13	scheduling	scheduling	NOUN
ijassa-1405	383	14	problem	problem	NOUN
ijassa-1405	383	15	.	.	PUNCT
ijassa-1405	384	1	ifac	ifac	NOUN
ijassa-1405	384	2	-	-	PUNCT
ijassa-1405	384	3	papersonline	papersonline	NOUN
ijassa-1405	384	4	,	,	PUNCT
ijassa-1405	384	5	55(10):2875–2880	55(10):2875–2880	NUM
ijassa-1405	384	6	,	,	PUNCT
ijassa-1405	384	7	2022	2022	NUM
ijassa-1405	384	8	.	.	PUNCT
ijassa-1405	385	1	[	[	X
ijassa-1405	385	2	5	5	NUM
ijassa-1405	385	3	]	]	PUNCT
ijassa-1405	385	4	r.	r.	PROPN
ijassa-1405	385	5	m.	m.	PROPN
ijassa-1405	385	6	karp	karp	PROPN
ijassa-1405	385	7	.	.	PUNCT
ijassa-1405	386	1	reducibility	reducibility	PROPN
ijassa-1405	386	2	among	among	ADP
ijassa-1405	386	3	combinatorial	combinatorial	ADJ
ijassa-1405	386	4	problems	problem	NOUN
ijassa-1405	386	5	.	.	PUNCT
ijassa-1405	387	1	springer	springer	NOUN
ijassa-1405	387	2	,	,	PUNCT
ijassa-1405	387	3	2010	2010	NUM
ijassa-1405	387	4	.	.	PUNCT
ijassa-1405	388	1	[	[	X
ijassa-1405	388	2	6	6	NUM
ijassa-1405	388	3	]	]	PUNCT
ijassa-1405	388	4	a.	a.	NOUN
ijassa-1405	388	5	lazarev	lazarev	PROPN
ijassa-1405	388	6	,	,	PUNCT
ijassa-1405	388	7	d.	d.	PROPN
ijassa-1405	388	8	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	388	9	,	,	PUNCT
ijassa-1405	388	10	n.	n.	NOUN
ijassa-1405	388	11	pravdivets	pravdivet	NOUN
ijassa-1405	388	12	,	,	PUNCT
ijassa-1405	388	13	and	and	CCONJ
ijassa-1405	388	14	f.	f.	PROPN
ijassa-1405	388	15	werner	werner	PROPN
ijassa-1405	388	16	.	.	PUNCT
ijassa-1405	389	1	polynomially	polynomially	ADV
ijassa-1405	389	2	solvable	solvable	ADJ
ijassa-1405	389	3	subcases	subcase	NOUN
ijassa-1405	389	4	for	for	ADP
ijassa-1405	389	5	the	the	DET
ijassa-1405	389	6	approximate	approximate	ADJ
ijassa-1405	389	7	solution	solution	NOUN
ijassa-1405	389	8	of	of	ADP
ijassa-1405	389	9	multi	multi	ADJ
ijassa-1405	389	10	-	-	ADJ
ijassa-1405	389	11	machine	machine	ADJ
ijassa-1405	389	12	scheduling	scheduling	NOUN
ijassa-1405	389	13	problems	problem	NOUN
ijassa-1405	389	14	.	.	PUNCT
ijassa-1405	390	1	in	in	ADP
ijassa-1405	390	2	advances	advance	NOUN
ijassa-1405	390	3	in	in	ADP
ijassa-1405	390	4	optimization	optimization	NOUN
ijassa-1405	390	5	and	and	CCONJ
ijassa-1405	390	6	applications	application	NOUN
ijassa-1405	390	7	:	:	PUNCT
ijassa-1405	390	8	11th	11th	ADJ
ijassa-1405	390	9	international	international	ADJ
ijassa-1405	390	10	conference	conference	NOUN
ijassa-1405	390	11	,	,	PUNCT
ijassa-1405	390	12	optima	optima	PROPN
ijassa-1405	390	13	2020	2020	NUM
ijassa-1405	390	14	,	,	PUNCT
ijassa-1405	390	15	moscow	moscow	PROPN
ijassa-1405	390	16	,	,	PUNCT
ijassa-1405	390	17	russia	russia	PROPN
ijassa-1405	390	18	,	,	PUNCT
ijassa-1405	390	19	september	september	PROPN
ijassa-1405	390	20	28	28	NUM
ijassa-1405	390	21	–	–	PUNCT
ijassa-1405	390	22	october	october	PROPN
ijassa-1405	390	23	2	2	NUM
ijassa-1405	390	24	,	,	PUNCT
ijassa-1405	390	25	2020	2020	NUM
ijassa-1405	390	26	,	,	PUNCT
ijassa-1405	390	27	revised	revise	VERB
ijassa-1405	390	28	selected	select	VERB
ijassa-1405	390	29	papers	paper	NOUN
ijassa-1405	390	30	11	11	NUM
ijassa-1405	390	31	,	,	PUNCT
ijassa-1405	390	32	pages	page	NOUN
ijassa-1405	390	33	211–223	211–223	NUM
ijassa-1405	390	34	.	.	PUNCT
ijassa-1405	390	35	springer	springer	NOUN
ijassa-1405	390	36	,	,	PUNCT
ijassa-1405	390	37	2020	2020	NUM
ijassa-1405	390	38	.	.	PUNCT
ijassa-1405	391	1	[	[	X
ijassa-1405	391	2	7	7	NUM
ijassa-1405	391	3	]	]	PUNCT
ijassa-1405	391	4	a.	a.	NOUN
ijassa-1405	391	5	a.	a.	NOUN
ijassa-1405	391	6	lazarev	lazarev	PROPN
ijassa-1405	391	7	,	,	PUNCT
ijassa-1405	391	8	d.	d.	PROPN
ijassa-1405	391	9	v.	v.	PROPN
ijassa-1405	391	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	391	11	,	,	PUNCT
ijassa-1405	391	12	and	and	CCONJ
ijassa-1405	391	13	n.	n.	PROPN
ijassa-1405	391	14	a.	a.	NOUN
ijassa-1405	391	15	pravdivets	pravdivet	NOUN
ijassa-1405	391	16	.	.	PUNCT
ijassa-1405	392	1	metric	metric	ADJ
ijassa-1405	392	2	approach	approach	NOUN
ijassa-1405	392	3	for	for	ADP
ijassa-1405	392	4	finding	find	VERB
ijassa-1405	392	5	approximate	approximate	ADJ
ijassa-1405	392	6	solutions	solution	NOUN
ijassa-1405	392	7	of	of	ADP
ijassa-1405	392	8	scheduling	scheduling	NOUN
ijassa-1405	392	9	problems	problem	NOUN
ijassa-1405	392	10	.	.	PUNCT
ijassa-1405	393	1	computational	computational	ADJ
ijassa-1405	393	2	mathematics	mathematic	NOUN
ijassa-1405	393	3	and	and	CCONJ
ijassa-1405	393	4	mathematical	mathematical	ADJ
ijassa-1405	393	5	physics	physics	NOUN
ijassa-1405	393	6	,	,	PUNCT
ijassa-1405	393	7	61:1169–1180	61:1169–1180	PROPN
ijassa-1405	393	8	,	,	PUNCT
ijassa-1405	393	9	2021	2021	NUM
ijassa-1405	393	10	.	.	PUNCT
ijassa-1405	394	1	[	[	X
ijassa-1405	394	2	8	8	NUM
ijassa-1405	394	3	]	]	PUNCT
ijassa-1405	394	4	a.	a.	NOUN
ijassa-1405	394	5	a.	a.	NOUN
ijassa-1405	394	6	lazarev	lazarev	PROPN
ijassa-1405	394	7	,	,	PUNCT
ijassa-1405	394	8	d.	d.	PROPN
ijassa-1405	394	9	v.	v.	PROPN
ijassa-1405	394	10	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	394	11	,	,	PUNCT
ijassa-1405	394	12	and	and	CCONJ
ijassa-1405	394	13	f.	f.	PROPN
ijassa-1405	394	14	werner	werner	PROPN
ijassa-1405	394	15	.	.	PUNCT
ijassa-1405	395	1	a	a	DET
ijassa-1405	395	2	metric	metric	ADJ
ijassa-1405	395	3	approach	approach	NOUN
ijassa-1405	395	4	for	for	ADP
ijassa-1405	395	5	scheduling	scheduling	NOUN
ijassa-1405	395	6	problems	problem	NOUN
ijassa-1405	395	7	with	with	ADP
ijassa-1405	395	8	minimizing	minimize	VERB
ijassa-1405	395	9	the	the	DET
ijassa-1405	395	10	maximum	maximum	ADJ
ijassa-1405	395	11	penalty	penalty	NOUN
ijassa-1405	395	12	.	.	PUNCT
ijassa-1405	396	1	applied	apply	VERB
ijassa-1405	396	2	mathematical	mathematical	ADJ
ijassa-1405	396	3	modelling	modelling	NOUN
ijassa-1405	396	4	,	,	PUNCT
ijassa-1405	396	5	89:1163–1176	89:1163–1176	NOUN
ijassa-1405	396	6	,	,	PUNCT
ijassa-1405	396	7	2021	2021	NUM
ijassa-1405	396	8	.	.	PUNCT
ijassa-1405	397	1	[	[	X
ijassa-1405	397	2	9	9	NUM
ijassa-1405	397	3	]	]	PUNCT
ijassa-1405	397	4	h.-g	h.-g	PROPN
ijassa-1405	397	5	.	.	PUNCT
ijassa-1405	398	1	yeh	yeh	PROPN
ijassa-1405	398	2	and	and	CCONJ
ijassa-1405	398	3	g.	g.	PROPN
ijassa-1405	398	4	j.	j.	PROPN
ijassa-1405	398	5	chang	chang	PROPN
ijassa-1405	398	6	.	.	PUNCT
ijassa-1405	399	1	algorithmic	algorithmic	ADJ
ijassa-1405	399	2	aspects	aspect	NOUN
ijassa-1405	399	3	of	of	ADP
ijassa-1405	399	4	majority	majority	NOUN
ijassa-1405	399	5	domination	domination	NOUN
ijassa-1405	399	6	.	.	PUNCT
ijassa-1405	400	1	taiwanese	taiwanese	ADJ
ijassa-1405	400	2	journal	journal	NOUN
ijassa-1405	400	3	of	of	ADP
ijassa-1405	400	4	mathematics	mathematic	NOUN
ijassa-1405	400	5	,	,	PUNCT
ijassa-1405	400	6	pages	page	NOUN
ijassa-1405	400	7	343–350	343–350	NUM
ijassa-1405	400	8	,	,	PUNCT
ijassa-1405	400	9	1997	1997	NUM
ijassa-1405	400	10	.	.	PUNCT
ijassa-1405	401	1	copyright	copyright	NOUN
ijassa-1405	401	2	©	©	PROPN
ijassa-1405	401	3	2023	2023	NUM
ijassa-1405	401	4	assa	assa	NOUN
ijassa-1405	401	5	.	.	PUNCT
ijassa-1405	402	1	adv	adv	PROPN
ijassa-1405	402	2	syst	syst	PROPN
ijassa-1405	402	3	sci	sci	PROPN
ijassa-1405	402	4	appl	appl	PROPN
ijassa-1405	402	5	(	(	PUNCT
ijassa-1405	402	6	2023	2023	NUM
ijassa-1405	402	7	)	)	PUNCT
ijassa-1405	402	8	https://doi.org/10.48550/arxiv.2212.03394	https://doi.org/10.48550/arxiv.2212.03394	PROPN
ijassa-1405	402	9	178	178	NUM
ijassa-1405	402	10	d.	d.	PROPN
ijassa-1405	402	11	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1405	402	12	,	,	PUNCT
ijassa-1405	402	13	p.	p.	PROPN
ijassa-1405	402	14	chebotarev	chebotarev	PROPN
ijassa-1405	402	15	,	,	PUNCT
ijassa-1405	402	16	m.	m.	NOUN
ijassa-1405	402	17	goubko	goubko	NOUN
ijassa-1405	402	18	,	,	PUNCT
ijassa-1405	402	19	m.	m.	NOUN
ijassa-1405	402	20	somov	somov	PROPN
ijassa-1405	402	21	,	,	PUNCT
ijassa-1405	402	22	n.	n.	PROPN
ijassa-1405	402	23	shushko	shushko	VERB
ijassa-1405	402	24	50	50	NUM
ijassa-1405	402	25	100	100	NUM
ijassa-1405	402	26	150	150	NUM
ijassa-1405	402	27	200	200	NUM
ijassa-1405	402	28	250	250	NUM
ijassa-1405	402	29	300	300	NUM
ijassa-1405	402	30	350	350	NUM
ijassa-1405	402	31	400	400	NUM
ijassa-1405	402	32	n	n	ADV
ijassa-1405	402	33	0.055	0.055	NUM
ijassa-1405	402	34	0.060	0.060	NUM
ijassa-1405	402	35	0.065	0.065	NUM
ijassa-1405	402	36	0.070	0.070	NUM
ijassa-1405	402	37	0.075	0.075	NUM
ijassa-1405	402	38	0.080	0.080	NUM
ijassa-1405	402	39	0.085	0.085	NUM
ijassa-1405	402	40	0.090	0.090	NUM
ijassa-1405	402	41	m	m	NOUN
ijassa-1405	402	42	ax	ax	NOUN
ijassa-1405	403	1	i	i	PRON
ijassa-1405	403	2	m	m	VERB
ijassa-1405	403	3	um	um	INTJ
ijassa-1405	403	4	re	re	X
ijassa-1405	403	5	la	la	X
ijassa-1405	403	6	tiv	tiv	PROPN
ijassa-1405	403	7	e	e	PROPN
ijassa-1405	403	8	er	er	INTJ
ijassa-1405	403	9	ro	ro	INTJ
ijassa-1405	403	10	r	r	NOUN
ijassa-1405	403	11	p	p	NOUN
ijassa-1405	403	12	=	=	SYM
ijassa-1405	403	13	0.6	0.6	NUM
ijassa-1405	403	14	fig	fig	NOUN
ijassa-1405	403	15	.	.	PUNCT
ijassa-1405	404	1	3.8	3.8	NUM
ijassa-1405	404	2	.	.	PUNCT
ijassa-1405	405	1	the	the	DET
ijassa-1405	405	2	dependence	dependence	NOUN
ijassa-1405	405	3	of	of	ADP
ijassa-1405	405	4	the	the	DET
ijassa-1405	405	5	maximum	maximum	ADJ
ijassa-1405	405	6	relative	relative	ADJ
ijassa-1405	405	7	error	error	NOUN
ijassa-1405	405	8	of	of	ADP
ijassa-1405	405	9	the	the	DET
ijassa-1405	405	10	objective	objective	ADJ
ijassa-1405	405	11	function	function	NOUN
ijassa-1405	405	12	on	on	ADP
ijassa-1405	405	13	the	the	DET
ijassa-1405	405	14	number	number	NOUN
ijassa-1405	405	15	of	of	ADP
ijassa-1405	405	16	vertices	vertex	NOUN
ijassa-1405	405	17	.	.	PUNCT
ijassa-1405	406	1	copyright	copyright	NOUN
ijassa-1405	406	2	©	©	PROPN
ijassa-1405	406	3	2023	2023	NUM
ijassa-1405	406	4	assa	assa	NOUN
ijassa-1405	406	5	.	.	PUNCT
ijassa-1405	407	1	adv	adv	PROPN
ijassa-1405	407	2	syst	syst	PROPN
ijassa-1405	407	3	sci	sci	PROPN
ijassa-1405	407	4	appl	appl	PROPN
ijassa-1405	407	5	(	(	PUNCT
ijassa-1405	407	6	2023	2023	NUM
ijassa-1405	407	7	)	)	PUNCT
ijassa-1405	407	8	pairwise	pairwise	NOUN
ijassa-1405	407	9	similarity	similarity	NOUN
ijassa-1405	407	10	estimation	estimation	NOUN
ijassa-1405	407	11	for	for	ADP
ijassa-1405	407	12	discrete	discrete	ADJ
ijassa-1405	407	13	optimization	optimization	NOUN
ijassa-1405	407	14	problems	problem	NOUN
ijassa-1405	407	15	179	179	NUM
ijassa-1405	407	16	density	density	NOUN
ijassa-1405	407	17	0.2	0.2	NUM
ijassa-1405	407	18	0.4	0.4	NUM
ijassa-1405	407	19	0.6	0.6	NUM
ijassa-1405	407	20	0.8	0.8	NUM
ijassa-1405	407	21	num	num	NOUN
ijassa-1405	407	22	be	be	AUX
ijassa-1405	407	23	r	r	NOUN
ijassa-1405	407	24	o	o	X
ijassa-1405	407	25	f	f	X
ijassa-1405	407	26	v	v	NUM
ijassa-1405	407	27	ert	ert	NOUN
ijassa-1405	407	28	ixe	ixe	PROPN
ijassa-1405	407	29	s	s	PROPN
ijassa-1405	407	30	50	50	NUM
ijassa-1405	407	31	100	100	NUM
ijassa-1405	407	32	150	150	NUM
ijassa-1405	407	33	200	200	NUM
ijassa-1405	407	34	250	250	NUM
ijassa-1405	407	35	300	300	NUM
ijassa-1405	407	36	350	350	NUM
ijassa-1405	407	37	400	400	NUM
ijassa-1405	407	38	m	m	NOUN
ijassa-1405	407	39	ax	ax	NOUN
ijassa-1405	408	1	i	i	PRON
ijassa-1405	408	2	m	m	VERB
ijassa-1405	408	3	um	um	INTJ
ijassa-1405	408	4	re	re	X
ijassa-1405	408	5	la	la	X
ijassa-1405	408	6	tiv	tiv	PROPN
ijassa-1405	408	7	e	e	PROPN
ijassa-1405	408	8	er	er	INTJ
ijassa-1405	408	9	ro	ro	X
ijassa-1405	408	10	r	r	NOUN
ijassa-1405	408	11	0.04	0.04	NUM
ijassa-1405	408	12	0.06	0.06	NUM
ijassa-1405	408	13	0.08	0.08	NUM
ijassa-1405	408	14	0.10	0.10	NUM
ijassa-1405	408	15	0.12	0.12	NUM
ijassa-1405	408	16	0.14	0.14	NUM
ijassa-1405	408	17	0.16	0.16	NUM
ijassa-1405	408	18	fig	fig	NOUN
ijassa-1405	408	19	.	.	PUNCT
ijassa-1405	409	1	3.9	3.9	NUM
ijassa-1405	409	2	.	.	PUNCT
ijassa-1405	410	1	the	the	DET
ijassa-1405	410	2	dependence	dependence	NOUN
ijassa-1405	410	3	of	of	ADP
ijassa-1405	410	4	the	the	DET
ijassa-1405	410	5	maximum	maximum	ADJ
ijassa-1405	410	6	relative	relative	ADJ
ijassa-1405	410	7	error	error	NOUN
ijassa-1405	410	8	of	of	ADP
ijassa-1405	410	9	the	the	DET
ijassa-1405	410	10	objective	objective	ADJ
ijassa-1405	410	11	function	function	NOUN
ijassa-1405	410	12	on	on	ADP
ijassa-1405	410	13	the	the	DET
ijassa-1405	410	14	density	density	NOUN
ijassa-1405	410	15	and	and	CCONJ
ijassa-1405	410	16	number	number	NOUN
ijassa-1405	410	17	of	of	ADP
ijassa-1405	410	18	vertices	vertex	NOUN
ijassa-1405	410	19	.	.	PUNCT
ijassa-1405	411	1	copyright	copyright	NOUN
ijassa-1405	411	2	©	©	PROPN
ijassa-1405	411	3	2023	2023	NUM
ijassa-1405	411	4	assa	assa	NOUN
ijassa-1405	411	5	.	.	PUNCT
ijassa-1405	412	1	adv	adv	PROPN
ijassa-1405	412	2	syst	syst	PROPN
ijassa-1405	412	3	sci	sci	PROPN
ijassa-1405	412	4	appl	appl	PROPN
ijassa-1405	412	5	(	(	PUNCT
ijassa-1405	412	6	2023	2023	NUM
ijassa-1405	412	7	)	)	PUNCT
ijassa-1405	412	8	introduction	introduction	NOUN
ijassa-1405	412	9	pairwise	pairwise	NOUN
ijassa-1405	412	10	similarity	similarity	NOUN
ijassa-1405	412	11	method	method	NOUN
ijassa-1405	412	12	applications	application	NOUN
ijassa-1405	412	13	of	of	ADP
ijassa-1405	412	14	the	the	DET
ijassa-1405	412	15	pairwise	pairwise	NOUN
ijassa-1405	412	16	similarity	similarity	NOUN
ijassa-1405	412	17	method	method	NOUN
ijassa-1405	412	18	majority	majority	NOUN
ijassa-1405	412	19	domination	domination	NOUN
ijassa-1405	412	20	problem	problem	NOUN
ijassa-1405	412	21	maximum	maximum	PROPN
ijassa-1405	412	22	cut	cut	NOUN
ijassa-1405	412	23	problem	problem	NOUN
ijassa-1405	412	24	conclusion	conclusion	NOUN