id	sid	tid	token	lemma	pos
bracis-28347	1	1	a	a	DET
bracis-28347	1	2	combinatorial	combinatorial	ADJ
bracis-28347	1	3	optimization	optimization	NOUN
bracis-28347	1	4	model	model	NOUN
bracis-28347	1	5	and	and	CCONJ
bracis-28347	1	6	 	 	SPACE
bracis-28347	1	7	polynomial	polynomial	ADJ
bracis-28347	1	8	time	time	NOUN
bracis-28347	1	9	heuristic	heuristic	ADJ
bracis-28347	1	10	for	for	ADP
bracis-28347	1	11	 	 	SPACE
bracis-28347	1	12	a	a	DET
bracis-28347	1	13	 	 	SPACE
bracis-28347	1	14	problem	problem	NOUN
bracis-28347	1	15	of	of	ADP
bracis-28347	1	16	 	 	SPACE
bracis-28347	1	17	finding	find	VERB
bracis-28347	1	18	specific	specific	ADJ
bracis-28347	1	19	structural	structural	ADJ
bracis-28347	1	20	patterns	pattern	NOUN
bracis-28347	1	21	in	in	ADP
bracis-28347	1	22	 	 	SPACE
bracis-28347	1	23	networks	network	NOUN
bracis-28347	1	24	|	|	ADV
bracis-28347	1	25	springer	springer	NOUN
bracis-28347	1	26	nature	nature	NOUN
bracis-28347	1	27	link	link	PROPN
bracis-28347	1	28	(	(	PUNCT
bracis-28347	1	29	formerly	formerly	ADV
bracis-28347	1	30	springerlink	springerlink	NOUN
bracis-28347	1	31	)	)	PUNCT
bracis-28347	1	32	skip	skip	VERB
bracis-28347	1	33	to	to	ADP
bracis-28347	1	34	main	main	ADJ
bracis-28347	1	35	content	content	NOUN
bracis-28347	1	36	advertisement	advertisement	NOUN
bracis-28347	1	37	log	log	NOUN
bracis-28347	1	38	in	in	ADP
bracis-28347	1	39	menu	menu	NOUN
bracis-28347	1	40	find	find	VERB
bracis-28347	1	41	a	a	DET
bracis-28347	1	42	journal	journal	NOUN
bracis-28347	1	43	publish	publish	VERB
bracis-28347	1	44	with	with	ADP
bracis-28347	1	45	us	we	PRON
bracis-28347	1	46	track	track	VERB
bracis-28347	1	47	your	your	PRON
bracis-28347	1	48	research	research	NOUN
bracis-28347	1	49	search	search	NOUN
bracis-28347	1	50	cart	cart	NOUN
bracis-28347	1	51	home	home	NOUN
bracis-28347	1	52	intelligent	intelligent	ADJ
bracis-28347	1	53	systems	system	NOUN
bracis-28347	1	54	conference	conference	NOUN
bracis-28347	1	55	paper	paper	NOUN
bracis-28347	1	56	a	a	DET
bracis-28347	1	57	combinatorial	combinatorial	ADJ
bracis-28347	1	58	optimization	optimization	NOUN
bracis-28347	1	59	model	model	NOUN
bracis-28347	1	60	and	and	CCONJ
bracis-28347	1	61	 	 	SPACE
bracis-28347	1	62	polynomial	polynomial	ADJ
bracis-28347	1	63	time	time	NOUN
bracis-28347	1	64	heuristic	heuristic	ADJ
bracis-28347	1	65	for	for	ADP
bracis-28347	1	66	 	 	SPACE
bracis-28347	1	67	a	a	DET
bracis-28347	1	68	 	 	SPACE
bracis-28347	1	69	problem	problem	NOUN
bracis-28347	1	70	of	of	ADP
bracis-28347	1	71	 	 	SPACE
bracis-28347	1	72	finding	find	VERB
bracis-28347	1	73	specific	specific	ADJ
bracis-28347	1	74	structural	structural	ADJ
bracis-28347	1	75	patterns	pattern	NOUN
bracis-28347	1	76	in	in	ADP
bracis-28347	1	77	 	 	SPACE
bracis-28347	1	78	networks	network	NOUN
bracis-28347	1	79	conference	conference	NOUN
bracis-28347	1	80	paper	paper	NOUN
bracis-28347	1	81	first	first	ADV
bracis-28347	1	82	online	online	ADV
bracis-28347	1	83	:	:	PUNCT
bracis-28347	1	84	12	12	NUM
bracis-28347	1	85	october	october	NOUN
bracis-28347	1	86	2023	2023	NUM
bracis-28347	1	87	pp	pp	ADP
bracis-28347	1	88	33–47	33–47	NUM
bracis-28347	1	89	cite	cite	VERB
bracis-28347	1	90	this	this	DET
bracis-28347	1	91	conference	conference	NOUN
bracis-28347	1	92	paper	paper	NOUN
bracis-28347	1	93	access	access	NOUN
bracis-28347	1	94	provided	provide	VERB
bracis-28347	1	95	by	by	ADP
bracis-28347	1	96	university	university	PROPN
bracis-28347	1	97	of	of	ADP
bracis-28347	1	98	notre	notre	PROPN
bracis-28347	1	99	dame	dame	PROPN
bracis-28347	1	100	hesburgh	hesburgh	PROPN
bracis-28347	1	101	library	library	PROPN
bracis-28347	1	102	download	download	PROPN
bracis-28347	1	103	book	book	NOUN
bracis-28347	1	104	pdf	pdf	PROPN
bracis-28347	1	105	download	download	NOUN
bracis-28347	1	106	book	book	NOUN
bracis-28347	1	107	epub	epub	PROPN
bracis-28347	1	108	intelligent	intelligent	ADJ
bracis-28347	1	109	systems	system	NOUN
bracis-28347	1	110	(	(	PUNCT
bracis-28347	1	111	bracis	bracis	NOUN
bracis-28347	1	112	2023	2023	NUM
bracis-28347	1	113	)	)	PUNCT
bracis-28347	1	114	a	a	DET
bracis-28347	1	115	combinatorial	combinatorial	ADJ
bracis-28347	1	116	optimization	optimization	NOUN
bracis-28347	1	117	model	model	NOUN
bracis-28347	1	118	and	and	CCONJ
bracis-28347	1	119	 	 	SPACE
bracis-28347	1	120	polynomial	polynomial	ADJ
bracis-28347	1	121	time	time	NOUN
bracis-28347	1	122	heuristic	heuristic	ADJ
bracis-28347	1	123	for	for	ADP
bracis-28347	1	124	 	 	SPACE
bracis-28347	1	125	a	a	DET
bracis-28347	1	126	 	 	SPACE
bracis-28347	1	127	problem	problem	NOUN
bracis-28347	1	128	of	of	ADP
bracis-28347	1	129	 	 	SPACE
bracis-28347	1	130	finding	find	VERB
bracis-28347	1	131	specific	specific	ADJ
bracis-28347	1	132	structural	structural	ADJ
bracis-28347	1	133	patterns	pattern	NOUN
bracis-28347	1	134	in	in	ADP
bracis-28347	1	135	 	 	SPACE
bracis-28347	1	136	networks	network	NOUN
bracis-28347	1	137	download	download	NOUN
bracis-28347	1	138	book	book	NOUN
bracis-28347	1	139	pdf	pdf	PROPN
bracis-28347	1	140	download	download	NOUN
bracis-28347	1	141	book	book	PROPN
bracis-28347	1	142	epub	epub	PROPN
bracis-28347	1	143	igor	igor	PROPN
bracis-28347	1	144	m.	m.	PROPN
bracis-28347	1	145	sampaio	sampaio	PROPN
bracis-28347	1	146	  	  	SPACE
bracis-28347	1	147	orcid	orcid	PROPN
bracis-28347	1	148	:	:	PUNCT
bracis-28347	1	149	orcid.org/0000-0002-0929-47339	orcid.org/0000-0002-0929-47339	PROPN
bracis-28347	1	150	&	&	CCONJ
bracis-28347	1	151	karla	karla	PROPN
bracis-28347	2	1	roberta	roberta	PROPN
bracis-28347	2	2	p.	p.	PROPN
bracis-28347	2	3	s.	s.	PROPN
bracis-28347	3	1	lima	lima	PROPN
bracis-28347	3	2	  	  	SPACE
bracis-28347	3	3	orcid	orcid	NOUN
bracis-28347	3	4	:	:	PUNCT
bracis-28347	3	5	orcid.org/0000-0001-5483-54669	orcid.org/0000-0001-5483-54669	PROPN
bracis-28347	3	6	  	  	SPACE
bracis-28347	3	7	part	part	NOUN
bracis-28347	3	8	of	of	ADP
bracis-28347	3	9	the	the	DET
bracis-28347	3	10	book	book	NOUN
bracis-28347	3	11	series	series	NOUN
bracis-28347	3	12	:	:	PUNCT
bracis-28347	3	13	lecture	lecture	NOUN
bracis-28347	3	14	notes	note	NOUN
bracis-28347	3	15	in	in	ADP
bracis-28347	3	16	computer	computer	NOUN
bracis-28347	3	17	science	science	NOUN
bracis-28347	3	18	(	(	PUNCT
bracis-28347	3	19	(	(	PUNCT
bracis-28347	3	20	lnai	lnai	ADJ
bracis-28347	3	21	,	,	PUNCT
bracis-28347	3	22	volume	volume	NOUN
bracis-28347	3	23	14195	14195	NUM
bracis-28347	3	24	)	)	PUNCT
bracis-28347	3	25	)	)	PUNCT
bracis-28347	3	26	included	include	VERB
bracis-28347	3	27	in	in	ADP
bracis-28347	3	28	the	the	DET
bracis-28347	3	29	following	follow	VERB
bracis-28347	3	30	conference	conference	NOUN
bracis-28347	3	31	series	series	NOUN
bracis-28347	3	32	:	:	PUNCT
bracis-28347	3	33	brazilian	brazilian	ADJ
bracis-28347	3	34	conference	conference	NOUN
bracis-28347	3	35	on	on	ADP
bracis-28347	3	36	intelligent	intelligent	ADJ
bracis-28347	3	37	systems	system	NOUN
bracis-28347	3	38	522	522	NUM
bracis-28347	3	39	accesses	access	NOUN
bracis-28347	3	40	abstract	abstract	VERB
bracis-28347	3	41	the	the	DET
bracis-28347	3	42	development	development	NOUN
bracis-28347	3	43	of	of	ADP
bracis-28347	3	44	tools	tool	NOUN
bracis-28347	3	45	based	base	VERB
bracis-28347	3	46	on	on	ADP
bracis-28347	3	47	robust	robust	ADJ
bracis-28347	3	48	mathematical	mathematical	ADJ
bracis-28347	3	49	models	model	NOUN
bracis-28347	3	50	to	to	PART
bracis-28347	3	51	deal	deal	VERB
bracis-28347	3	52	with	with	ADP
bracis-28347	3	53	real	real	ADJ
bracis-28347	3	54	-	-	PUNCT
bracis-28347	3	55	world	world	NOUN
bracis-28347	3	56	,	,	PUNCT
bracis-28347	3	57	computationally	computationally	ADV
bracis-28347	3	58	intractable	intractable	ADJ
bracis-28347	3	59	problems	problem	NOUN
bracis-28347	3	60	has	have	AUX
bracis-28347	3	61	increasingly	increasingly	ADV
bracis-28347	3	62	aligned	align	VERB
bracis-28347	3	63	with	with	ADP
bracis-28347	3	64	combinatorial	combinatorial	ADJ
bracis-28347	3	65	optimization	optimization	NOUN
bracis-28347	3	66	and	and	CCONJ
bracis-28347	3	67	integer	integer	NOUN
bracis-28347	3	68	linear	linear	ADJ
bracis-28347	3	69	programming	programming	NOUN
bracis-28347	3	70	techniques	technique	NOUN
bracis-28347	3	71	due	due	ADJ
bracis-28347	3	72	to	to	ADP
bracis-28347	3	73	enormous	enormous	ADJ
bracis-28347	3	74	technological	technological	ADJ
bracis-28347	3	75	advances	advance	NOUN
bracis-28347	3	76	and	and	CCONJ
bracis-28347	3	77	the	the	DET
bracis-28347	3	78	real	real	ADJ
bracis-28347	3	79	need	need	NOUN
bracis-28347	3	80	to	to	PART
bracis-28347	3	81	deal	deal	VERB
bracis-28347	3	82	with	with	ADP
bracis-28347	3	83	large	large	ADJ
bracis-28347	3	84	volumes	volume	NOUN
bracis-28347	3	85	of	of	ADP
bracis-28347	3	86	data	datum	NOUN
bracis-28347	3	87	.	.	PUNCT
bracis-28347	4	1	in	in	ADP
bracis-28347	4	2	this	this	DET
bracis-28347	4	3	paper	paper	NOUN
bracis-28347	4	4	,	,	PUNCT
bracis-28347	4	5	the	the	DET
bracis-28347	4	6	maximum	maximum	ADJ
bracis-28347	4	7	tropical	tropical	ADJ
bracis-28347	4	8	path	path	NOUN
bracis-28347	4	9	problem	problem	NOUN
bracis-28347	4	10	on	on	ADP
bracis-28347	4	11	graphs	graph	NOUN
bracis-28347	4	12	(	(	PUNCT
bracis-28347	4	13	mtpp	mtpp	PROPN
bracis-28347	4	14	)	)	PUNCT
bracis-28347	4	15	,	,	PUNCT
bracis-28347	4	16	which	which	PRON
bracis-28347	4	17	is	be	AUX
bracis-28347	4	18	known	know	VERB
bracis-28347	4	19	to	to	PART
bracis-28347	4	20	be	be	AUX
bracis-28347	4	21	np	np	INTJ
bracis-28347	4	22	-	-	PUNCT
bracis-28347	4	23	hard	hard	ADJ
bracis-28347	4	24	,	,	PUNCT
bracis-28347	4	25	was	be	AUX
bracis-28347	4	26	investigated	investigate	VERB
bracis-28347	4	27	.	.	PUNCT
bracis-28347	5	1	it	it	PRON
bracis-28347	5	2	is	be	AUX
bracis-28347	5	3	a	a	DET
bracis-28347	5	4	problem	problem	NOUN
bracis-28347	5	5	of	of	ADP
bracis-28347	5	6	searching	search	VERB
bracis-28347	5	7	for	for	ADP
bracis-28347	5	8	specific	specific	ADJ
bracis-28347	5	9	structural	structural	ADJ
bracis-28347	5	10	patterns	pattern	NOUN
bracis-28347	5	11	in	in	ADP
bracis-28347	5	12	networks	network	NOUN
bracis-28347	5	13	that	that	PRON
bracis-28347	5	14	can	can	AUX
bracis-28347	5	15	represent	represent	VERB
bracis-28347	5	16	various	various	ADJ
bracis-28347	5	17	applications	application	NOUN
bracis-28347	5	18	,	,	PUNCT
bracis-28347	5	19	among	among	ADP
bracis-28347	5	20	them	they	PRON
bracis-28347	5	21	biological	biological	ADJ
bracis-28347	5	22	interactions	interaction	NOUN
bracis-28347	5	23	,	,	PUNCT
bracis-28347	5	24	such	such	ADJ
bracis-28347	5	25	as	as	ADP
bracis-28347	5	26	metabolic	metabolic	NOUN
bracis-28347	5	27	,	,	PUNCT
bracis-28347	5	28	neurological	neurological	ADJ
bracis-28347	5	29	or	or	CCONJ
bracis-28347	5	30	protein	protein	NOUN
bracis-28347	5	31	interaction	interaction	NOUN
bracis-28347	5	32	networks	network	NOUN
bracis-28347	5	33	.	.	PUNCT
bracis-28347	6	1	the	the	DET
bracis-28347	6	2	main	main	ADJ
bracis-28347	6	3	result	result	NOUN
bracis-28347	6	4	of	of	ADP
bracis-28347	6	5	this	this	DET
bracis-28347	6	6	work	work	NOUN
bracis-28347	6	7	consists	consist	VERB
bracis-28347	6	8	of	of	ADP
bracis-28347	6	9	a	a	DET
bracis-28347	6	10	polynomial	polynomial	ADJ
bracis-28347	6	11	-	-	PUNCT
bracis-28347	6	12	time	time	NOUN
bracis-28347	6	13	heuristic	heuristic	ADJ
bracis-28347	6	14	algorithm	algorithm	NOUN
bracis-28347	6	15	that	that	SCONJ
bracis-28347	6	16	,	,	PUNCT
bracis-28347	6	17	according	accord	VERB
bracis-28347	6	18	to	to	ADP
bracis-28347	6	19	experimental	experimental	ADJ
bracis-28347	6	20	results	result	NOUN
bracis-28347	6	21	,	,	PUNCT
bracis-28347	6	22	finds	find	VERB
bracis-28347	6	23	good	good	ADJ
bracis-28347	6	24	solutions	solution	NOUN
bracis-28347	6	25	in	in	ADP
bracis-28347	6	26	practice	practice	NOUN
bracis-28347	6	27	.	.	PUNCT
bracis-28347	7	1	furthermore	furthermore	ADV
bracis-28347	7	2	,	,	PUNCT
bracis-28347	7	3	an	an	DET
bracis-28347	7	4	integer	integer	NOUN
bracis-28347	7	5	linear	linear	NOUN
bracis-28347	7	6	programming	programming	NOUN
bracis-28347	7	7	model	model	NOUN
bracis-28347	7	8	was	be	AUX
bracis-28347	7	9	developed	develop	VERB
bracis-28347	7	10	and	and	CCONJ
bracis-28347	7	11	implemented	implement	VERB
bracis-28347	7	12	so	so	SCONJ
bracis-28347	7	13	that	that	SCONJ
bracis-28347	7	14	it	it	PRON
bracis-28347	7	15	could	could	AUX
bracis-28347	7	16	be	be	AUX
bracis-28347	7	17	compared	compare	VERB
bracis-28347	7	18	with	with	ADP
bracis-28347	7	19	the	the	DET
bracis-28347	7	20	heuristic	heuristic	NOUN
bracis-28347	7	21	presented	present	VERB
bracis-28347	7	22	.	.	PUNCT
bracis-28347	8	1	to	to	PART
bracis-28347	8	2	conclude	conclude	VERB
bracis-28347	8	3	,	,	PUNCT
bracis-28347	8	4	an	an	DET
bracis-28347	8	5	empirical	empirical	ADJ
bracis-28347	8	6	analysis	analysis	NOUN
bracis-28347	8	7	was	be	AUX
bracis-28347	8	8	performed	perform	VERB
bracis-28347	8	9	through	through	ADP
bracis-28347	8	10	computational	computational	ADJ
bracis-28347	8	11	experiments	experiment	NOUN
bracis-28347	8	12	on	on	ADP
bracis-28347	8	13	both	both	CCONJ
bracis-28347	8	14	random	random	ADJ
bracis-28347	8	15	and	and	CCONJ
bracis-28347	8	16	real	real	ADJ
bracis-28347	8	17	-	-	PUNCT
bracis-28347	8	18	word	word	NOUN
bracis-28347	8	19	instances	instance	NOUN
bracis-28347	8	20	to	to	PART
bracis-28347	8	21	evaluate	evaluate	VERB
bracis-28347	8	22	the	the	DET
bracis-28347	8	23	results	result	NOUN
bracis-28347	8	24	presented	present	VERB
bracis-28347	8	25	in	in	ADP
bracis-28347	8	26	this	this	DET
bracis-28347	8	27	paper	paper	NOUN
bracis-28347	8	28	.	.	PUNCT
bracis-28347	9	1	this	this	DET
bracis-28347	9	2	work	work	NOUN
bracis-28347	9	3	was	be	AUX
bracis-28347	9	4	partially	partially	ADV
bracis-28347	9	5	supported	support	VERB
bracis-28347	9	6	by	by	ADP
bracis-28347	9	7	grant	grant	NOUN
bracis-28347	9	8	2021/07080	2021/07080	NUM
bracis-28347	9	9	-	-	SYM
bracis-28347	9	10	6	6	NUM
bracis-28347	9	11	,	,	PUNCT
bracis-28347	9	12	são	são	PROPN
bracis-28347	9	13	paulo	paulo	PROPN
bracis-28347	9	14	research	research	PROPN
bracis-28347	9	15	foundation	foundation	PROPN
bracis-28347	9	16	(	(	PUNCT
bracis-28347	9	17	fapesp	fapesp	NOUN
bracis-28347	9	18	)	)	PUNCT
bracis-28347	9	19	and	and	CCONJ
bracis-28347	9	20	by	by	ADP
bracis-28347	9	21	the	the	DET
bracis-28347	9	22	graduate	graduate	NOUN
bracis-28347	9	23	support	support	NOUN
bracis-28347	9	24	program	program	NOUN
bracis-28347	9	25	(	(	PUNCT
bracis-28347	9	26	proap)-capes	proap)-capes	PROPN
bracis-28347	9	27	.	.	NOUN
bracis-28347	9	28	access	access	NOUN
bracis-28347	9	29	provided	provide	VERB
bracis-28347	9	30	by	by	ADP
bracis-28347	9	31	university	university	PROPN
bracis-28347	9	32	of	of	ADP
bracis-28347	9	33	notre	notre	PROPN
bracis-28347	9	34	dame	dame	PROPN
bracis-28347	9	35	hesburgh	hesburgh	PROPN
bracis-28347	9	36	library	library	PROPN
bracis-28347	9	37	.	.	PUNCT
bracis-28347	10	1	download	download	PROPN
bracis-28347	10	2	conference	conference	NOUN
bracis-28347	10	3	paper	paper	NOUN
bracis-28347	10	4	pdf	pdf	NOUN
bracis-28347	10	5	similar	similar	ADJ
bracis-28347	10	6	content	content	NOUN
bracis-28347	10	7	being	be	AUX
bracis-28347	10	8	viewed	view	VERB
bracis-28347	10	9	by	by	ADP
bracis-28347	10	10	others	other	NOUN
bracis-28347	10	11	target	target	VERB
bracis-28347	10	12	controllability	controllability	NOUN
bracis-28347	10	13	of	of	ADP
bracis-28347	10	14	linear	linear	PROPN
bracis-28347	10	15	networks	network	NOUN
bracis-28347	10	16	chapter	chapter	NOUN
bracis-28347	10	17	©	©	PROPN
bracis-28347	10	18	2016	2016	NUM
bracis-28347	10	19	fixed	fix	VERB
bracis-28347	10	20	parameter	parameter	NOUN
bracis-28347	10	21	algorithms	algorithm	NOUN
bracis-28347	10	22	and	and	CCONJ
bracis-28347	10	23	hardness	hardness	NOUN
bracis-28347	10	24	of	of	ADP
bracis-28347	10	25	approximation	approximation	NOUN
bracis-28347	10	26	results	result	NOUN
bracis-28347	10	27	for	for	ADP
bracis-28347	10	28	the	the	DET
bracis-28347	10	29	structural	structural	ADJ
bracis-28347	10	30	target	target	NOUN
bracis-28347	10	31	controllability	controllability	NOUN
bracis-28347	10	32	problem	problem	NOUN
bracis-28347	10	33	chapter	chapter	NOUN
bracis-28347	10	34	©	©	PROPN
bracis-28347	10	35	2018	2018	NUM
bracis-28347	10	36	reconfiguring	reconfigure	VERB
bracis-28347	10	37	shortest	short	ADJ
bracis-28347	10	38	paths	path	NOUN
bracis-28347	10	39	in	in	ADP
bracis-28347	10	40	graphs	graph	NOUN
bracis-28347	10	41	article	article	NOUN
bracis-28347	10	42	open	open	ADJ
bracis-28347	10	43	access	access	NOUN
bracis-28347	10	44	27	27	NUM
bracis-28347	10	45	august	august	PROPN
bracis-28347	10	46	2024	2024	NUM
bracis-28347	10	47	explore	explore	NOUN
bracis-28347	10	48	related	relate	VERB
bracis-28347	10	49	subjects	subject	NOUN
bracis-28347	10	50	discover	discover	VERB
bracis-28347	10	51	the	the	DET
bracis-28347	10	52	latest	late	ADJ
bracis-28347	10	53	articles	article	NOUN
bracis-28347	10	54	,	,	PUNCT
bracis-28347	10	55	books	book	NOUN
bracis-28347	10	56	and	and	CCONJ
bracis-28347	10	57	news	news	NOUN
bracis-28347	10	58	in	in	ADP
bracis-28347	10	59	related	related	ADJ
bracis-28347	10	60	subjects	subject	NOUN
bracis-28347	10	61	,	,	PUNCT
bracis-28347	10	62	suggested	suggest	VERB
bracis-28347	10	63	using	use	VERB
bracis-28347	10	64	machine	machine	NOUN
bracis-28347	10	65	learning	learning	NOUN
bracis-28347	10	66	.	.	PUNCT
bracis-28347	11	1	combinatorics	combinatoric	NOUN
bracis-28347	11	2	complex	complex	PROPN
bracis-28347	11	3	networks	network	NOUN
bracis-28347	11	4	computational	computational	ADJ
bracis-28347	11	5	complexity	complexity	NOUN
bracis-28347	11	6	discrete	discrete	ADJ
bracis-28347	11	7	optimization	optimization	NOUN
bracis-28347	11	8	graph	graph	NOUN
bracis-28347	11	9	theory	theory	NOUN
bracis-28347	11	10	optimization	optimization	NOUN
bracis-28347	11	11	1	1	NUM
bracis-28347	11	12	introduction	introduction	NOUN
bracis-28347	11	13	the	the	DET
bracis-28347	11	14	tropical	tropical	ADJ
bracis-28347	11	15	path	path	NOUN
bracis-28347	11	16	search	search	NOUN
bracis-28347	11	17	problem	problem	NOUN
bracis-28347	11	18	in	in	ADP
bracis-28347	11	19	graphs	graph	NOUN
bracis-28347	11	20	represents	represent	VERB
bracis-28347	11	21	a	a	DET
bracis-28347	11	22	search	search	NOUN
bracis-28347	11	23	problem	problem	NOUN
bracis-28347	11	24	for	for	ADP
bracis-28347	11	25	specific	specific	ADJ
bracis-28347	11	26	structural	structural	ADJ
bracis-28347	11	27	patterns	pattern	NOUN
bracis-28347	11	28	in	in	ADP
bracis-28347	11	29	networks	network	NOUN
bracis-28347	11	30	.	.	PUNCT
bracis-28347	12	1	different	different	ADJ
bracis-28347	12	2	types	type	NOUN
bracis-28347	12	3	of	of	ADP
bracis-28347	12	4	pattern	pattern	NOUN
bracis-28347	12	5	search	search	NOUN
bracis-28347	12	6	have	have	AUX
bracis-28347	12	7	been	be	AUX
bracis-28347	12	8	presented	present	VERB
bracis-28347	12	9	in	in	ADP
bracis-28347	12	10	the	the	DET
bracis-28347	12	11	literature	literature	NOUN
bracis-28347	12	12	,	,	PUNCT
bracis-28347	12	13	taking	take	VERB
bracis-28347	12	14	into	into	ADP
bracis-28347	12	15	account	account	NOUN
bracis-28347	12	16	the	the	DET
bracis-28347	12	17	peculiarities	peculiarity	NOUN
bracis-28347	12	18	of	of	ADP
bracis-28347	12	19	each	each	DET
bracis-28347	12	20	application	application	NOUN
bracis-28347	12	21	;	;	PUNCT
bracis-28347	12	22	the	the	DET
bracis-28347	12	23	one	one	NOUN
bracis-28347	12	24	used	use	VERB
bracis-28347	12	25	in	in	ADP
bracis-28347	12	26	this	this	DET
bracis-28347	12	27	work	work	NOUN
bracis-28347	12	28	originates	originate	NOUN
bracis-28347	12	29	from	from	ADP
bracis-28347	12	30	the	the	DET
bracis-28347	12	31	problem	problem	NOUN
bracis-28347	12	32	of	of	ADP
bracis-28347	12	33	occurrence	occurrence	NOUN
bracis-28347	12	34	of	of	ADP
bracis-28347	12	35	the	the	DET
bracis-28347	12	36	motifs	motif	NOUN
bracis-28347	12	37	in	in	ADP
bracis-28347	12	38	graphs	graph	NOUN
bracis-28347	12	39	and	and	CCONJ
bracis-28347	12	40	was	be	AUX
bracis-28347	12	41	proposed	propose	VERB
bracis-28347	12	42	by	by	ADP
bracis-28347	12	43	lacroix	lacroix	PROPN
bracis-28347	12	44	et	et	PROPN
bracis-28347	12	45	al	al	PROPN
bracis-28347	12	46	.	.	PROPN
bracis-28347	13	1	(	(	PUNCT
bracis-28347	13	2	2006	2006	NUM
bracis-28347	13	3	)	)	PUNCT
bracis-28347	13	4	 	 	SPACE
bracis-28347	14	1	[	[	X
bracis-28347	14	2	10	10	NUM
bracis-28347	14	3	]	]	PUNCT
bracis-28347	14	4	.	.	PUNCT
bracis-28347	15	1	the	the	DET
bracis-28347	15	2	initial	initial	ADJ
bracis-28347	15	3	problem	problem	NOUN
bracis-28347	15	4	was	be	AUX
bracis-28347	15	5	investigated	investigate	VERB
bracis-28347	15	6	in	in	ADP
bracis-28347	15	7	the	the	DET
bracis-28347	15	8	context	context	NOUN
bracis-28347	15	9	of	of	ADP
bracis-28347	15	10	metabolic	metabolic	NOUN
bracis-28347	15	11	network	network	NOUN
bracis-28347	15	12	analysis	analysis	NOUN
bracis-28347	15	13	[	[	X
bracis-28347	15	14	5	5	NUM
bracis-28347	15	15	,	,	PUNCT
bracis-28347	15	16	9	9	NUM
bracis-28347	15	17	]	]	PUNCT
bracis-28347	15	18	,	,	PUNCT
bracis-28347	15	19	in	in	ADP
bracis-28347	15	20	which	which	PRON
bracis-28347	15	21	the	the	DET
bracis-28347	15	22	set	set	NOUN
bracis-28347	15	23	of	of	ADP
bracis-28347	15	24	reactions	reaction	NOUN
bracis-28347	15	25	involved	involve	VERB
bracis-28347	15	26	in	in	ADP
bracis-28347	15	27	the	the	DET
bracis-28347	15	28	synthesis	synthesis	NOUN
bracis-28347	15	29	and	and	CCONJ
bracis-28347	15	30	degradation	degradation	NOUN
bracis-28347	15	31	of	of	ADP
bracis-28347	15	32	certain	certain	ADJ
bracis-28347	15	33	molecules	molecule	NOUN
bracis-28347	15	34	is	be	AUX
bracis-28347	15	35	represented	represent	VERB
bracis-28347	15	36	through	through	ADP
bracis-28347	15	37	a	a	DET
bracis-28347	15	38	network	network	NOUN
bracis-28347	15	39	and	and	CCONJ
bracis-28347	15	40	the	the	DET
bracis-28347	15	41	motifs	motif	NOUN
bracis-28347	15	42	correspond	correspond	VERB
bracis-28347	15	43	to	to	ADP
bracis-28347	15	44	the	the	DET
bracis-28347	15	45	“	"	PUNCT
bracis-28347	15	46	modules	module	NOUN
bracis-28347	15	47	”	"	PUNCT
bracis-28347	15	48	into	into	ADP
bracis-28347	15	49	which	which	PRON
bracis-28347	15	50	this	this	DET
bracis-28347	15	51	network	network	NOUN
bracis-28347	15	52	can	can	AUX
bracis-28347	15	53	be	be	AUX
bracis-28347	15	54	decomposed	decompose	VERB
bracis-28347	15	55	in	in	ADP
bracis-28347	15	56	order	order	NOUN
bracis-28347	15	57	to	to	PART
bracis-28347	15	58	facilitate	facilitate	VERB
bracis-28347	15	59	the	the	DET
bracis-28347	15	60	interpretation	interpretation	NOUN
bracis-28347	15	61	of	of	ADP
bracis-28347	15	62	the	the	DET
bracis-28347	15	63	functions	function	NOUN
bracis-28347	15	64	that	that	PRON
bracis-28347	15	65	each	each	PRON
bracis-28347	15	66	of	of	ADP
bracis-28347	15	67	these	these	DET
bracis-28347	15	68	modules	module	NOUN
bracis-28347	15	69	plays	play	VERB
bracis-28347	15	70	in	in	ADP
bracis-28347	15	71	cellular	cellular	ADJ
bracis-28347	15	72	metabolism	metabolism	NOUN
bracis-28347	15	73	.	.	PUNCT
bracis-28347	16	1	in	in	ADP
bracis-28347	16	2	graph	graph	NOUN
bracis-28347	16	3	theory	theory	NOUN
bracis-28347	16	4	terms	term	NOUN
bracis-28347	16	5	,	,	PUNCT
bracis-28347	16	6	the	the	DET
bracis-28347	16	7	problem	problem	NOUN
bracis-28347	16	8	of	of	ADP
bracis-28347	16	9	searching	search	VERB
bracis-28347	16	10	for	for	ADP
bracis-28347	16	11	colored	colored	ADJ
bracis-28347	16	12	motifs	motif	NOUN
bracis-28347	16	13	in	in	ADP
bracis-28347	16	14	graphs	graph	NOUN
bracis-28347	16	15	consists	consist	VERB
bracis-28347	16	16	of	of	ADP
bracis-28347	16	17	finding	find	VERB
bracis-28347	16	18	a	a	DET
bracis-28347	16	19	subgraph	subgraph	NOUN
bracis-28347	16	20	whose	whose	DET
bracis-28347	16	21	set	set	NOUN
bracis-28347	16	22	of	of	ADP
bracis-28347	16	23	colors	color	NOUN
bracis-28347	16	24	matches	match	VERB
bracis-28347	16	25	the	the	DET
bracis-28347	16	26	multicolored	multicolore	VERB
bracis-28347	16	27	set	set	NOUN
bracis-28347	16	28	given	give	VERB
bracis-28347	16	29	as	as	ADP
bracis-28347	16	30	input	input	NOUN
bracis-28347	16	31	.	.	PUNCT
bracis-28347	17	1	contributions	contribution	NOUN
bracis-28347	17	2	.	.	PUNCT
bracis-28347	18	1	this	this	DET
bracis-28347	18	2	work	work	NOUN
bracis-28347	18	3	aims	aim	VERB
bracis-28347	18	4	to	to	PART
bracis-28347	18	5	present	present	VERB
bracis-28347	18	6	results	result	NOUN
bracis-28347	18	7	in	in	ADP
bracis-28347	18	8	the	the	DET
bracis-28347	18	9	line	line	NOUN
bracis-28347	18	10	of	of	ADP
bracis-28347	18	11	combinatorial	combinatorial	ADJ
bracis-28347	18	12	optimization	optimization	NOUN
bracis-28347	18	13	for	for	ADP
bracis-28347	18	14	a	a	DET
bracis-28347	18	15	problem	problem	NOUN
bracis-28347	18	16	with	with	ADP
bracis-28347	18	17	applications	application	NOUN
bracis-28347	18	18	in	in	ADP
bracis-28347	18	19	bioinformatics	bioinformatic	NOUN
bracis-28347	18	20	that	that	PRON
bracis-28347	18	21	represents	represent	VERB
bracis-28347	18	22	the	the	DET
bracis-28347	18	23	problem	problem	NOUN
bracis-28347	18	24	of	of	ADP
bracis-28347	18	25	searching	search	VERB
bracis-28347	18	26	for	for	ADP
bracis-28347	18	27	structural	structural	ADJ
bracis-28347	18	28	patterns	pattern	NOUN
bracis-28347	18	29	in	in	ADP
bracis-28347	18	30	graphs	graph	NOUN
bracis-28347	18	31	.	.	PUNCT
bracis-28347	19	1	specifically	specifically	ADV
bracis-28347	19	2	,	,	PUNCT
bracis-28347	19	3	the	the	DET
bracis-28347	19	4	main	main	ADJ
bracis-28347	19	5	contributions	contribution	NOUN
bracis-28347	19	6	of	of	ADP
bracis-28347	19	7	this	this	DET
bracis-28347	19	8	work	work	NOUN
bracis-28347	19	9	are	be	AUX
bracis-28347	19	10	as	as	SCONJ
bracis-28347	19	11	follows	follow	VERB
bracis-28347	19	12	:	:	PUNCT
bracis-28347	19	13	polynomial	polynomial	ADJ
bracis-28347	19	14	time	time	NOUN
bracis-28347	19	15	heuristic	heuristic	ADJ
bracis-28347	19	16	algorithm	algorithm	NOUN
bracis-28347	19	17	for	for	ADP
bracis-28347	19	18	the	the	DET
bracis-28347	19	19	mtpp	mtpp	NOUN
bracis-28347	19	20	that	that	PRON
bracis-28347	19	21	transforms	transform	VERB
bracis-28347	19	22	a	a	DET
bracis-28347	19	23	simple	simple	ADJ
bracis-28347	19	24	graph	graph	NOUN
bracis-28347	19	25	instance	instance	NOUN
bracis-28347	19	26	into	into	ADP
bracis-28347	19	27	a	a	DET
bracis-28347	19	28	cactus	cactus	NOUN
bracis-28347	19	29	graph	graph	NOUN
bracis-28347	19	30	instance	instance	NOUN
bracis-28347	19	31	and	and	CCONJ
bracis-28347	19	32	subsequently	subsequently	ADV
bracis-28347	19	33	runs	run	VERB
bracis-28347	19	34	an	an	DET
bracis-28347	19	35	algorithm	algorithm	NOUN
bracis-28347	19	36	that	that	PRON
bracis-28347	19	37	finds	find	VERB
bracis-28347	19	38	the	the	DET
bracis-28347	19	39	path	path	NOUN
bracis-28347	19	40	of	of	ADP
bracis-28347	19	41	interest	interest	NOUN
bracis-28347	19	42	.	.	PUNCT
bracis-28347	20	1	formulation	formulation	NOUN
bracis-28347	20	2	of	of	ADP
bracis-28347	20	3	an	an	DET
bracis-28347	20	4	integer	integer	NOUN
bracis-28347	20	5	linear	linear	NOUN
bracis-28347	20	6	programming	programming	NOUN
bracis-28347	20	7	(	(	PUNCT
bracis-28347	20	8	ilp	ilp	NOUN
bracis-28347	20	9	)	)	PUNCT
bracis-28347	20	10	model	model	NOUN
bracis-28347	20	11	for	for	ADP
bracis-28347	20	12	,	,	PUNCT
bracis-28347	20	13	given	give	VERB
bracis-28347	20	14	a	a	DET
bracis-28347	20	15	graph	graph	NOUN
bracis-28347	20	16	colored	color	VERB
bracis-28347	20	17	at	at	ADP
bracis-28347	20	18	the	the	DET
bracis-28347	20	19	vertices	vertex	NOUN
bracis-28347	20	20	,	,	PUNCT
bracis-28347	20	21	finding	find	VERB
bracis-28347	20	22	a	a	DET
bracis-28347	20	23	path	path	NOUN
bracis-28347	20	24	that	that	PRON
bracis-28347	20	25	maximizes	maximize	VERB
bracis-28347	20	26	the	the	DET
bracis-28347	20	27	number	number	NOUN
bracis-28347	20	28	of	of	ADP
bracis-28347	20	29	colors	color	NOUN
bracis-28347	20	30	used	use	VERB
bracis-28347	20	31	.	.	PUNCT
bracis-28347	21	1	tests	test	NOUN
bracis-28347	21	2	and	and	CCONJ
bracis-28347	21	3	analysis	analysis	NOUN
bracis-28347	21	4	of	of	ADP
bracis-28347	21	5	the	the	DET
bracis-28347	21	6	quality	quality	NOUN
bracis-28347	21	7	and	and	CCONJ
bracis-28347	21	8	performance	performance	NOUN
bracis-28347	21	9	of	of	ADP
bracis-28347	21	10	the	the	DET
bracis-28347	21	11	proposed	propose	VERB
bracis-28347	21	12	algorithm	algorithm	NOUN
bracis-28347	21	13	based	base	VERB
bracis-28347	21	14	on	on	ADP
bracis-28347	21	15	the	the	DET
bracis-28347	21	16	ilp	ilp	ADJ
bracis-28347	21	17	model	model	NOUN
bracis-28347	21	18	through	through	ADP
bracis-28347	21	19	large	large	ADJ
bracis-28347	21	20	instances	instance	NOUN
bracis-28347	21	21	,	,	PUNCT
bracis-28347	21	22	both	both	CCONJ
bracis-28347	21	23	real	real	ADJ
bracis-28347	21	24	-	-	PUNCT
bracis-28347	21	25	world	world	NOUN
bracis-28347	21	26	and	and	CCONJ
bracis-28347	21	27	random	random	ADJ
bracis-28347	21	28	.	.	PUNCT
bracis-28347	22	1	this	this	DET
bracis-28347	22	2	paper	paper	NOUN
bracis-28347	22	3	is	be	AUX
bracis-28347	22	4	organized	organize	VERB
bracis-28347	22	5	as	as	SCONJ
bracis-28347	22	6	follows	follow	VERB
bracis-28347	22	7	:	:	PUNCT
bracis-28347	22	8	sect	sect	NOUN
bracis-28347	22	9	.	.	PUNCT
bracis-28347	22	10	 	 	SPACE
bracis-28347	23	1	2	2	NUM
bracis-28347	23	2	presents	present	VERB
bracis-28347	23	3	some	some	DET
bracis-28347	23	4	initial	initial	ADJ
bracis-28347	23	5	concepts	concept	NOUN
bracis-28347	23	6	and	and	CCONJ
bracis-28347	23	7	a	a	DET
bracis-28347	23	8	brief	brief	ADJ
bracis-28347	23	9	review	review	NOUN
bracis-28347	23	10	of	of	ADP
bracis-28347	23	11	the	the	DET
bracis-28347	23	12	literature	literature	NOUN
bracis-28347	23	13	on	on	ADP
bracis-28347	23	14	the	the	DET
bracis-28347	23	15	tropical	tropical	ADJ
bracis-28347	23	16	path	path	NOUN
bracis-28347	23	17	problem	problem	NOUN
bracis-28347	23	18	in	in	ADP
bracis-28347	23	19	graphs	graph	NOUN
bracis-28347	23	20	;	;	PUNCT
bracis-28347	23	21	sect	sect	NOUN
bracis-28347	23	22	.	.	PUNCT
bracis-28347	23	23	 	 	SPACE
bracis-28347	24	1	3	3	NUM
bracis-28347	24	2	presents	present	VERB
bracis-28347	24	3	the	the	DET
bracis-28347	24	4	ilp	ilp	ADJ
bracis-28347	24	5	model	model	NOUN
bracis-28347	24	6	formulation	formulation	NOUN
bracis-28347	24	7	;	;	PUNCT
bracis-28347	24	8	sect	sect	NOUN
bracis-28347	24	9	.	.	PUNCT
bracis-28347	24	10	 	 	SPACE
bracis-28347	25	1	4	4	NUM
bracis-28347	25	2	presents	present	VERB
bracis-28347	25	3	the	the	DET
bracis-28347	25	4	proposed	propose	VERB
bracis-28347	25	5	heuristic	heuristic	ADJ
bracis-28347	25	6	algorithm	algorithm	NOUN
bracis-28347	25	7	;	;	PUNCT
bracis-28347	25	8	sect	sect	NOUN
bracis-28347	25	9	.	.	PUNCT
bracis-28347	25	10	 	 	SPACE
bracis-28347	26	1	5	5	NUM
bracis-28347	26	2	presents	present	VERB
bracis-28347	26	3	the	the	DET
bracis-28347	26	4	experimentation	experimentation	NOUN
bracis-28347	26	5	and	and	CCONJ
bracis-28347	26	6	results	result	NOUN
bracis-28347	26	7	;	;	PUNCT
bracis-28347	26	8	and	and	CCONJ
bracis-28347	26	9	sect	sect	NOUN
bracis-28347	26	10	.	.	PUNCT
bracis-28347	26	11	 	 	SPACE
bracis-28347	27	1	6	6	NUM
bracis-28347	27	2	presents	present	VERB
bracis-28347	27	3	the	the	DET
bracis-28347	27	4	concluding	concluding	NOUN
bracis-28347	27	5	remarks	remark	VERB
bracis-28347	27	6	.	.	PUNCT
bracis-28347	28	1	2	2	NUM
bracis-28347	28	2	concepts	concept	NOUN
bracis-28347	28	3	and	and	CCONJ
bracis-28347	28	4	 	 	SPACE
bracis-28347	28	5	related	relate	VERB
bracis-28347	28	6	work	work	NOUN
bracis-28347	28	7	a	a	DET
bracis-28347	28	8	simple	simple	ADJ
bracis-28347	28	9	graph	graph	NOUN
bracis-28347	28	10	g	g	PROPN
bracis-28347	28	11	is	be	AUX
bracis-28347	28	12	an	an	DET
bracis-28347	28	13	ordered	order	VERB
bracis-28347	28	14	pair	pair	NOUN
bracis-28347	28	15	(	(	PUNCT
bracis-28347	28	16	v	v	NOUN
bracis-28347	28	17	,	,	PUNCT
bracis-28347	28	18	 	 	SPACE
bracis-28347	28	19	e	e	NOUN
bracis-28347	28	20	)	)	PUNCT
bracis-28347	28	21	,	,	PUNCT
bracis-28347	28	22	where	where	SCONJ
bracis-28347	28	23	v	v	NOUN
bracis-28347	28	24	is	be	AUX
bracis-28347	28	25	a	a	DET
bracis-28347	28	26	finite	finite	ADJ
bracis-28347	28	27	set	set	NOUN
bracis-28347	28	28	of	of	ADP
bracis-28347	28	29	elements	element	NOUN
bracis-28347	28	30	called	call	VERB
bracis-28347	28	31	vertices	vertex	NOUN
bracis-28347	28	32	and	and	CCONJ
bracis-28347	28	33	e	e	NOUN
bracis-28347	28	34	is	be	AUX
bracis-28347	28	35	a	a	DET
bracis-28347	28	36	set	set	NOUN
bracis-28347	28	37	of	of	ADP
bracis-28347	28	38	elements	element	NOUN
bracis-28347	28	39	called	call	VERB
bracis-28347	28	40	edges	edge	NOUN
bracis-28347	28	41	,	,	PUNCT
bracis-28347	28	42	where	where	SCONJ
bracis-28347	28	43	each	each	DET
bracis-28347	28	44	edge	edge	NOUN
bracis-28347	28	45	is	be	AUX
bracis-28347	28	46	an	an	DET
bracis-28347	28	47	unordered	unordered	ADJ
bracis-28347	28	48	pair	pair	NOUN
bracis-28347	28	49	of	of	ADP
bracis-28347	28	50	distinct	distinct	ADJ
bracis-28347	28	51	vertices	vertex	NOUN
bracis-28347	28	52	(	(	PUNCT
bracis-28347	28	53	u	u	NOUN
bracis-28347	28	54	,	,	PUNCT
bracis-28347	28	55	 	 	SPACE
bracis-28347	28	56	v	v	NOUN
bracis-28347	28	57	)	)	PUNCT
bracis-28347	28	58	.	.	PUNCT
bracis-28347	29	1	if	if	SCONJ
bracis-28347	29	2	\(u	\(u	NOUN
bracis-28347	29	3	,	,	PUNCT
bracis-28347	29	4	v	v	ADP
bracis-28347	29	5	\in	\in	PROPN
bracis-28347	29	6	v\	v\	NOUN
bracis-28347	29	7	)	)	PUNCT
bracis-28347	29	8	is	be	AUX
bracis-28347	29	9	an	an	DET
bracis-28347	29	10	edge	edge	NOUN
bracis-28347	29	11	,	,	PUNCT
bracis-28347	29	12	then	then	ADV
bracis-28347	29	13	u	u	NOUN
bracis-28347	29	14	and	and	CCONJ
bracis-28347	29	15	v	v	NOUN
bracis-28347	29	16	are	be	AUX
bracis-28347	29	17	adjacent	adjacent	ADJ
bracis-28347	29	18	.	.	PUNCT
bracis-28347	30	1	a	a	DET
bracis-28347	30	2	path	path	NOUN
bracis-28347	30	3	in	in	ADP
bracis-28347	30	4	a	a	DET
bracis-28347	30	5	graph	graph	NOUN
bracis-28347	30	6	g	g	NOUN
bracis-28347	30	7	is	be	AUX
bracis-28347	30	8	a	a	DET
bracis-28347	30	9	sequence	sequence	NOUN
bracis-28347	30	10	of	of	ADP
bracis-28347	30	11	distinct	distinct	ADJ
bracis-28347	30	12	vertices	vertex	NOUN
bracis-28347	30	13	\(p=(v_1,v_2,\ldots	\(p=(v_1,v_2,\ldot	NOUN
bracis-28347	30	14	,	,	PUNCT
bracis-28347	30	15	v_k)\	v_k)\	PROPN
bracis-28347	30	16	)	)	PUNCT
bracis-28347	30	17	,	,	PUNCT
bracis-28347	30	18	such	such	ADJ
bracis-28347	30	19	that	that	SCONJ
bracis-28347	30	20	\(v_iv_{i+1}\in	\(v_iv_{i+1}\in	X
bracis-28347	30	21	e\	e\	NOUN
bracis-28347	30	22	)	)	PUNCT
bracis-28347	30	23	for	for	ADP
bracis-28347	30	24	\(i=1	\(i=1	NOUN
bracis-28347	30	25	,	,	PUNCT
bracis-28347	30	26	\ldots	\ldots	INTJ
bracis-28347	30	27	,	,	PUNCT
bracis-28347	30	28	k-1\	k-1\	PROPN
bracis-28347	30	29	)	)	PUNCT
bracis-28347	30	30	.	.	PUNCT
bracis-28347	31	1	a	a	DET
bracis-28347	31	2	graph	graph	NOUN
bracis-28347	31	3	g	g	NOUN
bracis-28347	31	4	is	be	AUX
bracis-28347	31	5	connected	connect	VERB
bracis-28347	31	6	,	,	PUNCT
bracis-28347	31	7	if	if	SCONJ
bracis-28347	31	8	for	for	ADP
bracis-28347	31	9	any	any	DET
bracis-28347	31	10	pair	pair	NOUN
bracis-28347	31	11	of	of	ADP
bracis-28347	31	12	distinct	distinct	ADJ
bracis-28347	31	13	vertices	vertex	NOUN
bracis-28347	31	14	u	u	NOUN
bracis-28347	31	15	and	and	CCONJ
bracis-28347	31	16	v	v	NOUN
bracis-28347	31	17	,	,	PUNCT
bracis-28347	31	18	there	there	PRON
bracis-28347	31	19	is	be	VERB
bracis-28347	31	20	a	a	DET
bracis-28347	31	21	path	path	NOUN
bracis-28347	31	22	from	from	ADP
bracis-28347	31	23	u	u	NOUN
bracis-28347	31	24	to	to	ADP
bracis-28347	31	25	v	v	NOUN
bracis-28347	31	26	in	in	ADP
bracis-28347	31	27	g.	g.	PROPN
bracis-28347	31	28	a	a	DET
bracis-28347	31	29	coloring	coloring	NOUN
bracis-28347	31	30	of	of	ADP
bracis-28347	31	31	a	a	DET
bracis-28347	31	32	graph	graph	NOUN
bracis-28347	31	33	\(g	\(g	NOUN
bracis-28347	31	34	=	=	SYM
bracis-28347	31	35	(	(	PUNCT
bracis-28347	31	36	v	v	NOUN
bracis-28347	31	37	,	,	PUNCT
bracis-28347	31	38	e)\	e)\	NOUN
bracis-28347	31	39	)	)	PUNCT
bracis-28347	31	40	is	be	AUX
bracis-28347	31	41	a	a	DET
bracis-28347	31	42	function	function	NOUN
bracis-28347	31	43	\(c	\(c	NOUN
bracis-28347	31	44	:	:	PUNCT
bracis-28347	31	45	v	v	NUM
bracis-28347	31	46	\rightarrow	\rightarrow	PROPN
bracis-28347	31	47	\mathcal	\mathcal	PROPN
bracis-28347	31	48	{	{	PUNCT
bracis-28347	31	49	c}\	c}\	NUM
bracis-28347	31	50	)	)	PUNCT
bracis-28347	31	51	,	,	PUNCT
bracis-28347	31	52	where	where	SCONJ
bracis-28347	31	53	\(\mathcal	\(\mathcal	ADJ
bracis-28347	31	54	{	{	PUNCT
bracis-28347	31	55	c}\	c}\	NUM
bracis-28347	31	56	)	)	PUNCT
bracis-28347	31	57	is	be	AUX
bracis-28347	31	58	a	a	DET
bracis-28347	31	59	set	set	NOUN
bracis-28347	31	60	of	of	ADP
bracis-28347	31	61	colors	color	NOUN
bracis-28347	31	62	.	.	PUNCT
bracis-28347	32	1	the	the	DET
bracis-28347	32	2	coloring	coloring	NOUN
bracis-28347	32	3	defined	define	VERB
bracis-28347	32	4	here	here	ADV
bracis-28347	32	5	corresponds	correspond	VERB
bracis-28347	32	6	to	to	ADP
bracis-28347	32	7	a	a	DET
bracis-28347	32	8	simple	simple	ADJ
bracis-28347	32	9	assigning	assigning	NOUN
bracis-28347	32	10	of	of	ADP
bracis-28347	32	11	colors	color	NOUN
bracis-28347	32	12	to	to	ADP
bracis-28347	32	13	the	the	DET
bracis-28347	32	14	vertices	vertex	NOUN
bracis-28347	32	15	of	of	ADP
bracis-28347	32	16	the	the	DET
bracis-28347	32	17	graph	graph	NOUN
bracis-28347	32	18	,	,	PUNCT
bracis-28347	32	19	without	without	ADP
bracis-28347	32	20	any	any	DET
bracis-28347	32	21	restrictions	restriction	NOUN
bracis-28347	32	22	.	.	PUNCT
bracis-28347	33	1	a	a	DET
bracis-28347	33	2	color	color	NOUN
bracis-28347	33	3	graph	graph	NOUN
bracis-28347	33	4	\(g^c\	\(g^c\	NOUN
bracis-28347	33	5	)	)	PUNCT
bracis-28347	33	6	consists	consist	VERB
bracis-28347	33	7	of	of	ADP
bracis-28347	33	8	a	a	DET
bracis-28347	33	9	graph	graph	NOUN
bracis-28347	33	10	g	g	NOUN
bracis-28347	33	11	and	and	CCONJ
bracis-28347	33	12	a	a	DET
bracis-28347	33	13	coloring	color	VERB
bracis-28347	33	14	c	c	NOUN
bracis-28347	33	15	of	of	ADP
bracis-28347	33	16	the	the	DET
bracis-28347	33	17	vertices	vertex	NOUN
bracis-28347	33	18	of	of	ADP
bracis-28347	33	19	g.	g.	NOUN
bracis-28347	33	20	given	give	VERB
bracis-28347	33	21	a	a	DET
bracis-28347	33	22	graph	graph	NOUN
bracis-28347	33	23	g	g	NOUN
bracis-28347	33	24	colored	color	VERB
bracis-28347	33	25	at	at	ADP
bracis-28347	33	26	the	the	DET
bracis-28347	33	27	vertices	vertex	NOUN
bracis-28347	33	28	,	,	PUNCT
bracis-28347	33	29	a	a	DET
bracis-28347	33	30	path	path	NOUN
bracis-28347	33	31	p	p	NOUN
bracis-28347	33	32	in	in	ADP
bracis-28347	33	33	g	g	PROPN
bracis-28347	33	34	is	be	AUX
bracis-28347	33	35	said	say	VERB
bracis-28347	33	36	to	to	PART
bracis-28347	33	37	be	be	AUX
bracis-28347	33	38	tropical	tropical	ADJ
bracis-28347	33	39	if	if	SCONJ
bracis-28347	33	40	each	each	DET
bracis-28347	33	41	color	color	NOUN
bracis-28347	33	42	,	,	PUNCT
bracis-28347	33	43	assigned	assign	VERB
bracis-28347	33	44	to	to	ADP
bracis-28347	33	45	some	some	DET
bracis-28347	33	46	vertex	vertex	NOUN
bracis-28347	33	47	in	in	ADP
bracis-28347	33	48	the	the	DET
bracis-28347	33	49	input	input	NOUN
bracis-28347	33	50	graph	graph	NOUN
bracis-28347	33	51	,	,	PUNCT
bracis-28347	33	52	appears	appear	VERB
bracis-28347	33	53	at	at	ADP
bracis-28347	33	54	least	least	ADJ
bracis-28347	33	55	once	once	ADV
bracis-28347	33	56	in	in	ADP
bracis-28347	33	57	the	the	DET
bracis-28347	33	58	p.	p.	NOUN
bracis-28347	33	59	a	a	DET
bracis-28347	33	60	cactus	cactus	NOUN
bracis-28347	33	61	graph	graph	NOUN
bracis-28347	33	62	is	be	AUX
bracis-28347	33	63	a	a	DET
bracis-28347	33	64	connected	connected	ADJ
bracis-28347	33	65	graph	graph	NOUN
bracis-28347	33	66	in	in	ADP
bracis-28347	33	67	which	which	PRON
bracis-28347	33	68	any	any	DET
bracis-28347	33	69	two	two	NUM
bracis-28347	33	70	simple	simple	ADJ
bracis-28347	33	71	cycles	cycle	NOUN
bracis-28347	33	72	have	have	VERB
bracis-28347	33	73	at	at	ADP
bracis-28347	33	74	most	most	ADV
bracis-28347	33	75	one	one	NUM
bracis-28347	33	76	vertex	vertex	NOUN
bracis-28347	33	77	in	in	ADP
bracis-28347	33	78	common	common	ADJ
bracis-28347	33	79	;	;	PUNCT
bracis-28347	33	80	equivalently	equivalently	ADV
bracis-28347	33	81	,	,	PUNCT
bracis-28347	33	82	each	each	DET
bracis-28347	33	83	edge	edge	NOUN
bracis-28347	33	84	belongs	belong	VERB
bracis-28347	33	85	to	to	ADP
bracis-28347	33	86	at	at	ADP
bracis-28347	33	87	most	most	ADV
bracis-28347	33	88	one	one	NUM
bracis-28347	33	89	simple	simple	ADJ
bracis-28347	33	90	cycle	cycle	NOUN
bracis-28347	33	91	.	.	PUNCT
bracis-28347	34	1	a	a	DET
bracis-28347	34	2	cactus	cactus	NOUN
bracis-28347	34	3	g	g	NOUN
bracis-28347	34	4	in	in	ADP
bracis-28347	34	5	which	which	PRON
bracis-28347	34	6	a	a	DET
bracis-28347	34	7	vertex	vertex	NOUN
bracis-28347	34	8	is	be	AUX
bracis-28347	34	9	defined	define	VERB
bracis-28347	34	10	as	as	ADP
bracis-28347	34	11	a	a	DET
bracis-28347	34	12	root	root	NOUN
bracis-28347	34	13	is	be	AUX
bracis-28347	34	14	called	call	VERB
bracis-28347	34	15	a	a	DET
bracis-28347	34	16	rooted	rooted	ADJ
bracis-28347	34	17	cactus	cactus	NOUN
bracis-28347	34	18	.	.	PUNCT
bracis-28347	35	1	the	the	DET
bracis-28347	35	2	root	root	NOUN
bracis-28347	35	3	of	of	ADP
bracis-28347	35	4	a	a	DET
bracis-28347	35	5	cactus	cactus	NOUN
bracis-28347	35	6	g	g	NOUN
bracis-28347	35	7	is	be	AUX
bracis-28347	35	8	denoted	denote	VERB
bracis-28347	35	9	by	by	ADP
bracis-28347	35	10	root(g	root(g	NOUN
bracis-28347	35	11	)	)	PUNCT
bracis-28347	35	12	.	.	PUNCT
bracis-28347	36	1	the	the	DET
bracis-28347	36	2	problem	problem	NOUN
bracis-28347	36	3	of	of	ADP
bracis-28347	36	4	interest	interest	NOUN
bracis-28347	36	5	consists	consist	VERB
bracis-28347	36	6	of	of	ADP
bracis-28347	36	7	,	,	PUNCT
bracis-28347	36	8	given	give	VERB
bracis-28347	36	9	a	a	DET
bracis-28347	36	10	colored	colored	ADJ
bracis-28347	36	11	graph	graph	NOUN
bracis-28347	36	12	of	of	ADP
bracis-28347	36	13	vertices	vertex	NOUN
bracis-28347	36	14	,	,	PUNCT
bracis-28347	36	15	finding	find	VERB
bracis-28347	36	16	a	a	DET
bracis-28347	36	17	path	path	NOUN
bracis-28347	36	18	whose	whose	DET
bracis-28347	36	19	vertices	vertex	NOUN
bracis-28347	36	20	use	use	VERB
bracis-28347	36	21	the	the	DET
bracis-28347	36	22	greatest	great	ADJ
bracis-28347	36	23	number	number	NOUN
bracis-28347	36	24	of	of	ADP
bracis-28347	36	25	distinct	distinct	ADJ
bracis-28347	36	26	colors	color	NOUN
bracis-28347	36	27	.	.	PUNCT
bracis-28347	37	1	this	this	DET
bracis-28347	37	2	problem	problem	NOUN
bracis-28347	37	3	will	will	AUX
bracis-28347	37	4	be	be	AUX
bracis-28347	37	5	referred	refer	VERB
bracis-28347	37	6	to	to	ADP
bracis-28347	37	7	as	as	ADP
bracis-28347	37	8	maximum	maximum	ADJ
bracis-28347	37	9	tropical	tropical	ADJ
bracis-28347	37	10	path	path	NOUN
bracis-28347	37	11	problem	problem	NOUN
bracis-28347	37	12	(	(	PUNCT
bracis-28347	37	13	mtpp	mtpp	PROPN
bracis-28347	37	14	)	)	PUNCT
bracis-28347	37	15	.	.	PUNCT
bracis-28347	38	1	note	note	VERB
bracis-28347	38	2	that	that	SCONJ
bracis-28347	38	3	any	any	DET
bracis-28347	38	4	solution	solution	NOUN
bracis-28347	38	5	to	to	ADP
bracis-28347	38	6	the	the	DET
bracis-28347	38	7	mtpp	mtpp	NOUN
bracis-28347	38	8	is	be	AUX
bracis-28347	38	9	optimal	optimal	ADJ
bracis-28347	38	10	if	if	SCONJ
bracis-28347	38	11	the	the	DET
bracis-28347	38	12	path	path	NOUN
bracis-28347	38	13	found	find	VERB
bracis-28347	38	14	is	be	AUX
bracis-28347	38	15	tropical	tropical	ADJ
bracis-28347	38	16	and	and	CCONJ
bracis-28347	38	17	not	not	PART
bracis-28347	38	18	every	every	DET
bracis-28347	38	19	optimal	optimal	ADJ
bracis-28347	38	20	solution	solution	NOUN
bracis-28347	38	21	is	be	AUX
bracis-28347	38	22	a	a	DET
bracis-28347	38	23	tropical	tropical	ADJ
bracis-28347	38	24	path	path	NOUN
bracis-28347	38	25	(	(	PUNCT
bracis-28347	38	26	fig	fig	NOUN
bracis-28347	38	27	.	.	PUNCT
bracis-28347	38	28	 	 	SPACE
bracis-28347	38	29	1	1	NUM
bracis-28347	38	30	)	)	PUNCT
bracis-28347	38	31	.	.	PUNCT
bracis-28347	39	1	furthermore	furthermore	ADV
bracis-28347	39	2	,	,	PUNCT
bracis-28347	39	3	if	if	SCONJ
bracis-28347	39	4	each	each	DET
bracis-28347	39	5	vertex	vertex	NOUN
bracis-28347	39	6	in	in	ADP
bracis-28347	39	7	the	the	DET
bracis-28347	39	8	input	input	NOUN
bracis-28347	39	9	graph	graph	NOUN
bracis-28347	39	10	has	have	VERB
bracis-28347	39	11	a	a	DET
bracis-28347	39	12	color	color	NOUN
bracis-28347	39	13	distinct	distinct	NOUN
bracis-28347	39	14	from	from	ADP
bracis-28347	39	15	the	the	DET
bracis-28347	39	16	others	other	NOUN
bracis-28347	39	17	,	,	PUNCT
bracis-28347	39	18	mtpp	mtpp	PROPN
bracis-28347	39	19	reduces	reduce	VERB
bracis-28347	39	20	to	to	ADP
bracis-28347	39	21	the	the	DET
bracis-28347	39	22	classical	classical	ADJ
bracis-28347	39	23	hamiltonian	hamiltonian	ADJ
bracis-28347	39	24	path	path	NOUN
bracis-28347	39	25	problem	problem	NOUN
bracis-28347	39	26	.	.	PUNCT
bracis-28347	40	1	cohen	cohen	PROPN
bracis-28347	40	2	et	et	PROPN
bracis-28347	40	3	al	al	PROPN
bracis-28347	40	4	.	.	PROPN
bracis-28347	41	1	(	(	PUNCT
bracis-28347	41	2	2017	2017	NUM
bracis-28347	41	3	)	)	PUNCT
bracis-28347	42	1	[	[	X
bracis-28347	42	2	4	4	X
bracis-28347	42	3	]	]	PUNCT
bracis-28347	42	4	proved	prove	VERB
bracis-28347	42	5	that	that	SCONJ
bracis-28347	42	6	mtpp	mtpp	PROPN
bracis-28347	42	7	is	be	AUX
bracis-28347	42	8	np	np	NOUN
bracis-28347	42	9	-	-	ADJ
bracis-28347	42	10	hard	hard	ADJ
bracis-28347	42	11	even	even	ADV
bracis-28347	42	12	on	on	ADP
bracis-28347	42	13	dags	dag	NOUN
bracis-28347	42	14	(	(	PUNCT
bracis-28347	42	15	acyclic	acyclic	ADJ
bracis-28347	42	16	directed	direct	VERB
bracis-28347	42	17	graph	graph	NOUN
bracis-28347	42	18	)	)	PUNCT
bracis-28347	42	19	,	,	PUNCT
bracis-28347	42	20	cactus	cactus	NOUN
bracis-28347	42	21	graphs	graph	NOUN
bracis-28347	42	22	,	,	PUNCT
bracis-28347	42	23	and	and	CCONJ
bracis-28347	42	24	interval	interval	NOUN
bracis-28347	42	25	graphs	graph	NOUN
bracis-28347	42	26	,	,	PUNCT
bracis-28347	42	27	and	and	CCONJ
bracis-28347	42	28	it	it	PRON
bracis-28347	42	29	can	can	AUX
bracis-28347	42	30	be	be	AUX
bracis-28347	42	31	solved	solve	VERB
bracis-28347	42	32	in	in	ADP
bracis-28347	42	33	polynomial	polynomial	ADJ
bracis-28347	42	34	time	time	NOUN
bracis-28347	42	35	for	for	ADP
bracis-28347	42	36	some	some	DET
bracis-28347	42	37	specific	specific	ADJ
bracis-28347	42	38	classes	class	NOUN
bracis-28347	42	39	,	,	PUNCT
bracis-28347	42	40	such	such	ADJ
bracis-28347	42	41	as	as	ADP
bracis-28347	42	42	trees	tree	NOUN
bracis-28347	42	43	,	,	PUNCT
bracis-28347	42	44	block	block	NOUN
bracis-28347	42	45	graphs	graph	NOUN
bracis-28347	42	46	,	,	PUNCT
bracis-28347	42	47	proper	proper	ADJ
bracis-28347	42	48	interval	interval	NOUN
bracis-28347	42	49	graphs	graph	NOUN
bracis-28347	42	50	,	,	PUNCT
bracis-28347	42	51	bipartite	bipartite	ADJ
bracis-28347	42	52	chain	chain	NOUN
bracis-28347	42	53	graphs	graph	NOUN
bracis-28347	42	54	and	and	CCONJ
bracis-28347	42	55	threshold	threshold	NOUN
bracis-28347	42	56	graphs	graph	NOUN
bracis-28347	42	57	.	.	PUNCT
bracis-28347	43	1	chapelle	chapelle	PROPN
bracis-28347	43	2	et	et	PROPN
bracis-28347	43	3	al	al	PROPN
bracis-28347	43	4	.	.	PROPN
bracis-28347	44	1	(	(	PUNCT
bracis-28347	44	2	2017	2017	NUM
bracis-28347	44	3	)	)	PUNCT
bracis-28347	45	1	[	[	X
bracis-28347	45	2	2	2	X
bracis-28347	45	3	]	]	PUNCT
bracis-28347	45	4	proposed	propose	VERB
bracis-28347	45	5	exact	exact	ADJ
bracis-28347	45	6	algorithms	algorithm	NOUN
bracis-28347	45	7	for	for	ADP
bracis-28347	45	8	the	the	DET
bracis-28347	45	9	problem	problem	NOUN
bracis-28347	45	10	of	of	ADP
bracis-28347	45	11	searching	search	VERB
bracis-28347	45	12	for	for	ADP
bracis-28347	45	13	a	a	DET
bracis-28347	45	14	tropical	tropical	ADJ
bracis-28347	45	15	subset	subset	NOUN
bracis-28347	45	16	of	of	ADP
bracis-28347	45	17	minimum	minimum	ADJ
bracis-28347	45	18	size	size	NOUN
bracis-28347	45	19	.	.	PUNCT
bracis-28347	46	1	anglès	anglès	PROPN
bracis-28347	46	2	et	et	PROPN
bracis-28347	46	3	al	al	PROPN
bracis-28347	46	4	.	.	PROPN
bracis-28347	47	1	(	(	PUNCT
bracis-28347	47	2	2018	2018	NUM
bracis-28347	47	3	)	)	PUNCT
bracis-28347	48	1	[	[	X
bracis-28347	48	2	1	1	X
bracis-28347	48	3	]	]	PUNCT
bracis-28347	48	4	studied	study	VERB
bracis-28347	48	5	tropical	tropical	ADJ
bracis-28347	48	6	subsets	subset	NOUN
bracis-28347	48	7	in	in	ADP
bracis-28347	48	8	graphs	graph	NOUN
bracis-28347	48	9	from	from	ADP
bracis-28347	48	10	a	a	DET
bracis-28347	48	11	structural	structural	ADJ
bracis-28347	48	12	and	and	CCONJ
bracis-28347	48	13	algorithmic	algorithmic	ADJ
bracis-28347	48	14	point	point	NOUN
bracis-28347	48	15	of	of	ADP
bracis-28347	48	16	view	view	NOUN
bracis-28347	48	17	and	and	CCONJ
bracis-28347	48	18	obtained	obtain	VERB
bracis-28347	48	19	results	result	NOUN
bracis-28347	48	20	on	on	ADP
bracis-28347	48	21	the	the	DET
bracis-28347	48	22	line	line	NOUN
bracis-28347	48	23	of	of	ADP
bracis-28347	48	24	inapproximability	inapproximability	NOUN
bracis-28347	48	25	.	.	PUNCT
bracis-28347	49	1	in	in	ADP
bracis-28347	49	2	general	general	ADJ
bracis-28347	49	3	the	the	DET
bracis-28347	49	4	problem	problem	NOUN
bracis-28347	49	5	of	of	ADP
bracis-28347	49	6	searching	search	VERB
bracis-28347	49	7	for	for	ADP
bracis-28347	49	8	tropical	tropical	ADJ
bracis-28347	49	9	subgraphs	subgraph	NOUN
bracis-28347	49	10	in	in	ADP
bracis-28347	49	11	vertex	vertex	NOUN
bracis-28347	49	12	colored	color	VERB
bracis-28347	49	13	graphs	graph	NOUN
bracis-28347	49	14	has	have	AUX
bracis-28347	49	15	been	be	AUX
bracis-28347	49	16	explored	explore	VERB
bracis-28347	49	17	extensively	extensively	ADV
bracis-28347	49	18	for	for	ADP
bracis-28347	49	19	some	some	DET
bracis-28347	49	20	classes	class	NOUN
bracis-28347	49	21	of	of	ADP
bracis-28347	49	22	graphs	graph	NOUN
bracis-28347	49	23	;	;	PUNCT
bracis-28347	49	24	for	for	SCONJ
bracis-28347	49	25	more	more	ADJ
bracis-28347	49	26	details	detail	NOUN
bracis-28347	49	27	see	see	VERB
bracis-28347	49	28	[	[	X
bracis-28347	49	29	1	1	NUM
bracis-28347	49	30	,	,	PUNCT
bracis-28347	49	31	3	3	NUM
bracis-28347	49	32	,	,	PUNCT
bracis-28347	49	33	6	6	NUM
bracis-28347	49	34	]	]	PUNCT
bracis-28347	49	35	.	.	PUNCT
bracis-28347	50	1	fig	fig	NOUN
bracis-28347	50	2	.	.	PUNCT
bracis-28347	51	1	1	1	X
bracis-28347	51	2	.	.	PUNCT
bracis-28347	51	3	an	an	DET
bracis-28347	51	4	optimal	optimal	ADJ
bracis-28347	51	5	solution	solution	NOUN
bracis-28347	51	6	with	with	ADP
bracis-28347	51	7	7	7	NUM
bracis-28347	51	8	vertices	vertex	NOUN
bracis-28347	51	9	and	and	CCONJ
bracis-28347	51	10	6	6	NUM
bracis-28347	51	11	colors	color	NOUN
bracis-28347	51	12	.	.	PUNCT
bracis-28347	52	1	the	the	DET
bracis-28347	52	2	instance	instance	NOUN
bracis-28347	52	3	has	have	VERB
bracis-28347	52	4	7	7	NUM
bracis-28347	52	5	colors	color	NOUN
bracis-28347	52	6	.	.	PUNCT
bracis-28347	53	1	see	see	VERB
bracis-28347	53	2	that	that	SCONJ
bracis-28347	53	3	in	in	ADP
bracis-28347	53	4	the	the	DET
bracis-28347	53	5	solution	solution	NOUN
bracis-28347	53	6	it	it	PRON
bracis-28347	53	7	is	be	AUX
bracis-28347	53	8	allowed	allow	VERB
bracis-28347	53	9	to	to	PART
bracis-28347	53	10	repeat	repeat	VERB
bracis-28347	53	11	colors	color	NOUN
bracis-28347	53	12	.	.	PUNCT
bracis-28347	54	1	full	full	ADJ
bracis-28347	54	2	size	size	NOUN
bracis-28347	54	3	image	image	NOUN
bracis-28347	54	4	3	3	NUM
bracis-28347	54	5	an	an	DET
bracis-28347	54	6	ip	ip	NOUN
bracis-28347	54	7	model	model	NOUN
bracis-28347	54	8	for	for	ADP
bracis-28347	54	9	 	 	SPACE
bracis-28347	54	10	mtpp	mtpp	PROPN
bracis-28347	54	11	in	in	ADP
bracis-28347	54	12	this	this	DET
bracis-28347	54	13	section	section	NOUN
bracis-28347	54	14	,	,	PUNCT
bracis-28347	54	15	the	the	DET
bracis-28347	54	16	integer	integer	NOUN
bracis-28347	54	17	linear	linear	PROPN
bracis-28347	54	18	programming	programming	NOUN
bracis-28347	54	19	model	model	NOUN
bracis-28347	54	20	developed	develop	VERB
bracis-28347	54	21	for	for	ADP
bracis-28347	54	22	the	the	DET
bracis-28347	54	23	mtpp	mtpp	PROPN
bracis-28347	54	24	problem	problem	NOUN
bracis-28347	54	25	is	be	AUX
bracis-28347	54	26	presented	present	VERB
bracis-28347	54	27	.	.	PUNCT
bracis-28347	55	1	the	the	DET
bracis-28347	55	2	initial	initial	ADJ
bracis-28347	55	3	purpose	purpose	NOUN
bracis-28347	55	4	of	of	ADP
bracis-28347	55	5	developing	develop	VERB
bracis-28347	55	6	an	an	DET
bracis-28347	55	7	integer	integer	NOUN
bracis-28347	55	8	linear	linear	NOUN
bracis-28347	55	9	programming	programming	NOUN
bracis-28347	55	10	model	model	NOUN
bracis-28347	55	11	for	for	ADP
bracis-28347	55	12	the	the	DET
bracis-28347	55	13	mtpp	mtpp	NOUN
bracis-28347	55	14	was	be	AUX
bracis-28347	55	15	to	to	PART
bracis-28347	55	16	explore	explore	VERB
bracis-28347	55	17	the	the	DET
bracis-28347	55	18	combinatorial	combinatorial	ADJ
bracis-28347	55	19	structures	structure	NOUN
bracis-28347	55	20	of	of	ADP
bracis-28347	55	21	the	the	DET
bracis-28347	55	22	problem	problem	NOUN
bracis-28347	55	23	and	and	CCONJ
bracis-28347	55	24	obtain	obtain	VERB
bracis-28347	55	25	algorithms	algorithm	NOUN
bracis-28347	55	26	involving	involve	VERB
bracis-28347	55	27	branch	branch	NOUN
bracis-28347	55	28	-	-	PUNCT
bracis-28347	55	29	and	and	CCONJ
bracis-28347	55	30	-	-	PUNCT
bracis-28347	55	31	bound	bind	VERB
bracis-28347	55	32	and	and	CCONJ
bracis-28347	55	33	branch	branch	NOUN
bracis-28347	55	34	-	-	PUNCT
bracis-28347	55	35	and	and	CCONJ
bracis-28347	55	36	-	-	PUNCT
bracis-28347	55	37	cut	cut	VERB
bracis-28347	55	38	techniques	technique	NOUN
bracis-28347	55	39	,	,	PUNCT
bracis-28347	55	40	for	for	ADP
bracis-28347	55	41	example	example	NOUN
bracis-28347	55	42	.	.	PUNCT
bracis-28347	56	1	however	however	ADV
bracis-28347	56	2	,	,	PUNCT
bracis-28347	56	3	the	the	DET
bracis-28347	56	4	model	model	NOUN
bracis-28347	56	5	was	be	AUX
bracis-28347	56	6	satisfactorily	satisfactorily	ADV
bracis-28347	56	7	used	use	VERB
bracis-28347	56	8	to	to	PART
bracis-28347	56	9	directly	directly	ADV
bracis-28347	56	10	obtain	obtain	VERB
bracis-28347	56	11	the	the	DET
bracis-28347	56	12	optimal	optimal	ADJ
bracis-28347	56	13	solution	solution	NOUN
bracis-28347	56	14	for	for	ADP
bracis-28347	56	15	large	large	ADJ
bracis-28347	56	16	instances	instance	NOUN
bracis-28347	56	17	to	to	PART
bracis-28347	56	18	be	be	AUX
bracis-28347	56	19	compared	compare	VERB
bracis-28347	56	20	to	to	ADP
bracis-28347	56	21	the	the	DET
bracis-28347	56	22	heuristics	heuristic	NOUN
bracis-28347	56	23	proposed	propose	VERB
bracis-28347	56	24	in	in	ADP
bracis-28347	56	25	this	this	DET
bracis-28347	56	26	paper	paper	NOUN
bracis-28347	56	27	.	.	PUNCT
bracis-28347	57	1	to	to	PART
bracis-28347	57	2	formulate	formulate	VERB
bracis-28347	57	3	the	the	DET
bracis-28347	57	4	mtpp	mtpp	NOUN
bracis-28347	57	5	as	as	ADP
bracis-28347	57	6	an	an	DET
bracis-28347	57	7	integer	integer	NOUN
bracis-28347	57	8	linear	linear	PROPN
bracis-28347	57	9	program	program	NOUN
bracis-28347	57	10	,	,	PUNCT
bracis-28347	57	11	an	an	DET
bracis-28347	57	12	instance	instance	NOUN
bracis-28347	57	13	of	of	ADP
bracis-28347	57	14	this	this	DET
bracis-28347	57	15	problem	problem	NOUN
bracis-28347	57	16	is	be	AUX
bracis-28347	57	17	considered	consider	VERB
bracis-28347	57	18	to	to	PART
bracis-28347	57	19	consist	consist	VERB
bracis-28347	57	20	of	of	ADP
bracis-28347	57	21	a	a	DET
bracis-28347	57	22	graph	graph	NOUN
bracis-28347	57	23	colored	color	VERB
bracis-28347	57	24	at	at	ADP
bracis-28347	57	25	the	the	DET
bracis-28347	57	26	vertices	vertex	NOUN
bracis-28347	57	27	\(g^c	\(g^c	PROPN
bracis-28347	57	28	=	=	SYM
bracis-28347	57	29	(	(	PUNCT
bracis-28347	57	30	g	g	NOUN
bracis-28347	57	31	,	,	PUNCT
bracis-28347	57	32	c)\	c)\	PROPN
bracis-28347	57	33	)	)	PUNCT
bracis-28347	57	34	.	.	PUNCT
bracis-28347	58	1	in	in	ADP
bracis-28347	58	2	the	the	DET
bracis-28347	58	3	presented	present	VERB
bracis-28347	58	4	formulation	formulation	NOUN
bracis-28347	58	5	,	,	PUNCT
bracis-28347	58	6	each	each	DET
bracis-28347	58	7	edge	edge	NOUN
bracis-28347	58	8	\((u	\((u	PROPN
bracis-28347	58	9	,	,	PUNCT
bracis-28347	58	10	v	v	NOUN
bracis-28347	58	11	)	)	PUNCT
bracis-28347	58	12	\in	\in	PROPN
bracis-28347	58	13	e(g)\	e(g)\	NOUN
bracis-28347	58	14	)	)	PUNCT
bracis-28347	58	15	is	be	AUX
bracis-28347	58	16	replaced	replace	VERB
bracis-28347	58	17	by	by	ADP
bracis-28347	58	18	two	two	NUM
bracis-28347	58	19	directed	direct	VERB
bracis-28347	58	20	arcs	arc	NOUN
bracis-28347	58	21	uv	uv	NOUN
bracis-28347	58	22	and	and	CCONJ
bracis-28347	58	23	vu	vu	PROPN
bracis-28347	58	24	.	.	PUNCT
bracis-28347	59	1	variables	variable	NOUN
bracis-28347	59	2	\(x_{uc}\	\(x_{uc}\	PROPN
bracis-28347	59	3	)	)	PUNCT
bracis-28347	59	4	,	,	PUNCT
bracis-28347	59	5	\(y_{uv}\	\(y_{uv}\	NOUN
bracis-28347	59	6	)	)	PUNCT
bracis-28347	59	7	,	,	PUNCT
bracis-28347	59	8	and	and	CCONJ
bracis-28347	59	9	\(z_c\	\(z_c\	NUM
bracis-28347	59	10	)	)	PUNCT
bracis-28347	59	11	,	,	PUNCT
bracis-28347	59	12	\(\forall	\(\forall	ADV
bracis-28347	59	13	u	u	X
bracis-28347	59	14	\in	\in	PROPN
bracis-28347	59	15	v	v	NOUN
bracis-28347	59	16	,	,	PUNCT
bracis-28347	59	17	\forall	\forall	DET
bracis-28347	59	18	uv	uv	PROPN
bracis-28347	59	19	\in	\in	PROPN
bracis-28347	59	20	a\	a\	PROPN
bracis-28347	59	21	)	)	PUNCT
bracis-28347	59	22	,	,	PUNCT
bracis-28347	59	23	and	and	CCONJ
bracis-28347	59	24	\(\forall	\(\forall	ADV
bracis-28347	59	25	c\in	c\in	PROPN
bracis-28347	59	26	\mathcal	\mathcal	PROPN
bracis-28347	59	27	{	{	PUNCT
bracis-28347	59	28	c}\	c}\	NOUN
bracis-28347	59	29	)	)	PUNCT
bracis-28347	59	30	are	be	AUX
bracis-28347	59	31	used	use	VERB
bracis-28347	59	32	and	and	CCONJ
bracis-28347	59	33	are	be	AUX
bracis-28347	59	34	associated	associate	VERB
bracis-28347	59	35	with	with	ADP
bracis-28347	59	36	vertices	vertex	NOUN
bracis-28347	59	37	,	,	PUNCT
bracis-28347	59	38	arcs	arc	NOUN
bracis-28347	59	39	,	,	PUNCT
bracis-28347	59	40	and	and	CCONJ
bracis-28347	59	41	colors	color	NOUN
bracis-28347	59	42	,	,	PUNCT
bracis-28347	59	43	respectively	respectively	ADV
bracis-28347	59	44	.	.	PUNCT
bracis-28347	60	1	the	the	DET
bracis-28347	60	2	variable	variable	ADJ
bracis-28347	60	3	\(x_{u	\(x_{u	NOUN
bracis-28347	60	4	,	,	PUNCT
bracis-28347	60	5	c}=	c}=	PROPN
bracis-28347	60	6	1\	1\	NUM
bracis-28347	60	7	)	)	PUNCT
bracis-28347	60	8	indicates	indicate	VERB
bracis-28347	60	9	that	that	SCONJ
bracis-28347	60	10	the	the	DET
bracis-28347	60	11	vertex	vertex	NOUN
bracis-28347	60	12	u	u	NOUN
bracis-28347	60	13	of	of	ADP
bracis-28347	60	14	color	color	NOUN
bracis-28347	60	15	c	c	NOUN
bracis-28347	60	16	is	be	AUX
bracis-28347	60	17	in	in	ADP
bracis-28347	60	18	the	the	DET
bracis-28347	60	19	solution	solution	NOUN
bracis-28347	60	20	,	,	PUNCT
bracis-28347	60	21	the	the	DET
bracis-28347	60	22	variable	variable	NOUN
bracis-28347	60	23	\(y_{uv	\(y_{uv	PROPN
bracis-28347	60	24	}	}	PUNCT
bracis-28347	60	25	=	=	SYM
bracis-28347	60	26	1	1	NUM
bracis-28347	60	27	\	\	NOUN
bracis-28347	60	28	)	)	PUNCT
bracis-28347	60	29	indicates	indicate	VERB
bracis-28347	60	30	that	that	SCONJ
bracis-28347	60	31	the	the	DET
bracis-28347	60	32	arc	arc	NOUN
bracis-28347	60	33	uv	uv	NOUN
bracis-28347	60	34	is	be	AUX
bracis-28347	60	35	in	in	ADP
bracis-28347	60	36	the	the	DET
bracis-28347	60	37	solution	solution	NOUN
bracis-28347	60	38	,	,	PUNCT
bracis-28347	60	39	and	and	CCONJ
bracis-28347	60	40	the	the	DET
bracis-28347	60	41	variable	variable	NOUN
bracis-28347	60	42	\(z_c	\(z_c	X
bracis-28347	60	43	=	=	SYM
bracis-28347	60	44	1\	1\	NUM
bracis-28347	60	45	)	)	PUNCT
bracis-28347	60	46	imposes	impose	VERB
bracis-28347	60	47	that	that	SCONJ
bracis-28347	60	48	the	the	DET
bracis-28347	60	49	color	color	NOUN
bracis-28347	60	50	c	c	NOUN
bracis-28347	60	51	is	be	AUX
bracis-28347	60	52	in	in	ADP
bracis-28347	60	53	the	the	DET
bracis-28347	60	54	solution	solution	NOUN
bracis-28347	60	55	.	.	PUNCT
bracis-28347	61	1	additionally	additionally	ADV
bracis-28347	61	2	,	,	PUNCT
bracis-28347	61	3	the	the	DET
bracis-28347	61	4	variable	variable	ADJ
bracis-28347	61	5	\(l_v	\(l_v	PROPN
bracis-28347	61	6	\ge	\ge	PROPN
bracis-28347	61	7	0	0	PUNCT
bracis-28347	62	1	~\forall	~\forall	PRON
bracis-28347	62	2	v\in	v\in	VERB
bracis-28347	62	3	v	v	ADP
bracis-28347	62	4	\	\	NOUN
bracis-28347	62	5	)	)	PUNCT
bracis-28347	62	6	is	be	AUX
bracis-28347	62	7	created	create	VERB
bracis-28347	62	8	,	,	PUNCT
bracis-28347	62	9	which	which	PRON
bracis-28347	62	10	allows	allow	VERB
bracis-28347	62	11	us	we	PRON
bracis-28347	62	12	to	to	PART
bracis-28347	62	13	number	number	NOUN
bracis-28347	62	14	(	(	PUNCT
bracis-28347	62	15	label	label	NOUN
bracis-28347	62	16	)	)	PUNCT
bracis-28347	62	17	the	the	DET
bracis-28347	62	18	vertices	vertex	NOUN
bracis-28347	62	19	along	along	ADP
bracis-28347	62	20	the	the	DET
bracis-28347	62	21	path	path	NOUN
bracis-28347	62	22	in	in	ADP
bracis-28347	62	23	increasing	increase	VERB
bracis-28347	62	24	order	order	NOUN
bracis-28347	62	25	.	.	PUNCT
bracis-28347	63	1	this	this	DET
bracis-28347	63	2	variable	variable	NOUN
bracis-28347	63	3	is	be	AUX
bracis-28347	63	4	used	use	VERB
bracis-28347	63	5	in	in	ADP
bracis-28347	63	6	the	the	DET
bracis-28347	63	7	constraint	constraint	NOUN
bracis-28347	63	8	proposed	propose	VERB
bracis-28347	63	9	by	by	ADP
bracis-28347	63	10	miller	miller	PROPN
bracis-28347	63	11	,	,	PUNCT
bracis-28347	63	12	tucker	tucker	PROPN
bracis-28347	63	13	,	,	PUNCT
bracis-28347	63	14	and	and	CCONJ
bracis-28347	63	15	zemlin	zemlin	PROPN
bracis-28347	63	16	(	(	PUNCT
bracis-28347	63	17	1960	1960	NUM
bracis-28347	63	18	)	)	PUNCT
bracis-28347	64	1	[	[	X
bracis-28347	64	2	12	12	NUM
bracis-28347	64	3	]	]	PUNCT
bracis-28347	64	4	to	to	PART
bracis-28347	64	5	eliminate	eliminate	VERB
bracis-28347	64	6	circuits	circuit	NOUN
bracis-28347	64	7	in	in	ADP
bracis-28347	64	8	the	the	DET
bracis-28347	64	9	solution	solution	NOUN
bracis-28347	64	10	.	.	PUNCT
bracis-28347	65	1	3.1	3.1	NUM
bracis-28347	65	2	ilp	ilp	NOUN
bracis-28347	65	3	for	for	ADP
bracis-28347	65	4	 	 	SPACE
bracis-28347	65	5	general	general	ADJ
bracis-28347	65	6	graphs	graph	NOUN
bracis-28347	65	7	in	in	ADP
bracis-28347	65	8	summary	summary	NOUN
bracis-28347	65	9	,	,	PUNCT
bracis-28347	65	10	the	the	DET
bracis-28347	65	11	objective	objective	ADJ
bracis-28347	65	12	function	function	NOUN
bracis-28347	65	13	maximizes	maximize	VERB
bracis-28347	65	14	the	the	DET
bracis-28347	65	15	number	number	NOUN
bracis-28347	65	16	of	of	ADP
bracis-28347	65	17	colors	color	NOUN
bracis-28347	65	18	that	that	PRON
bracis-28347	65	19	should	should	AUX
bracis-28347	65	20	compose	compose	VERB
bracis-28347	65	21	the	the	DET
bracis-28347	65	22	solution	solution	NOUN
bracis-28347	65	23	.	.	PUNCT
bracis-28347	66	1	the	the	DET
bracis-28347	66	2	constraint	constraint	NOUN
bracis-28347	66	3	(	(	PUNCT
bracis-28347	66	4	1	1	X
bracis-28347	66	5	)	)	PUNCT
bracis-28347	66	6	prevents	prevent	VERB
bracis-28347	66	7	the	the	DET
bracis-28347	66	8	variable	variable	NOUN
bracis-28347	66	9	\(z_c\	\(z_c\	ADV
bracis-28347	66	10	)	)	PUNCT
bracis-28347	66	11	from	from	ADP
bracis-28347	66	12	assuming	assume	VERB
bracis-28347	66	13	value	value	NOUN
bracis-28347	66	14	1	1	NUM
bracis-28347	66	15	without	without	ADP
bracis-28347	66	16	at	at	ADV
bracis-28347	66	17	least	least	ADV
bracis-28347	66	18	one	one	NUM
bracis-28347	66	19	vertex	vertex	NOUN
bracis-28347	66	20	of	of	ADP
bracis-28347	66	21	color	color	NOUN
bracis-28347	66	22	c	c	NOUN
bracis-28347	66	23	being	be	AUX
bracis-28347	66	24	in	in	ADP
bracis-28347	66	25	the	the	DET
bracis-28347	66	26	solution	solution	NOUN
bracis-28347	66	27	.	.	PUNCT
bracis-28347	67	1	given	give	VERB
bracis-28347	67	2	a	a	DET
bracis-28347	67	3	vertex	vertex	NOUN
bracis-28347	67	4	v	v	NOUN
bracis-28347	67	5	,	,	PUNCT
bracis-28347	67	6	the	the	DET
bracis-28347	67	7	constraints	constraint	NOUN
bracis-28347	67	8	(	(	PUNCT
bracis-28347	67	9	2	2	NUM
bracis-28347	67	10	)	)	PUNCT
bracis-28347	67	11	and	and	CCONJ
bracis-28347	67	12	(	(	PUNCT
bracis-28347	67	13	3	3	X
bracis-28347	67	14	)	)	PUNCT
bracis-28347	67	15	guarantee	guarantee	VERB
bracis-28347	67	16	that	that	SCONJ
bracis-28347	67	17	if	if	SCONJ
bracis-28347	67	18	a	a	DET
bracis-28347	67	19	vertex	vertex	NOUN
bracis-28347	67	20	v	v	NOUN
bracis-28347	67	21	is	be	AUX
bracis-28347	67	22	in	in	ADP
bracis-28347	67	23	the	the	DET
bracis-28347	67	24	solution	solution	NOUN
bracis-28347	67	25	,	,	PUNCT
bracis-28347	67	26	the	the	DET
bracis-28347	67	27	number	number	NOUN
bracis-28347	67	28	of	of	ADP
bracis-28347	67	29	incoming	incoming	ADJ
bracis-28347	67	30	and	and	CCONJ
bracis-28347	67	31	outgoing	outgoing	ADJ
bracis-28347	67	32	arcs	arc	NOUN
bracis-28347	67	33	of	of	ADP
bracis-28347	67	34	v	v	NOUN
bracis-28347	67	35	will	will	AUX
bracis-28347	67	36	be	be	AUX
bracis-28347	67	37	at	at	ADP
bracis-28347	67	38	most	most	ADV
bracis-28347	67	39	1	1	NUM
bracis-28347	67	40	,	,	PUNCT
bracis-28347	67	41	respectively	respectively	ADV
bracis-28347	67	42	;	;	PUNCT
bracis-28347	67	43	the	the	DET
bracis-28347	67	44	constraint	constraint	NOUN
bracis-28347	67	45	(	(	PUNCT
bracis-28347	67	46	4	4	X
bracis-28347	67	47	)	)	PUNCT
bracis-28347	67	48	makes	make	VERB
bracis-28347	67	49	use	use	NOUN
bracis-28347	67	50	of	of	ADP
bracis-28347	67	51	the	the	DET
bracis-28347	67	52	function	function	NOUN
bracis-28347	67	53	\(l_v\	\(l_v\	NOUN
bracis-28347	67	54	)	)	PUNCT
bracis-28347	67	55	that	that	PRON
bracis-28347	67	56	allows	allow	VERB
bracis-28347	67	57	to	to	PART
bracis-28347	67	58	number	number	VERB
bracis-28347	67	59	the	the	DET
bracis-28347	67	60	vertices	vertex	NOUN
bracis-28347	67	61	along	along	ADP
bracis-28347	67	62	the	the	DET
bracis-28347	67	63	path	path	NOUN
bracis-28347	67	64	in	in	ADP
bracis-28347	67	65	increasing	increase	VERB
bracis-28347	67	66	order	order	NOUN
bracis-28347	67	67	.	.	PUNCT
bracis-28347	68	1	this	this	DET
bracis-28347	68	2	inequality	inequality	NOUN
bracis-28347	68	3	is	be	AUX
bracis-28347	68	4	essential	essential	ADJ
bracis-28347	68	5	to	to	PART
bracis-28347	68	6	avoid	avoid	VERB
bracis-28347	68	7	cycles	cycle	NOUN
bracis-28347	68	8	in	in	ADP
bracis-28347	68	9	the	the	DET
bracis-28347	68	10	solution	solution	NOUN
bracis-28347	68	11	.	.	PUNCT
bracis-28347	69	1	the	the	DET
bracis-28347	69	2	equality	equality	NOUN
bracis-28347	69	3	(	(	PUNCT
bracis-28347	69	4	5	5	NUM
bracis-28347	69	5	)	)	PUNCT
bracis-28347	69	6	guarantees	guarantee	VERB
bracis-28347	69	7	that	that	SCONJ
bracis-28347	69	8	the	the	DET
bracis-28347	69	9	difference	difference	NOUN
bracis-28347	69	10	between	between	ADP
bracis-28347	69	11	the	the	DET
bracis-28347	69	12	number	number	NOUN
bracis-28347	69	13	of	of	ADP
bracis-28347	69	14	vertices	vertex	NOUN
bracis-28347	69	15	and	and	CCONJ
bracis-28347	69	16	the	the	DET
bracis-28347	69	17	number	number	NOUN
bracis-28347	69	18	of	of	ADP
bracis-28347	69	19	edges	edge	NOUN
bracis-28347	69	20	that	that	PRON
bracis-28347	69	21	make	make	VERB
bracis-28347	69	22	up	up	ADP
bracis-28347	69	23	the	the	DET
bracis-28347	69	24	solution	solution	NOUN
bracis-28347	69	25	is	be	AUX
bracis-28347	69	26	exactly	exactly	ADV
bracis-28347	69	27	1	1	NUM
bracis-28347	69	28	.	.	PUNCT
bracis-28347	70	1	the	the	DET
bracis-28347	70	2	constraints	constraint	NOUN
bracis-28347	70	3	(	(	PUNCT
bracis-28347	70	4	6	6	NUM
bracis-28347	70	5	)	)	PUNCT
bracis-28347	70	6	and	and	CCONJ
bracis-28347	70	7	(	(	PUNCT
bracis-28347	70	8	7	7	X
bracis-28347	70	9	)	)	PUNCT
bracis-28347	70	10	guarantee	guarantee	VERB
bracis-28347	70	11	the	the	DET
bracis-28347	70	12	integrality	integrality	NOUN
bracis-28347	70	13	of	of	ADP
bracis-28347	70	14	variables	variable	NOUN
bracis-28347	70	15	.	.	PUNCT
bracis-28347	71	1	$	$	SYM
bracis-28347	71	2	$	$	SYM
bracis-28347	71	3	\begin{aligned	\begin{aligne	VERB
bracis-28347	71	4	}	}	PUNCT
bracis-28347	71	5	\!\!\!\!\!\!\!\!\	\!\!\!\!\!\!\!\!\	PROPN
bracis-28347	71	6	!	!	PUNCT
bracis-28347	71	7	{	{	PUNCT
bracis-28347	71	8	}	}	PUNCT
bracis-28347	71	9	&	&	CCONJ
bracis-28347	71	10	{	{	PUNCT
bracis-28347	71	11	}	}	PUNCT
bracis-28347	71	12	&	&	CCONJ
bracis-28347	71	13	\,\,\,\,\,\,\,\,\,\,\text	\,\,\,\,\,\,\,\,\,\,\text	PROPN
bracis-28347	71	14	{	{	PUNCT
bracis-28347	71	15	max	max	PROPN
bracis-28347	71	16	}	}	PUNCT
bracis-28347	71	17	\	\	PROPN
bracis-28347	71	18	,	,	PUNCT
bracis-28347	71	19	\sum	\sum	NOUN
bracis-28347	71	20	_	_	PUNCT
bracis-28347	71	21	{	{	PUNCT
bracis-28347	71	22	c	c	PROPN
bracis-28347	71	23	\in	\in	PROPN
bracis-28347	71	24	\mathcal	\mathcal	PROPN
bracis-28347	71	25	{	{	PUNCT
bracis-28347	71	26	c	c	NOUN
bracis-28347	71	27	}	}	PUNCT
bracis-28347	71	28	}	}	PUNCT
bracis-28347	71	29	z_{c	z_{c	NOUN
bracis-28347	71	30	}	}	PUNCT
bracis-28347	71	31	\nonumber	\nonumber	PROPN
bracis-28347	71	32	\\	\\	NOUN
bracis-28347	71	33	{	{	PUNCT
bracis-28347	71	34	}	}	PUNCT
bracis-28347	71	35	&	&	CCONJ
bracis-28347	71	36	{	{	PUNCT
bracis-28347	71	37	}	}	PUNCT
bracis-28347	71	38	\text	\text	PROPN
bracis-28347	71	39	{	{	PUNCT
bracis-28347	71	40	s.	s.	PROPN
bracis-28347	71	41	t.	t.	PROPN
bracis-28347	71	42	}	}	PUNCT
bracis-28347	71	43	\	\	PROPN
bracis-28347	71	44	,	,	PUNCT
bracis-28347	71	45	\	\	PROPN
bracis-28347	71	46	,	,	PUNCT
bracis-28347	71	47	{	{	PUNCT
bracis-28347	71	48	}	}	PUNCT
bracis-28347	71	49	&	&	CCONJ
bracis-28347	71	50	{	{	PUNCT
bracis-28347	71	51	}	}	PUNCT
bracis-28347	71	52	{	{	PUNCT
bracis-28347	71	53	}	}	PUNCT
bracis-28347	71	54	&	&	CCONJ
bracis-28347	71	55	{	{	PUNCT
bracis-28347	71	56	}	}	SYM
bracis-28347	71	57	\nonumber	\nonumber	PROPN
bracis-28347	71	58	\\	\\	NOUN
bracis-28347	71	59	{	{	PUNCT
bracis-28347	71	60	}	}	PUNCT
bracis-28347	71	61	&	&	CCONJ
bracis-28347	71	62	{	{	PUNCT
bracis-28347	71	63	}	}	PUNCT
bracis-28347	71	64	&	&	CCONJ
bracis-28347	71	65	z_{c	z_{c	PROPN
bracis-28347	71	66	}	}	PUNCT
bracis-28347	71	67	\le	\le	NOUN
bracis-28347	71	68	\sum	\sum	NOUN
bracis-28347	71	69	_	_	PUNCT
bracis-28347	71	70	{	{	PUNCT
bracis-28347	71	71	u	u	NOUN
bracis-28347	71	72	\in	\in	PROPN
bracis-28347	71	73	v	v	NOUN
bracis-28347	71	74	}	}	PUNCT
bracis-28347	71	75	x_{uc	x_{uc	PROPN
bracis-28347	71	76	}	}	PUNCT
bracis-28347	71	77	,	,	PUNCT
bracis-28347	71	78	{	{	PUNCT
bracis-28347	71	79	}	}	PUNCT
bracis-28347	71	80	&	&	CCONJ
bracis-28347	71	81	{	{	PUNCT
bracis-28347	71	82	}	}	PUNCT
bracis-28347	71	83	\forall	\forall	PRON
bracis-28347	71	84	c	c	PROPN
bracis-28347	71	85	\in	\in	PROPN
bracis-28347	71	86	\mathcal	\mathcal	PROPN
bracis-28347	71	87	{	{	PUNCT
bracis-28347	71	88	c	c	NOUN
bracis-28347	71	89	}	}	PUNCT
bracis-28347	71	90	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	71	91	(	(	PUNCT
bracis-28347	71	92	1	1	NUM
bracis-28347	71	93	)	)	PUNCT
bracis-28347	71	94	$	$	SYM
bracis-28347	71	95	$	$	SYM
bracis-28347	71	96	\begin{aligned	\begin{aligne	VERB
bracis-28347	71	97	}	}	PUNCT
bracis-28347	71	98	{	{	PUNCT
bracis-28347	71	99	}	}	PUNCT
bracis-28347	71	100	&	&	CCONJ
bracis-28347	71	101	{	{	PUNCT
bracis-28347	71	102	}	}	PUNCT
bracis-28347	71	103	&	&	CCONJ
bracis-28347	71	104	\sum	\sum	NOUN
bracis-28347	71	105	_	_	PUNCT
bracis-28347	71	106	{	{	PUNCT
bracis-28347	71	107	c	c	PROPN
bracis-28347	71	108	\in	\in	PROPN
bracis-28347	71	109	\mathcal	\mathcal	PROPN
bracis-28347	71	110	{	{	PUNCT
bracis-28347	71	111	c	c	NOUN
bracis-28347	71	112	}	}	PUNCT
bracis-28347	71	113	}	}	PUNCT
bracis-28347	71	114	x_{vc	x_{vc	ADJ
bracis-28347	71	115	}	}	PUNCT
bracis-28347	71	116	\sum	\sum	NOUN
bracis-28347	72	1	_	_	PUNCT
bracis-28347	72	2	{	{	PUNCT
bracis-28347	72	3	u	u	PROPN
bracis-28347	72	4	\in	\in	PROPN
bracis-28347	72	5	\delta	\delta	PROPN
bracis-28347	72	6	^-(v	^-(v	PROPN
bracis-28347	72	7	)	)	PUNCT
bracis-28347	72	8	}	}	PUNCT
bracis-28347	72	9	y_{uv	y_{uv	NOUN
bracis-28347	72	10	}	}	PUNCT
bracis-28347	72	11	\ge	\ge	PROPN
bracis-28347	72	12	0	0	NUM
bracis-28347	72	13	,	,	PUNCT
bracis-28347	72	14	{	{	PUNCT
bracis-28347	72	15	}	}	PUNCT
bracis-28347	72	16	&	&	CCONJ
bracis-28347	72	17	{	{	PUNCT
bracis-28347	72	18	}	}	PUNCT
bracis-28347	72	19	\forall	\forall	PRON
bracis-28347	72	20	v	v	ADP
bracis-28347	72	21	\in	\in	PROPN
bracis-28347	72	22	v	v	NOUN
bracis-28347	72	23	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	72	24	(	(	PUNCT
bracis-28347	72	25	2	2	NUM
bracis-28347	72	26	)	)	PUNCT
bracis-28347	72	27	$	$	SYM
bracis-28347	72	28	$	$	SYM
bracis-28347	72	29	\begin{aligned	\begin{aligne	VERB
bracis-28347	72	30	}	}	PUNCT
bracis-28347	72	31	{	{	PUNCT
bracis-28347	72	32	}	}	PUNCT
bracis-28347	72	33	&	&	CCONJ
bracis-28347	72	34	{	{	PUNCT
bracis-28347	72	35	}	}	PUNCT
bracis-28347	72	36	&	&	CCONJ
bracis-28347	72	37	\sum	\sum	NOUN
bracis-28347	72	38	_	_	PUNCT
bracis-28347	72	39	{	{	PUNCT
bracis-28347	72	40	c	c	PROPN
bracis-28347	72	41	\in	\in	PROPN
bracis-28347	72	42	\mathcal	\mathcal	PROPN
bracis-28347	72	43	{	{	PUNCT
bracis-28347	72	44	c	c	NOUN
bracis-28347	72	45	}	}	PUNCT
bracis-28347	72	46	}	}	PUNCT
bracis-28347	72	47	x_{vc	x_{vc	ADJ
bracis-28347	72	48	}	}	PUNCT
bracis-28347	72	49	\sum	\sum	NOUN
bracis-28347	73	1	_	_	PUNCT
bracis-28347	73	2	{	{	PUNCT
bracis-28347	73	3	w	w	PROPN
bracis-28347	73	4	\in	\in	PROPN
bracis-28347	73	5	\delta	\delta	PROPN
bracis-28347	73	6	^+(v	^+(v	PUNCT
bracis-28347	73	7	)	)	PUNCT
bracis-28347	73	8	}	}	PUNCT
bracis-28347	73	9	y_{vw	y_{vw	NOUN
bracis-28347	73	10	}	}	PUNCT
bracis-28347	73	11	\ge	\ge	PROPN
bracis-28347	73	12	0	0	NUM
bracis-28347	73	13	,	,	PUNCT
bracis-28347	73	14	{	{	PUNCT
bracis-28347	73	15	}	}	PUNCT
bracis-28347	73	16	&	&	CCONJ
bracis-28347	73	17	{	{	PUNCT
bracis-28347	73	18	}	}	PUNCT
bracis-28347	73	19	\forall	\forall	PRON
bracis-28347	73	20	v	v	ADP
bracis-28347	73	21	\in	\in	PROPN
bracis-28347	73	22	v	v	NOUN
bracis-28347	73	23	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	73	24	(	(	PUNCT
bracis-28347	73	25	3	3	NUM
bracis-28347	73	26	)	)	PUNCT
bracis-28347	73	27	$	$	SYM
bracis-28347	73	28	$	$	SYM
bracis-28347	73	29	\begin{aligned	\begin{aligne	VERB
bracis-28347	73	30	}	}	PUNCT
bracis-28347	73	31	{	{	PUNCT
bracis-28347	73	32	}	}	PUNCT
bracis-28347	73	33	&	&	CCONJ
bracis-28347	73	34	{	{	PUNCT
bracis-28347	73	35	}	}	PUNCT
bracis-28347	73	36	&	&	CCONJ
bracis-28347	73	37	(	(	PUNCT
bracis-28347	73	38	l_v	l_v	PROPN
bracis-28347	73	39	l_u	l_u	PRON
bracis-28347	73	40	)	)	PUNCT
bracis-28347	73	41	\ge	\ge	PROPN
bracis-28347	73	42	_	_	NOUN
bracis-28347	73	43	{	{	PUNCT
bracis-28347	73	44	}	}	PUNCT
bracis-28347	73	45	y_{uv	y_{uv	NOUN
bracis-28347	73	46	}	}	PUNCT
bracis-28347	73	47	(	(	PUNCT
bracis-28347	73	48	1	1	NUM
bracis-28347	73	49	y_{uv})n	y_{uv})n	NOUN
bracis-28347	73	50	,	,	PUNCT
bracis-28347	73	51	{	{	PUNCT
bracis-28347	73	52	}	}	PUNCT
bracis-28347	73	53	&	&	CCONJ
bracis-28347	73	54	{	{	PUNCT
bracis-28347	73	55	}	}	PUNCT
bracis-28347	73	56	\forall	\forall	DET
bracis-28347	73	57	uv	uv	PROPN
bracis-28347	73	58	\in	\in	PROPN
bracis-28347	73	59	a	a	PRON
bracis-28347	73	60	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	73	61	(	(	PUNCT
bracis-28347	73	62	4	4	NUM
bracis-28347	73	63	)	)	PUNCT
bracis-28347	73	64	$	$	SYM
bracis-28347	73	65	$	$	SYM
bracis-28347	73	66	\begin{aligned	\begin{aligne	VERB
bracis-28347	73	67	}	}	PUNCT
bracis-28347	73	68	{	{	PUNCT
bracis-28347	73	69	}	}	PUNCT
bracis-28347	73	70	&	&	CCONJ
bracis-28347	73	71	{	{	PUNCT
bracis-28347	73	72	}	}	PUNCT
bracis-28347	73	73	&	&	CCONJ
bracis-28347	73	74	\sum	\sum	NOUN
bracis-28347	73	75	_	_	PUNCT
bracis-28347	73	76	{	{	PUNCT
bracis-28347	73	77	u	u	NOUN
bracis-28347	73	78	\in	\in	PROPN
bracis-28347	73	79	v	v	NOUN
bracis-28347	73	80	}	}	PUNCT
bracis-28347	73	81	\sum	\sum	NOUN
bracis-28347	74	1	_	_	PUNCT
bracis-28347	74	2	{	{	PUNCT
bracis-28347	74	3	c	c	PROPN
bracis-28347	74	4	\in	\in	PROPN
bracis-28347	74	5	\mathcal	\mathcal	PROPN
bracis-28347	74	6	{	{	PUNCT
bracis-28347	74	7	c	c	NOUN
bracis-28347	74	8	}	}	PUNCT
bracis-28347	74	9	}	}	PUNCT
bracis-28347	74	10	x_{uc	x_{uc	ADJ
bracis-28347	74	11	}	}	PUNCT
bracis-28347	74	12	\sum	\sum	NOUN
bracis-28347	75	1	_	_	PUNCT
bracis-28347	75	2	{	{	PUNCT
bracis-28347	75	3	u	u	NOUN
bracis-28347	75	4	\in	\in	PROPN
bracis-28347	75	5	v	v	NOUN
bracis-28347	75	6	}	}	PUNCT
bracis-28347	75	7	\sum	\sum	NOUN
bracis-28347	76	1	_	_	PUNCT
bracis-28347	76	2	{	{	PUNCT
bracis-28347	76	3	v	v	ADP
bracis-28347	76	4	\in	\in	PROPN
bracis-28347	76	5	v	v	NOUN
bracis-28347	76	6	}	}	PUNCT
bracis-28347	76	7	y_{uv	y_{uv	NOUN
bracis-28347	76	8	}	}	PUNCT
bracis-28347	76	9	=	=	SYM
bracis-28347	76	10	1	1	NUM
bracis-28347	76	11	,	,	PUNCT
bracis-28347	76	12	{	{	PUNCT
bracis-28347	76	13	}	}	PUNCT
bracis-28347	76	14	&	&	CCONJ
bracis-28347	76	15	{	{	PUNCT
bracis-28347	76	16	}	}	PUNCT
bracis-28347	76	17	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	76	18	(	(	PUNCT
bracis-28347	76	19	5	5	NUM
bracis-28347	76	20	)	)	PUNCT
bracis-28347	76	21	$	$	SYM
bracis-28347	76	22	$	$	SYM
bracis-28347	76	23	\begin{aligned	\begin{aligne	VERB
bracis-28347	76	24	}	}	PUNCT
bracis-28347	76	25	{	{	PUNCT
bracis-28347	76	26	}	}	PUNCT
bracis-28347	76	27	&	&	CCONJ
bracis-28347	76	28	{	{	PUNCT
bracis-28347	76	29	}	}	PUNCT
bracis-28347	76	30	&	&	CCONJ
bracis-28347	76	31	x_{uc	x_{uc	PROPN
bracis-28347	76	32	}	}	PUNCT
bracis-28347	76	33	,	,	PUNCT
bracis-28347	76	34	y_{uv	y_{uv	NOUN
bracis-28347	76	35	}	}	PUNCT
bracis-28347	76	36	\in	\in	PROPN
bracis-28347	76	37	\left\	\left\	PROPN
bracis-28347	76	38	{	{	PUNCT
bracis-28347	76	39	0,1\right\	0,1\right\	NOUN
bracis-28347	76	40	}	}	PUNCT
bracis-28347	76	41	_	_	NOUN
bracis-28347	76	42	{	{	PUNCT
bracis-28347	76	43	}	}	PUNCT
bracis-28347	76	44	,	,	PUNCT
bracis-28347	76	45	{	{	PUNCT
bracis-28347	76	46	}	}	PUNCT
bracis-28347	76	47	&	&	CCONJ
bracis-28347	76	48	{	{	PUNCT
bracis-28347	76	49	}	}	PUNCT
bracis-28347	76	50	\forall	\forall	DET
bracis-28347	76	51	u	u	NOUN
bracis-28347	76	52	\in	\in	PROPN
bracis-28347	76	53	v	v	NOUN
bracis-28347	76	54	,	,	PUNCT
bracis-28347	76	55	\forall	\forall	DET
bracis-28347	76	56	uv	uv	PROPN
bracis-28347	76	57	\in	\in	PROPN
bracis-28347	76	58	a	a	NOUN
bracis-28347	76	59	,	,	PUNCT
bracis-28347	76	60	\forall	\forall	DET
bracis-28347	76	61	c\in	c\in	PROPN
bracis-28347	77	1	\mathcal	\mathcal	ADJ
bracis-28347	77	2	{	{	PUNCT
bracis-28347	77	3	c	c	NOUN
bracis-28347	77	4	}	}	PUNCT
bracis-28347	77	5	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	77	6	(	(	PUNCT
bracis-28347	77	7	6	6	NUM
bracis-28347	77	8	)	)	PUNCT
bracis-28347	77	9	$	$	SYM
bracis-28347	77	10	$	$	SYM
bracis-28347	77	11	\begin{aligned	\begin{aligne	VERB
bracis-28347	77	12	}	}	PUNCT
bracis-28347	77	13	{	{	PUNCT
bracis-28347	77	14	}	}	PUNCT
bracis-28347	77	15	&	&	CCONJ
bracis-28347	77	16	{	{	PUNCT
bracis-28347	77	17	}	}	PUNCT
bracis-28347	77	18	&	&	CCONJ
bracis-28347	77	19	z_c	z_c	PROPN
bracis-28347	77	20	\in	\in	PROPN
bracis-28347	77	21	\left\	\left\	PROPN
bracis-28347	77	22	{	{	PUNCT
bracis-28347	77	23	0,1\right\	0,1\right\	NOUN
bracis-28347	77	24	}	}	PUNCT
bracis-28347	77	25	,	,	PUNCT
bracis-28347	77	26	l_v	l_v	PROPN
bracis-28347	78	1	\ge	\ge	PROPN
bracis-28347	78	2	0	0	NUM
bracis-28347	78	3	;	;	PUNCT
bracis-28347	78	4	{	{	PUNCT
bracis-28347	78	5	}	}	PUNCT
bracis-28347	78	6	&	&	CCONJ
bracis-28347	78	7	{	{	PUNCT
bracis-28347	78	8	}	}	PUNCT
bracis-28347	78	9	\forall	\forall	DET
bracis-28347	78	10	v\in	v\in	VERB
bracis-28347	78	11	v	v	NOUN
bracis-28347	78	12	,	,	PUNCT
bracis-28347	78	13	\forall	\forall	DET
bracis-28347	78	14	c	c	PROPN
bracis-28347	78	15	\in	\in	PROPN
bracis-28347	78	16	\mathcal	\mathcal	PROPN
bracis-28347	78	17	{	{	PUNCT
bracis-28347	78	18	c	c	NOUN
bracis-28347	78	19	}	}	PUNCT
bracis-28347	78	20	\end{aligned}$$	\end{aligned}$$	X
bracis-28347	78	21	(	(	PUNCT
bracis-28347	78	22	7	7	X
bracis-28347	78	23	)	)	PUNCT
bracis-28347	78	24	note	note	NOUN
bracis-28347	78	25	that	that	SCONJ
bracis-28347	78	26	the	the	DET
bracis-28347	78	27	proposed	propose	VERB
bracis-28347	78	28	formulation	formulation	NOUN
bracis-28347	78	29	has	have	VERB
bracis-28347	78	30	a	a	DET
bracis-28347	78	31	linear	linear	ADJ
bracis-28347	78	32	amount	amount	NOUN
bracis-28347	78	33	of	of	ADP
bracis-28347	78	34	inequalities	inequality	NOUN
bracis-28347	78	35	added	add	VERB
bracis-28347	78	36	to	to	ADP
bracis-28347	78	37	the	the	DET
bracis-28347	78	38	model	model	NOUN
bracis-28347	78	39	as	as	SCONJ
bracis-28347	78	40	the	the	DET
bracis-28347	78	41	(	(	PUNCT
bracis-28347	78	42	1	1	NUM
bracis-28347	78	43	)	)	PUNCT
bracis-28347	78	44	constraints	constraint	NOUN
bracis-28347	78	45	add	add	VERB
bracis-28347	78	46	\(|\mathcal	\(|\mathcal	PUNCT
bracis-28347	78	47	{	{	PUNCT
bracis-28347	78	48	c}|\	c}|\	NOUN
bracis-28347	78	49	)	)	PUNCT
bracis-28347	78	50	inequalities	inequality	NOUN
bracis-28347	78	51	to	to	ADP
bracis-28347	78	52	the	the	DET
bracis-28347	78	53	model	model	NOUN
bracis-28347	78	54	,	,	PUNCT
bracis-28347	78	55	while	while	SCONJ
bracis-28347	78	56	the	the	DET
bracis-28347	78	57	(	(	PUNCT
bracis-28347	78	58	2	2	NUM
bracis-28347	78	59	)	)	PUNCT
bracis-28347	78	60	and	and	CCONJ
bracis-28347	78	61	(	(	PUNCT
bracis-28347	78	62	3	3	X
bracis-28347	78	63	)	)	PUNCT
bracis-28347	78	64	constraints	constraint	NOUN
bracis-28347	78	65	each	each	PRON
bracis-28347	78	66	add	add	VERB
bracis-28347	78	67	|v|	|v|	NUM
bracis-28347	78	68	inequalities	inequality	NOUN
bracis-28347	78	69	,	,	PUNCT
bracis-28347	78	70	and	and	CCONJ
bracis-28347	78	71	the	the	DET
bracis-28347	78	72	(	(	PUNCT
bracis-28347	78	73	4	4	NUM
bracis-28347	78	74	)	)	PUNCT
bracis-28347	78	75	constraints	constraint	NOUN
bracis-28347	78	76	add	add	VERB
bracis-28347	78	77	2|a|	2|a|	NUM
bracis-28347	78	78	inequalities	inequality	NOUN
bracis-28347	78	79	.	.	PUNCT
bracis-28347	79	1	last	last	ADJ
bracis-28347	79	2	,	,	PUNCT
bracis-28347	79	3	the	the	DET
bracis-28347	79	4	(	(	PUNCT
bracis-28347	79	5	5	5	NUM
bracis-28347	79	6	)	)	PUNCT
bracis-28347	79	7	adds	add	VERB
bracis-28347	79	8	only	only	ADV
bracis-28347	79	9	one	one	NUM
bracis-28347	79	10	inequality	inequality	NOUN
bracis-28347	79	11	to	to	ADP
bracis-28347	79	12	the	the	DET
bracis-28347	79	13	model	model	NOUN
bracis-28347	79	14	,	,	PUNCT
bracis-28347	79	15	totaling	total	VERB
bracis-28347	79	16	a	a	DET
bracis-28347	79	17	set	set	NOUN
bracis-28347	79	18	of	of	ADP
bracis-28347	79	19	\(|\mathcal	\(|\mathcal	X
bracis-28347	79	20	{	{	PUNCT
bracis-28347	79	21	c}|	c}|	NOUN
bracis-28347	79	22	+	+	SYM
bracis-28347	79	23	2|v|	2|v|	NUM
bracis-28347	79	24	+	+	CCONJ
bracis-28347	79	25	2|a|	2|a|	NUM
bracis-28347	79	26	+	+	CCONJ
bracis-28347	79	27	1\	1\	NUM
bracis-28347	79	28	)	)	PUNCT
bracis-28347	79	29	linear	linear	ADJ
bracis-28347	79	30	inequalities	inequality	NOUN
bracis-28347	79	31	.	.	PUNCT
bracis-28347	80	1	theorem	theorem	VERB
bracis-28347	80	2	1	1	NUM
bracis-28347	80	3	the	the	DET
bracis-28347	80	4	restricted	restrict	VERB
bracis-28347	80	5	solution	solution	NOUN
bracis-28347	80	6	x	x	X
bracis-28347	80	7	of	of	ADP
bracis-28347	80	8	the	the	DET
bracis-28347	80	9	integer	integer	NOUN
bracis-28347	80	10	solutions	solution	NOUN
bracis-28347	80	11	(	(	PUNCT
bracis-28347	80	12	x	x	NOUN
bracis-28347	80	13	,	,	PUNCT
bracis-28347	80	14	 	 	SPACE
bracis-28347	80	15	y	y	PROPN
bracis-28347	80	16	,	,	PUNCT
bracis-28347	80	17	 	 	SPACE
bracis-28347	80	18	z	z	NOUN
bracis-28347	80	19	)	)	PUNCT
bracis-28347	80	20	for	for	ADP
bracis-28347	80	21	the	the	DET
bracis-28347	80	22	formulation	formulation	NOUN
bracis-28347	80	23	from	from	ADP
bracis-28347	80	24	(	(	PUNCT
bracis-28347	80	25	1	1	NUM
bracis-28347	80	26	)	)	PUNCT
bracis-28347	80	27	to	to	ADP
bracis-28347	80	28	(	(	PUNCT
bracis-28347	80	29	7	7	X
bracis-28347	80	30	)	)	PUNCT
bracis-28347	80	31	defines	define	VERB
bracis-28347	80	32	a	a	DET
bracis-28347	80	33	path	path	NOUN
bracis-28347	80	34	on	on	ADP
bracis-28347	80	35	the	the	DET
bracis-28347	80	36	graph	graph	NOUN
bracis-28347	80	37	(	(	PUNCT
bracis-28347	80	38	g	g	NOUN
bracis-28347	80	39	,	,	PUNCT
bracis-28347	80	40	 	 	SPACE
bracis-28347	80	41	c	c	NOUN
bracis-28347	80	42	)	)	PUNCT
bracis-28347	80	43	that	that	PRON
bracis-28347	80	44	uses	use	VERB
bracis-28347	80	45	\(|\mathcal	\(|\mathcal	NOUN
bracis-28347	80	46	{	{	PUNCT
bracis-28347	80	47	c'}|\	c'}|\	NOUN
bracis-28347	80	48	)	)	PUNCT
bracis-28347	80	49	colors	color	NOUN
bracis-28347	80	50	,	,	PUNCT
bracis-28347	80	51	where	where	SCONJ
bracis-28347	80	52	\(\mathcal	\(\mathcal	ADJ
bracis-28347	80	53	{	{	PUNCT
bracis-28347	80	54	c	c	NOUN
bracis-28347	80	55	'	'	PUNCT
bracis-28347	80	56	}	}	PUNCT
bracis-28347	80	57	\subseteq	\subseteq	PROPN
bracis-28347	80	58	\mathcal	\mathcal	PROPN
bracis-28347	80	59	{	{	PUNCT
bracis-28347	80	60	c}\	c}\	NUM
bracis-28347	80	61	)	)	PUNCT
bracis-28347	80	62	.	.	PUNCT
bracis-28347	81	1	proof	proof	NOUN
bracis-28347	81	2	for	for	ADP
bracis-28347	81	3	any	any	DET
bracis-28347	81	4	feasible	feasible	ADJ
bracis-28347	81	5	integer	integer	NOUN
bracis-28347	81	6	solution	solution	NOUN
bracis-28347	81	7	(	(	PUNCT
bracis-28347	81	8	x	x	NOUN
bracis-28347	81	9	,	,	PUNCT
bracis-28347	81	10	 	 	SPACE
bracis-28347	81	11	y	y	PROPN
bracis-28347	81	12	,	,	PUNCT
bracis-28347	81	13	 	 	SPACE
bracis-28347	81	14	z	z	NOUN
bracis-28347	81	15	)	)	PUNCT
bracis-28347	81	16	of	of	ADP
bracis-28347	81	17	the	the	DET
bracis-28347	81	18	formulation	formulation	NOUN
bracis-28347	81	19	,	,	PUNCT
bracis-28347	81	20	let	let	VERB
bracis-28347	81	21	\(v_{p	\(v_{p	NOUN
bracis-28347	81	22	}	}	PUNCT
bracis-28347	81	23	=	=	PUNCT
bracis-28347	81	24	\{u	\{u	ADV
bracis-28347	81	25	:	:	PUNCT
bracis-28347	81	26	x_{uc}=1\}\	x_{uc}=1\}\	PROPN
bracis-28347	81	27	)	)	PUNCT
bracis-28347	81	28	,	,	PUNCT
bracis-28347	81	29	\(a_{p	\(a_{p	VERB
bracis-28347	81	30	}	}	PUNCT
bracis-28347	81	31	=	=	SYM
bracis-28347	81	32	\{uv	\{uv	NOUN
bracis-28347	81	33	:	:	PUNCT
bracis-28347	81	34	y_{uv}=1\}\	y_{uv}=1\}\	NOUN
bracis-28347	81	35	)	)	PUNCT
bracis-28347	81	36	,	,	PUNCT
bracis-28347	81	37	and	and	CCONJ
bracis-28347	81	38	\(c_p	\(c_p	PROPN
bracis-28347	81	39	=	=	SYM
bracis-28347	81	40	\{c	\{c	PROPN
bracis-28347	81	41	:	:	PUNCT
bracis-28347	81	42	z_c	z_c	PUNCT
bracis-28347	81	43	=	=	SYM
bracis-28347	81	44	1\}\	1\}\	NUM
bracis-28347	81	45	)	)	PUNCT
bracis-28347	81	46	.	.	PUNCT
bracis-28347	82	1	note	note	VERB
bracis-28347	82	2	that	that	SCONJ
bracis-28347	82	3	if	if	SCONJ
bracis-28347	82	4	a	a	DET
bracis-28347	82	5	vertex	vertex	NOUN
bracis-28347	82	6	\(u\in	\(u\in	X
bracis-28347	82	7	v_{p}\	v_{p}\	PROPN
bracis-28347	82	8	)	)	PUNCT
bracis-28347	82	9	,	,	PUNCT
bracis-28347	82	10	then	then	ADV
bracis-28347	82	11	\(c	\(c	PROPN
bracis-28347	82	12	\in	\in	PROPN
bracis-28347	82	13	c_p\	c_p\	PROPN
bracis-28347	82	14	)	)	PUNCT
bracis-28347	82	15	.	.	PUNCT
bracis-28347	83	1	let	let	VERB
bracis-28347	83	2	\(\mathcal	\(\mathcal	ADJ
bracis-28347	83	3	{	{	PUNCT
bracis-28347	83	4	c'}\	c'}\	NOUN
bracis-28347	83	5	)	)	PUNCT
bracis-28347	83	6	be	be	VERB
bracis-28347	83	7	the	the	DET
bracis-28347	83	8	set	set	NOUN
bracis-28347	83	9	formed	form	VERB
bracis-28347	83	10	by	by	ADP
bracis-28347	83	11	the	the	DET
bracis-28347	83	12	colors	color	NOUN
bracis-28347	83	13	of	of	ADP
bracis-28347	83	14	vertices	vertex	NOUN
bracis-28347	83	15	where	where	SCONJ
bracis-28347	83	16	\(x_{uc}=1\	\(x_{uc}=1\	NOUN
bracis-28347	83	17	)	)	PUNCT
bracis-28347	83	18	.	.	PUNCT
bracis-28347	84	1	if	if	SCONJ
bracis-28347	84	2	an	an	DET
bracis-28347	84	3	arc	arc	NOUN
bracis-28347	84	4	\(uv	\(uv	NOUN
bracis-28347	84	5	\in	\in	PROPN
bracis-28347	84	6	a_p\	a_p\	NOUN
bracis-28347	84	7	)	)	PUNCT
bracis-28347	84	8	,	,	PUNCT
bracis-28347	84	9	by	by	ADP
bracis-28347	84	10	the	the	DET
bracis-28347	84	11	constraint	constraint	NOUN
bracis-28347	84	12	(	(	PUNCT
bracis-28347	84	13	2	2	NUM
bracis-28347	84	14	)	)	PUNCT
bracis-28347	84	15	,	,	PUNCT
bracis-28347	84	16	\(\sum	\(\sum	VERB
bracis-28347	84	17	_	_	PRON
bracis-28347	84	18	{	{	PUNCT
bracis-28347	84	19	c	c	PROPN
bracis-28347	84	20	\in	\in	PROPN
bracis-28347	84	21	\mathcal	\mathcal	PROPN
bracis-28347	84	22	{	{	PUNCT
bracis-28347	84	23	c	c	NOUN
bracis-28347	84	24	}	}	PUNCT
bracis-28347	84	25	}	}	PUNCT
bracis-28347	84	26	x_{vc	x_{vc	ADJ
bracis-28347	84	27	}	}	PUNCT
bracis-28347	84	28	=	=	SYM
bracis-28347	84	29	1\	1\	NUM
bracis-28347	84	30	)	)	PUNCT
bracis-28347	84	31	,	,	PUNCT
bracis-28347	84	32	and	and	CCONJ
bracis-28347	84	33	by	by	ADP
bracis-28347	84	34	the	the	DET
bracis-28347	84	35	constraint	constraint	NOUN
bracis-28347	84	36	(	(	PUNCT
bracis-28347	84	37	3	3	NUM
bracis-28347	84	38	)	)	PUNCT
bracis-28347	84	39	,	,	PUNCT
bracis-28347	84	40	\(\sum	\(\sum	VERB
bracis-28347	85	1	_	_	PRON
bracis-28347	85	2	{	{	PUNCT
bracis-28347	85	3	c	c	PROPN
bracis-28347	85	4	\in	\in	PROPN
bracis-28347	85	5	\mathcal	\mathcal	PROPN
bracis-28347	85	6	{	{	PUNCT
bracis-28347	85	7	c	c	NOUN
bracis-28347	85	8	}	}	PUNCT
bracis-28347	85	9	}	}	PUNCT
bracis-28347	85	10	x_{uc	x_{uc	ADJ
bracis-28347	85	11	}	}	PUNCT
bracis-28347	85	12	=	=	SYM
bracis-28347	85	13	1\	1\	NUM
bracis-28347	85	14	)	)	PUNCT
bracis-28347	85	15	,	,	PUNCT
bracis-28347	85	16	so	so	ADV
bracis-28347	85	17	\(u	\(u	NOUN
bracis-28347	85	18	,	,	PUNCT
bracis-28347	85	19	v	v	ADP
bracis-28347	85	20	\in	\in	PROPN
bracis-28347	85	21	v_p\	v_p\	NOUN
bracis-28347	85	22	)	)	PUNCT
bracis-28347	85	23	.	.	PUNCT
bracis-28347	86	1	by	by	ADP
bracis-28347	86	2	the	the	DET
bracis-28347	86	3	same	same	ADJ
bracis-28347	86	4	conditions	condition	NOUN
bracis-28347	86	5	imposed	impose	VERB
bracis-28347	86	6	in	in	ADP
bracis-28347	86	7	constraints	constraint	NOUN
bracis-28347	86	8	(	(	PUNCT
bracis-28347	86	9	2	2	NUM
bracis-28347	86	10	)	)	PUNCT
bracis-28347	86	11	and	and	CCONJ
bracis-28347	86	12	(	(	PUNCT
bracis-28347	86	13	3	3	NUM
bracis-28347	86	14	)	)	PUNCT
bracis-28347	86	15	,	,	PUNCT
bracis-28347	86	16	for	for	ADP
bracis-28347	86	17	each	each	DET
bracis-28347	86	18	\(u	\(u	ADJ
bracis-28347	86	19	\in	\in	ADJ
bracis-28347	86	20	v_p\	v_p\	NOUN
bracis-28347	86	21	)	)	PUNCT
bracis-28347	86	22	,	,	PUNCT
bracis-28347	86	23	there	there	PRON
bracis-28347	86	24	is	be	VERB
bracis-28347	86	25	at	at	ADP
bracis-28347	86	26	most	most	ADV
bracis-28347	86	27	one	one	NUM
bracis-28347	86	28	outgoing	outgoing	ADJ
bracis-28347	86	29	arc	arc	NOUN
bracis-28347	86	30	in	in	ADP
bracis-28347	86	31	u	u	NOUN
bracis-28347	86	32	and	and	CCONJ
bracis-28347	86	33	at	at	ADP
bracis-28347	86	34	most	most	ADJ
bracis-28347	86	35	one	one	NUM
bracis-28347	86	36	incoming	incoming	ADJ
bracis-28347	86	37	arc	arc	NOUN
bracis-28347	86	38	in	in	ADP
bracis-28347	86	39	u.	u.	PROPN
bracis-28347	86	40	note	note	PROPN
bracis-28347	86	41	that	that	SCONJ
bracis-28347	86	42	the	the	DET
bracis-28347	86	43	subgraph	subgraph	NOUN
bracis-28347	86	44	\(g	\(g	PROPN
bracis-28347	86	45	=	=	SYM
bracis-28347	86	46	(	(	PUNCT
bracis-28347	86	47	v_p	v_p	PROPN
bracis-28347	86	48	,	,	PUNCT
bracis-28347	86	49	a_p	a_p	NUM
bracis-28347	86	50	,	,	PUNCT
bracis-28347	86	51	c_p)\	c_p)\	NOUN
bracis-28347	86	52	)	)	PUNCT
bracis-28347	86	53	is	be	AUX
bracis-28347	86	54	well	well	ADV
bracis-28347	86	55	defined	define	VERB
bracis-28347	86	56	but	but	CCONJ
bracis-28347	86	57	not	not	PART
bracis-28347	86	58	necessarily	necessarily	ADV
bracis-28347	86	59	connected	connect	VERB
bracis-28347	86	60	.	.	PUNCT
bracis-28347	87	1	if	if	SCONJ
bracis-28347	87	2	an	an	DET
bracis-28347	87	3	arc	arc	NOUN
bracis-28347	87	4	\(uv	\(uv	NOUN
bracis-28347	87	5	\in	\in	PROPN
bracis-28347	87	6	a_p\	a_p\	NOUN
bracis-28347	87	7	)	)	PUNCT
bracis-28347	87	8	,	,	PUNCT
bracis-28347	87	9	by	by	ADP
bracis-28347	87	10	the	the	DET
bracis-28347	87	11	constraint	constraint	NOUN
bracis-28347	87	12	(	(	PUNCT
bracis-28347	87	13	4	4	X
bracis-28347	87	14	)	)	PUNCT
bracis-28347	87	15	\(y_{uv}=1\	\(y_{uv}=1\	NOUN
bracis-28347	87	16	)	)	PUNCT
bracis-28347	87	17	and	and	CCONJ
bracis-28347	87	18	the	the	DET
bracis-28347	87	19	difference	difference	NOUN
bracis-28347	87	20	between	between	ADP
bracis-28347	87	21	the	the	DET
bracis-28347	87	22	labels	label	NOUN
bracis-28347	87	23	of	of	ADP
bracis-28347	87	24	vertices	vertex	NOUN
bracis-28347	87	25	u	u	NOUN
bracis-28347	87	26	and	and	CCONJ
bracis-28347	87	27	v	v	NOUN
bracis-28347	87	28	has	have	VERB
bracis-28347	87	29	to	to	PART
bracis-28347	87	30	be	be	AUX
bracis-28347	87	31	at	at	ADP
bracis-28347	87	32	least	least	ADJ
bracis-28347	87	33	one	one	NUM
bracis-28347	87	34	,	,	PUNCT
bracis-28347	87	35	which	which	PRON
bracis-28347	87	36	prohibits	prohibit	VERB
bracis-28347	87	37	circuits	circuit	NOUN
bracis-28347	87	38	,	,	PUNCT
bracis-28347	87	39	finally	finally	ADV
bracis-28347	87	40	,	,	PUNCT
bracis-28347	87	41	the	the	DET
bracis-28347	87	42	connectivity	connectivity	NOUN
bracis-28347	87	43	of	of	ADP
bracis-28347	87	44	g	g	PROPN
bracis-28347	87	45	is	be	AUX
bracis-28347	87	46	established	establish	VERB
bracis-28347	87	47	by	by	ADP
bracis-28347	87	48	adding	add	VERB
bracis-28347	87	49	the	the	DET
bracis-28347	87	50	constraint	constraint	NOUN
bracis-28347	87	51	(	(	PUNCT
bracis-28347	87	52	5	5	NUM
bracis-28347	87	53	)	)	PUNCT
bracis-28347	87	54	and	and	CCONJ
bracis-28347	87	55	thus	thus	ADV
bracis-28347	87	56	x	x	PRON
bracis-28347	87	57	indicates	indicate	VERB
bracis-28347	87	58	a	a	DET
bracis-28347	87	59	path	path	NOUN
bracis-28347	87	60	that	that	PRON
bracis-28347	87	61	uses	use	VERB
bracis-28347	87	62	\(\mathcal	\(\mathcal	ADJ
bracis-28347	87	63	{	{	PUNCT
bracis-28347	87	64	c'}\	c'}\	NOUN
bracis-28347	87	65	)	)	PUNCT
bracis-28347	87	66	colors	color	NOUN
bracis-28347	87	67	,	,	PUNCT
bracis-28347	87	68	which	which	PRON
bracis-28347	87	69	completes	complete	VERB
bracis-28347	87	70	the	the	DET
bracis-28347	87	71	proof	proof	NOUN
bracis-28347	87	72	.	.	PUNCT
bracis-28347	88	1	although	although	SCONJ
bracis-28347	88	2	not	not	PART
bracis-28347	88	3	done	do	VERB
bracis-28347	88	4	in	in	ADP
bracis-28347	88	5	this	this	DET
bracis-28347	88	6	paper	paper	NOUN
bracis-28347	88	7	,	,	PUNCT
bracis-28347	88	8	one	one	NUM
bracis-28347	88	9	way	way	NOUN
bracis-28347	88	10	to	to	PART
bracis-28347	88	11	evaluate	evaluate	VERB
bracis-28347	88	12	the	the	DET
bracis-28347	88	13	strength	strength	NOUN
bracis-28347	88	14	of	of	ADP
bracis-28347	88	15	the	the	DET
bracis-28347	88	16	ilp	ilp	ADJ
bracis-28347	88	17	model	model	NOUN
bracis-28347	88	18	would	would	AUX
bracis-28347	88	19	be	be	AUX
bracis-28347	88	20	to	to	PART
bracis-28347	88	21	compare	compare	VERB
bracis-28347	88	22	the	the	DET
bracis-28347	88	23	value	value	NOUN
bracis-28347	88	24	of	of	ADP
bracis-28347	88	25	the	the	DET
bracis-28347	88	26	integer	integer	NOUN
bracis-28347	88	27	optimal	optimal	ADJ
bracis-28347	88	28	solution	solution	NOUN
bracis-28347	88	29	to	to	ADP
bracis-28347	88	30	the	the	DET
bracis-28347	88	31	value	value	NOUN
bracis-28347	88	32	of	of	ADP
bracis-28347	88	33	the	the	DET
bracis-28347	88	34	optimal	optimal	ADJ
bracis-28347	88	35	solution	solution	NOUN
bracis-28347	88	36	of	of	ADP
bracis-28347	88	37	the	the	DET
bracis-28347	88	38	model	model	NOUN
bracis-28347	88	39	without	without	ADP
bracis-28347	88	40	the	the	DET
bracis-28347	88	41	integrality	integrality	NOUN
bracis-28347	88	42	conditions	condition	NOUN
bracis-28347	88	43	.	.	PUNCT
bracis-28347	89	1	this	this	PRON
bracis-28347	89	2	is	be	AUX
bracis-28347	89	3	the	the	DET
bracis-28347	89	4	integrality	integrality	NOUN
bracis-28347	89	5	gap	gap	NOUN
bracis-28347	89	6	.	.	PUNCT
bracis-28347	90	1	4	4	NUM
bracis-28347	90	2	polynomial	polynomial	ADJ
bracis-28347	90	3	-	-	PUNCT
bracis-28347	90	4	time	time	NOUN
bracis-28347	90	5	heuristic	heuristic	NOUN
bracis-28347	90	6	for	for	ADP
bracis-28347	90	7	 	 	SPACE
bracis-28347	90	8	mtpp	mtpp	NOUN
bracis-28347	90	9	it	it	PRON
bracis-28347	90	10	is	be	AUX
bracis-28347	90	11	known	know	VERB
bracis-28347	90	12	that	that	SCONJ
bracis-28347	90	13	mtpp	mtpp	PROPN
bracis-28347	90	14	is	be	AUX
bracis-28347	90	15	np	np	NOUN
bracis-28347	90	16	-	-	PUNCT
bracis-28347	90	17	hard	hard	ADJ
bracis-28347	90	18	for	for	ADP
bracis-28347	90	19	simple	simple	ADJ
bracis-28347	90	20	graphs	graph	NOUN
bracis-28347	90	21	in	in	ADP
bracis-28347	90	22	general	general	ADJ
bracis-28347	90	23	,	,	PUNCT
bracis-28347	90	24	especially	especially	ADV
bracis-28347	90	25	for	for	ADP
bracis-28347	90	26	dags	dag	NOUN
bracis-28347	90	27	,	,	PUNCT
bracis-28347	90	28	cactus	cactus	NOUN
bracis-28347	90	29	graphs	graph	NOUN
bracis-28347	90	30	,	,	PUNCT
bracis-28347	90	31	and	and	CCONJ
bracis-28347	90	32	interval	interval	NOUN
bracis-28347	90	33	graphs	graph	NOUN
bracis-28347	90	34	.	.	PUNCT
bracis-28347	91	1	the	the	DET
bracis-28347	91	2	inherent	inherent	ADJ
bracis-28347	91	3	intractability	intractability	NOUN
bracis-28347	91	4	of	of	ADP
bracis-28347	91	5	mtpp	mtpp	PROPN
bracis-28347	91	6	encourages	encourage	VERB
bracis-28347	91	7	the	the	DET
bracis-28347	91	8	development	development	NOUN
bracis-28347	91	9	of	of	ADP
bracis-28347	91	10	heuristics	heuristic	NOUN
bracis-28347	91	11	that	that	PRON
bracis-28347	91	12	are	be	AUX
bracis-28347	91	13	designed	design	VERB
bracis-28347	91	14	to	to	PART
bracis-28347	91	15	find	find	VERB
bracis-28347	91	16	bounds	bound	NOUN
bracis-28347	91	17	,	,	PUNCT
bracis-28347	91	18	in	in	ADP
bracis-28347	91	19	particular	particular	ADJ
bracis-28347	91	20	lower	low	ADJ
bracis-28347	91	21	bounds	bound	NOUN
bracis-28347	91	22	,	,	PUNCT
bracis-28347	91	23	for	for	ADP
bracis-28347	91	24	the	the	DET
bracis-28347	91	25	problem	problem	NOUN
bracis-28347	91	26	.	.	PUNCT
bracis-28347	92	1	in	in	ADP
bracis-28347	92	2	this	this	DET
bracis-28347	92	3	section	section	NOUN
bracis-28347	92	4	,	,	PUNCT
bracis-28347	92	5	it	it	PRON
bracis-28347	92	6	is	be	AUX
bracis-28347	92	7	presented	present	VERB
bracis-28347	92	8	a	a	DET
bracis-28347	92	9	polynomial	polynomial	ADJ
bracis-28347	92	10	-	-	PUNCT
bracis-28347	92	11	time	time	NOUN
bracis-28347	92	12	heuristic	heuristic	NOUN
bracis-28347	92	13	called	call	VERB
bracis-28347	92	14	the	the	DET
bracis-28347	92	15	tropical	tropical	ADJ
bracis-28347	92	16	-	-	PUNCT
bracis-28347	92	17	cactus	cactus	NOUN
bracis-28347	92	18	algorithm	algorithm	NOUN
bracis-28347	92	19	for	for	ADP
bracis-28347	92	20	finding	find	VERB
bracis-28347	92	21	maximum	maximum	ADJ
bracis-28347	92	22	tropical	tropical	ADJ
bracis-28347	92	23	paths	path	NOUN
bracis-28347	92	24	in	in	ADP
bracis-28347	92	25	vertex	vertex	NOUN
bracis-28347	92	26	-	-	PUNCT
bracis-28347	92	27	colored	color	VERB
bracis-28347	92	28	graphs	graph	NOUN
bracis-28347	92	29	.	.	PUNCT
bracis-28347	93	1	for	for	ADP
bracis-28347	93	2	this	this	PRON
bracis-28347	93	3	the	the	DET
bracis-28347	93	4	algorithm	algorithm	NOUN
bracis-28347	93	5	makes	make	VERB
bracis-28347	93	6	use	use	NOUN
bracis-28347	93	7	of	of	ADP
bracis-28347	93	8	the	the	DET
bracis-28347	93	9	algorithm	algorithm	NOUN
bracis-28347	93	10	presented	present	VERB
bracis-28347	93	11	in	in	ADP
bracis-28347	93	12	sect	sect	NOUN
bracis-28347	93	13	.	.	PUNCT
bracis-28347	93	14	 	 	SPACE
bracis-28347	93	15	4.2	4.2	NUM
bracis-28347	93	16	.	.	PUNCT
bracis-28347	94	1	existing	exist	VERB
bracis-28347	94	2	literature	literature	NOUN
bracis-28347	94	3	does	do	AUX
bracis-28347	94	4	not	not	PART
bracis-28347	94	5	provide	provide	VERB
bracis-28347	94	6	any	any	DET
bracis-28347	94	7	exact	exact	ADJ
bracis-28347	94	8	,	,	PUNCT
bracis-28347	94	9	approximation	approximation	NOUN
bracis-28347	94	10	,	,	PUNCT
bracis-28347	94	11	or	or	CCONJ
bracis-28347	94	12	heuristic	heuristic	ADJ
bracis-28347	94	13	algorithms	algorithm	NOUN
bracis-28347	94	14	for	for	ADP
bracis-28347	94	15	the	the	DET
bracis-28347	94	16	mtpp	mtpp	PROPN
bracis-28347	94	17	.	.	PUNCT
bracis-28347	95	1	tropical	tropical	ADJ
bracis-28347	95	2	-	-	PUNCT
bracis-28347	95	3	cactus	cactus	NOUN
bracis-28347	95	4	algorithm	algorithm	NOUN
bracis-28347	95	5	is	be	AUX
bracis-28347	95	6	inspired	inspire	VERB
bracis-28347	95	7	by	by	ADP
bracis-28347	95	8	a	a	DET
bracis-28347	95	9	linear	linear	ADJ
bracis-28347	95	10	-	-	PUNCT
bracis-28347	95	11	time	time	NOUN
bracis-28347	95	12	algorithm	algorithm	NOUN
bracis-28347	95	13	proposed	propose	VERB
bracis-28347	95	14	by	by	ADP
bracis-28347	95	15	markov	markov	PROPN
bracis-28347	95	16	et	et	PROPN
bracis-28347	95	17	al	al	PROPN
bracis-28347	95	18	.	.	PROPN
bracis-28347	96	1	(	(	PUNCT
bracis-28347	96	2	2012	2012	NUM
bracis-28347	96	3	)	)	PUNCT
bracis-28347	97	1	[	[	X
bracis-28347	97	2	11	11	NUM
bracis-28347	97	3	]	]	PUNCT
bracis-28347	97	4	for	for	ADP
bracis-28347	97	5	calculating	calculate	VERB
bracis-28347	97	6	the	the	DET
bracis-28347	97	7	longest	long	ADJ
bracis-28347	97	8	paths	path	NOUN
bracis-28347	97	9	in	in	ADP
bracis-28347	97	10	cactus	cactus	NOUN
bracis-28347	97	11	graphs	graph	NOUN
bracis-28347	97	12	.	.	PUNCT
bracis-28347	98	1	cleverly	cleverly	ADV
bracis-28347	98	2	,	,	PUNCT
bracis-28347	98	3	the	the	DET
bracis-28347	98	4	algorithm	algorithm	NOUN
bracis-28347	98	5	finds	find	VERB
bracis-28347	98	6	a	a	DET
bracis-28347	98	7	path	path	NOUN
bracis-28347	98	8	whose	whose	DET
bracis-28347	98	9	number	number	NOUN
bracis-28347	98	10	of	of	ADP
bracis-28347	98	11	colors	color	NOUN
bracis-28347	98	12	empirically	empirically	ADV
bracis-28347	98	13	comes	come	VERB
bracis-28347	98	14	very	very	ADV
bracis-28347	98	15	close	close	ADV
bracis-28347	98	16	to	to	ADP
bracis-28347	98	17	an	an	DET
bracis-28347	98	18	optimal	optimal	ADJ
bracis-28347	98	19	solution	solution	NOUN
bracis-28347	98	20	.	.	PUNCT
bracis-28347	99	1	additionally	additionally	ADV
bracis-28347	99	2	,	,	PUNCT
bracis-28347	99	3	an	an	DET
bracis-28347	99	4	auxiliary	auxiliary	ADJ
bracis-28347	99	5	algorithm	algorithm	NOUN
bracis-28347	99	6	,	,	PUNCT
bracis-28347	99	7	presented	present	VERB
bracis-28347	99	8	in	in	ADP
bracis-28347	99	9	sect	sect	NOUN
bracis-28347	99	10	.	.	PUNCT
bracis-28347	99	11	 	 	SPACE
bracis-28347	100	1	4.1	4.1	NUM
bracis-28347	100	2	called	call	VERB
bracis-28347	100	3	the	the	DET
bracis-28347	100	4	cactus	cactus	NOUN
bracis-28347	100	5	-	-	PUNCT
bracis-28347	100	6	graph	graph	NOUN
bracis-28347	100	7	algorithm	algorithm	NOUN
bracis-28347	100	8	was	be	AUX
bracis-28347	100	9	developed	develop	VERB
bracis-28347	100	10	to	to	PART
bracis-28347	100	11	construct	construct	VERB
bracis-28347	100	12	a	a	DET
bracis-28347	100	13	cactus	cactus	NOUN
bracis-28347	100	14	graph	graph	NOUN
bracis-28347	100	15	from	from	ADP
bracis-28347	100	16	a	a	DET
bracis-28347	100	17	simple	simple	ADJ
bracis-28347	100	18	graph	graph	NOUN
bracis-28347	100	19	.	.	PUNCT
bracis-28347	101	1	4.1	4.1	NUM
bracis-28347	101	2	cactus	cactus	NOUN
bracis-28347	101	3	-	-	PUNCT
bracis-28347	101	4	graph	graph	NOUN
bracis-28347	101	5	algorithm	algorithm	NOUN
bracis-28347	101	6	given	give	VERB
bracis-28347	101	7	a	a	DET
bracis-28347	101	8	simple	simple	ADJ
bracis-28347	101	9	graph	graph	NOUN
bracis-28347	101	10	g	g	NOUN
bracis-28347	101	11	,	,	PUNCT
bracis-28347	101	12	the	the	DET
bracis-28347	101	13	cactus	cactus	NOUN
bracis-28347	101	14	-	-	PUNCT
bracis-28347	101	15	graph	graph	NOUN
bracis-28347	101	16	algorithm	algorithm	NOUN
bracis-28347	101	17	extracts	extract	NOUN
bracis-28347	101	18	from	from	ADP
bracis-28347	101	19	g	g	ADP
bracis-28347	101	20	a	a	DET
bracis-28347	101	21	cactus	cactus	NOUN
bracis-28347	101	22	graph	graph	NOUN
bracis-28347	101	23	\(g'\	\(g'\	NOUN
bracis-28347	101	24	)	)	PUNCT
bracis-28347	101	25	that	that	PRON
bracis-28347	101	26	will	will	AUX
bracis-28347	101	27	be	be	AUX
bracis-28347	101	28	the	the	DET
bracis-28347	101	29	input	input	NOUN
bracis-28347	101	30	of	of	ADP
bracis-28347	101	31	the	the	DET
bracis-28347	101	32	tropical	tropical	ADJ
bracis-28347	101	33	-	-	PUNCT
bracis-28347	101	34	cactus	cactus	NOUN
bracis-28347	101	35	algorithm	algorithm	NOUN
bracis-28347	101	36	.	.	PUNCT
bracis-28347	102	1	to	to	PART
bracis-28347	102	2	perform	perform	VERB
bracis-28347	102	3	this	this	DET
bracis-28347	102	4	process	process	NOUN
bracis-28347	102	5	,	,	PUNCT
bracis-28347	102	6	it	it	PRON
bracis-28347	102	7	is	be	AUX
bracis-28347	102	8	necessary	necessary	ADJ
bracis-28347	102	9	to	to	PART
bracis-28347	102	10	find	find	VERB
bracis-28347	102	11	long	long	ADJ
bracis-28347	102	12	cycles	cycle	NOUN
bracis-28347	102	13	in	in	ADP
bracis-28347	102	14	the	the	DET
bracis-28347	102	15	graph	graph	NOUN
bracis-28347	102	16	.	.	PUNCT
bracis-28347	103	1	given	give	VERB
bracis-28347	103	2	an	an	DET
bracis-28347	103	3	integer	integer	NOUN
bracis-28347	103	4	\(k	\(k	NOUN
bracis-28347	103	5	\ge	\ge	PROPN
bracis-28347	103	6	3\	3\	NUM
bracis-28347	103	7	)	)	PUNCT
bracis-28347	103	8	,	,	PUNCT
bracis-28347	103	9	a	a	DET
bracis-28347	103	10	cycle	cycle	NOUN
bracis-28347	103	11	in	in	ADP
bracis-28347	103	12	an	an	DET
bracis-28347	103	13	undirected	undirected	ADJ
bracis-28347	103	14	graph	graph	NOUN
bracis-28347	103	15	is	be	AUX
bracis-28347	103	16	called	call	VERB
bracis-28347	103	17	long	long	ADV
bracis-28347	103	18	if	if	SCONJ
bracis-28347	103	19	it	it	PRON
bracis-28347	103	20	has	have	VERB
bracis-28347	103	21	at	at	ADP
bracis-28347	103	22	least	least	ADJ
bracis-28347	103	23	k	k	NOUN
bracis-28347	103	24	edges	edge	NOUN
bracis-28347	103	25	.	.	PUNCT
bracis-28347	104	1	the	the	DET
bracis-28347	104	2	cactus	cactus	NOUN
bracis-28347	104	3	-	-	PUNCT
bracis-28347	104	4	graph	graph	NOUN
bracis-28347	104	5	algorithm	algorithm	NOUN
bracis-28347	104	6	uses	use	VERB
bracis-28347	104	7	as	as	ADP
bracis-28347	104	8	a	a	DET
bracis-28347	104	9	subroutine	subroutine	NOUN
bracis-28347	104	10	the	the	DET
bracis-28347	104	11	algorithm	algorithm	NOUN
bracis-28347	104	12	presented	present	VERB
bracis-28347	104	13	in	in	ADP
bracis-28347	104	14	[	[	X
bracis-28347	104	15	7	7	X
bracis-28347	104	16	]	]	PUNCT
bracis-28347	104	17	that	that	PRON
bracis-28347	104	18	finds	find	VERB
bracis-28347	104	19	a	a	DET
bracis-28347	104	20	path	path	NOUN
bracis-28347	104	21	of	of	ADP
bracis-28347	104	22	length	length	NOUN
bracis-28347	104	23	\(exp(\varomega	\(exp(\varomega	PROPN
bracis-28347	104	24	(	(	PUNCT
bracis-28347	104	25	\sqrt{log	\sqrt{log	PROPN
bracis-28347	104	26	\	\	PROPN
bracis-28347	104	27	l}))\	l}))\	PROPN
bracis-28347	104	28	)	)	PUNCT
bracis-28347	104	29	,	,	PUNCT
bracis-28347	104	30	where	where	SCONJ
bracis-28347	104	31	l	l	NOUN
bracis-28347	104	32	is	be	AUX
bracis-28347	104	33	the	the	DET
bracis-28347	104	34	length	length	NOUN
bracis-28347	104	35	of	of	ADP
bracis-28347	104	36	the	the	DET
bracis-28347	104	37	longest	long	ADJ
bracis-28347	104	38	path	path	NOUN
bracis-28347	104	39	(	(	PUNCT
bracis-28347	104	40	the	the	DET
bracis-28347	104	41	details	detail	NOUN
bracis-28347	104	42	of	of	ADP
bracis-28347	104	43	this	this	DET
bracis-28347	104	44	algorithm	algorithm	NOUN
bracis-28347	104	45	will	will	AUX
bracis-28347	104	46	be	be	AUX
bracis-28347	104	47	omitted	omit	VERB
bracis-28347	104	48	here	here	ADV
bracis-28347	104	49	)	)	PUNCT
bracis-28347	104	50	.	.	PUNCT
bracis-28347	105	1	this	this	DET
bracis-28347	105	2	subroutine	subroutine	NOUN
bracis-28347	105	3	will	will	AUX
bracis-28347	105	4	be	be	AUX
bracis-28347	105	5	called	call	VERB
bracis-28347	105	6	in	in	ADP
bracis-28347	105	7	this	this	DET
bracis-28347	105	8	paper	paper	NOUN
bracis-28347	105	9	findcycle(g	findcycle(g	NOUN
bracis-28347	105	10	,	,	PUNCT
bracis-28347	105	11	 	 	SPACE
bracis-28347	105	12	v	v	NOUN
bracis-28347	105	13	)	)	PUNCT
bracis-28347	105	14	and	and	CCONJ
bracis-28347	105	15	receives	receive	VERB
bracis-28347	105	16	as	as	ADP
bracis-28347	105	17	input	input	NOUN
bracis-28347	105	18	a	a	DET
bracis-28347	105	19	cactus	cactus	NOUN
bracis-28347	105	20	graph	graph	NOUN
bracis-28347	105	21	g	g	NOUN
bracis-28347	105	22	and	and	CCONJ
bracis-28347	105	23	a	a	DET
bracis-28347	105	24	vertex	vertex	NOUN
bracis-28347	105	25	v.	v.	ADP
bracis-28347	105	26	extraction	extraction	NOUN
bracis-28347	105	27	step	step	NOUN
bracis-28347	105	28	of	of	ADP
bracis-28347	105	29	a	a	DET
bracis-28347	105	30	cactus	cactus	NOUN
bracis-28347	105	31	graph	graph	NOUN
bracis-28347	105	32	from	from	ADP
bracis-28347	105	33	a	a	DET
bracis-28347	105	34	graph	graph	NOUN
bracis-28347	105	35	g	g	NOUN
bracis-28347	105	36	:	:	PUNCT
bracis-28347	105	37	given	give	VERB
bracis-28347	105	38	a	a	DET
bracis-28347	105	39	simple	simple	ADJ
bracis-28347	105	40	graph	graph	NOUN
bracis-28347	105	41	g	g	NOUN
bracis-28347	105	42	,	,	PUNCT
bracis-28347	105	43	any	any	DET
bracis-28347	105	44	vertex	vertex	NOUN
bracis-28347	105	45	\(v	\(v	X
bracis-28347	105	46	\in	\in	PROPN
bracis-28347	105	47	g\	g\	PROPN
bracis-28347	105	48	)	)	PUNCT
bracis-28347	105	49	,	,	PUNCT
bracis-28347	105	50	and	and	CCONJ
bracis-28347	105	51	a	a	DET
bracis-28347	105	52	positive	positive	ADJ
bracis-28347	105	53	integer	integer	NOUN
bracis-28347	105	54	\(k	\(k	NOUN
bracis-28347	105	55	\ge	\ge	PROPN
bracis-28347	105	56	3\	3\	NUM
bracis-28347	105	57	)	)	PUNCT
bracis-28347	105	58	,	,	PUNCT
bracis-28347	105	59	the	the	DET
bracis-28347	105	60	constructed	construct	VERB
bracis-28347	105	61	graph	graph	NOUN
bracis-28347	105	62	is	be	AUX
bracis-28347	105	63	defined	define	VERB
bracis-28347	105	64	by	by	ADP
bracis-28347	105	65	\(a_k\	\(a_k\	NOUN
bracis-28347	105	66	)	)	PUNCT
bracis-28347	105	67	.	.	PUNCT
bracis-28347	106	1	two	two	NUM
bracis-28347	106	2	types	type	NOUN
bracis-28347	106	3	of	of	ADP
bracis-28347	106	4	components	component	NOUN
bracis-28347	106	5	form	form	VERB
bracis-28347	106	6	\(a_k\	\(a_k\	PROPN
bracis-28347	106	7	)	)	PUNCT
bracis-28347	106	8	.	.	PUNCT
bracis-28347	107	1	a	a	DET
bracis-28347	107	2	component	component	NOUN
bracis-28347	107	3	in	in	ADP
bracis-28347	107	4	\(a_k\	\(a_k\	NOUN
bracis-28347	107	5	)	)	PUNCT
bracis-28347	107	6	is	be	AUX
bracis-28347	107	7	either	either	CCONJ
bracis-28347	107	8	a	a	DET
bracis-28347	107	9	singular	singular	ADJ
bracis-28347	107	10	component	component	NOUN
bracis-28347	107	11	or	or	CCONJ
bracis-28347	107	12	a	a	DET
bracis-28347	107	13	circuit	circuit	NOUN
bracis-28347	107	14	component	component	NOUN
bracis-28347	107	15	.	.	PUNCT
bracis-28347	108	1	a	a	DET
bracis-28347	108	2	singular	singular	ADJ
bracis-28347	108	3	component	component	NOUN
bracis-28347	108	4	corresponds	correspond	VERB
bracis-28347	108	5	to	to	ADP
bracis-28347	108	6	a	a	DET
bracis-28347	108	7	single	single	ADJ
bracis-28347	108	8	vertex	vertex	NOUN
bracis-28347	108	9	\(u	\(u	NOUN
bracis-28347	108	10	\in	\in	PROPN
bracis-28347	108	11	g\	g\	PROPN
bracis-28347	108	12	)	)	PUNCT
bracis-28347	108	13	and	and	CCONJ
bracis-28347	108	14	defines	define	VERB
bracis-28347	108	15	a	a	DET
bracis-28347	108	16	vertex	vertex	NOUN
bracis-28347	108	17	in	in	ADP
bracis-28347	108	18	\(a_k\	\(a_k\	NOUN
bracis-28347	108	19	)	)	PUNCT
bracis-28347	108	20	,	,	PUNCT
bracis-28347	108	21	while	while	SCONJ
bracis-28347	108	22	a	a	DET
bracis-28347	108	23	circuit	circuit	NOUN
bracis-28347	108	24	component	component	NOUN
bracis-28347	108	25	corresponds	correspond	VERB
bracis-28347	108	26	to	to	ADP
bracis-28347	108	27	a	a	DET
bracis-28347	108	28	circuit	circuit	NOUN
bracis-28347	108	29	\(c\in	\(c\in	PUNCT
bracis-28347	108	30	g\	g\	NOUN
bracis-28347	108	31	)	)	PUNCT
bracis-28347	108	32	and	and	CCONJ
bracis-28347	108	33	defines	define	VERB
bracis-28347	108	34	a	a	DET
bracis-28347	108	35	circuit	circuit	NOUN
bracis-28347	108	36	in	in	ADP
bracis-28347	108	37	\(a_k\	\(a_k\	NOUN
bracis-28347	108	38	)	)	PUNCT
bracis-28347	108	39	.	.	PUNCT
bracis-28347	109	1	the	the	DET
bracis-28347	109	2	fig	fig	NOUN
bracis-28347	109	3	.	.	PUNCT
bracis-28347	109	4	 	 	SPACE
bracis-28347	109	5	2	2	NUM
bracis-28347	109	6	demonstrates	demonstrate	VERB
bracis-28347	109	7	an	an	DET
bracis-28347	109	8	example	example	NOUN
bracis-28347	109	9	of	of	ADP
bracis-28347	109	10	transforming	transform	VERB
bracis-28347	109	11	a	a	DET
bracis-28347	109	12	simple	simple	ADJ
bracis-28347	109	13	graph	graph	NOUN
bracis-28347	109	14	g	g	NOUN
bracis-28347	109	15	into	into	ADP
bracis-28347	109	16	a	a	DET
bracis-28347	109	17	cactus	cactus	NOUN
bracis-28347	109	18	graph	graph	NOUN
bracis-28347	109	19	\(a_k\	\(a_k\	PROPN
bracis-28347	109	20	)	)	PUNCT
bracis-28347	109	21	,	,	PUNCT
bracis-28347	109	22	where	where	SCONJ
bracis-28347	109	23	k	k	PROPN
bracis-28347	109	24	is	be	AUX
bracis-28347	109	25	the	the	DET
bracis-28347	109	26	minimum	minimum	ADJ
bracis-28347	109	27	circuit	circuit	NOUN
bracis-28347	109	28	size	size	NOUN
bracis-28347	109	29	.	.	PUNCT
bracis-28347	110	1	note	note	VERB
bracis-28347	110	2	that	that	SCONJ
bracis-28347	110	3	the	the	DET
bracis-28347	110	4	set	set	NOUN
bracis-28347	110	5	of	of	ADP
bracis-28347	110	6	vertices	vertex	NOUN
bracis-28347	110	7	circled	circle	VERB
bracis-28347	110	8	by	by	ADP
bracis-28347	110	9	the	the	DET
bracis-28347	110	10	red	red	ADJ
bracis-28347	110	11	line	line	NOUN
bracis-28347	110	12	represents	represent	VERB
bracis-28347	110	13	a	a	DET
bracis-28347	110	14	circuit	circuit	NOUN
bracis-28347	110	15	component	component	NOUN
bracis-28347	110	16	in	in	ADP
bracis-28347	110	17	the	the	DET
bracis-28347	110	18	graph	graph	NOUN
bracis-28347	110	19	\(a_k\	\(a_k\	NOUN
bracis-28347	110	20	)	)	PUNCT
bracis-28347	110	21	and	and	CCONJ
bracis-28347	110	22	has	have	VERB
bracis-28347	110	23	a	a	DET
bracis-28347	110	24	length	length	NOUN
bracis-28347	110	25	of	of	ADP
bracis-28347	110	26	9	9	NUM
bracis-28347	110	27	.	.	PUNCT
bracis-28347	111	1	the	the	DET
bracis-28347	111	2	vertices	vertex	NOUN
bracis-28347	111	3	circled	circle	VERB
bracis-28347	111	4	by	by	ADP
bracis-28347	111	5	the	the	DET
bracis-28347	111	6	blue	blue	ADJ
bracis-28347	111	7	line	line	NOUN
bracis-28347	111	8	represent	represent	VERB
bracis-28347	111	9	singular	singular	ADJ
bracis-28347	111	10	components	component	NOUN
bracis-28347	111	11	in	in	ADP
bracis-28347	111	12	the	the	DET
bracis-28347	111	13	graph	graph	NOUN
bracis-28347	111	14	\(a_k\	\(a_k\	NOUN
bracis-28347	111	15	)	)	PUNCT
bracis-28347	111	16	.	.	PUNCT
bracis-28347	112	1	note	note	VERB
bracis-28347	112	2	that	that	SCONJ
bracis-28347	112	3	vertex	vertex	NOUN
bracis-28347	112	4	7	7	NUM
bracis-28347	112	5	could	could	AUX
bracis-28347	112	6	be	be	AUX
bracis-28347	112	7	a	a	DET
bracis-28347	112	8	neighbor	neighbor	NOUN
bracis-28347	112	9	of	of	ADP
bracis-28347	112	10	2	2	NUM
bracis-28347	112	11	,	,	PUNCT
bracis-28347	112	12	 	 	SPACE
bracis-28347	112	13	6	6	NUM
bracis-28347	112	14	,	,	PUNCT
bracis-28347	112	15	or	or	CCONJ
bracis-28347	112	16	11	11	NUM
bracis-28347	112	17	in	in	ADP
bracis-28347	112	18	the	the	DET
bracis-28347	112	19	graph	graph	NOUN
bracis-28347	112	20	\(a_k\	\(a_k\	NOUN
bracis-28347	112	21	)	)	PUNCT
bracis-28347	112	22	,	,	PUNCT
bracis-28347	112	23	and	and	CCONJ
bracis-28347	112	24	in	in	ADP
bracis-28347	112	25	a	a	DET
bracis-28347	112	26	second	second	ADJ
bracis-28347	112	27	execution	execution	NOUN
bracis-28347	112	28	of	of	ADP
bracis-28347	112	29	the	the	DET
bracis-28347	112	30	algorithm	algorithm	NOUN
bracis-28347	112	31	,	,	PUNCT
bracis-28347	112	32	a	a	DET
bracis-28347	112	33	circuit	circuit	NOUN
bracis-28347	112	34	of	of	ADP
bracis-28347	112	35	different	different	ADJ
bracis-28347	112	36	size	size	NOUN
bracis-28347	112	37	could	could	AUX
bracis-28347	112	38	be	be	AUX
bracis-28347	112	39	found	find	VERB
bracis-28347	112	40	.	.	PUNCT
bracis-28347	113	1	the	the	DET
bracis-28347	113	2	first	first	ADJ
bracis-28347	113	3	vertex	vertex	NOUN
bracis-28347	113	4	to	to	PART
bracis-28347	113	5	become	become	VERB
bracis-28347	113	6	part	part	NOUN
bracis-28347	113	7	of	of	ADP
bracis-28347	113	8	\(a_k\	\(a_k\	NOUN
bracis-28347	113	9	)	)	PUNCT
bracis-28347	113	10	is	be	AUX
bracis-28347	113	11	the	the	DET
bracis-28347	113	12	given	give	VERB
bracis-28347	113	13	vertex	vertex	NOUN
bracis-28347	113	14	v	v	NOUN
bracis-28347	113	15	,	,	PUNCT
bracis-28347	113	16	and	and	CCONJ
bracis-28347	113	17	after	after	ADP
bracis-28347	113	18	the	the	DET
bracis-28347	113	19	execution	execution	NOUN
bracis-28347	113	20	of	of	ADP
bracis-28347	113	21	the	the	DET
bracis-28347	113	22	algorithm	algorithm	NOUN
bracis-28347	113	23	,	,	PUNCT
bracis-28347	113	24	v	v	NOUN
bracis-28347	113	25	may	may	AUX
bracis-28347	113	26	be	be	AUX
bracis-28347	113	27	a	a	DET
bracis-28347	113	28	singular	singular	ADJ
bracis-28347	113	29	component	component	NOUN
bracis-28347	113	30	or	or	CCONJ
bracis-28347	113	31	become	become	VERB
bracis-28347	113	32	part	part	NOUN
bracis-28347	113	33	of	of	ADP
bracis-28347	113	34	a	a	DET
bracis-28347	113	35	circuit	circuit	NOUN
bracis-28347	113	36	-	-	PUNCT
bracis-28347	113	37	component	component	NOUN
bracis-28347	113	38	in	in	ADP
bracis-28347	113	39	\(a_k\	\(a_k\	NOUN
bracis-28347	113	40	)	)	PUNCT
bracis-28347	113	41	.	.	PUNCT
bracis-28347	114	1	it	it	PRON
bracis-28347	114	2	is	be	AUX
bracis-28347	114	3	also	also	ADV
bracis-28347	114	4	generally	generally	ADV
bracis-28347	114	5	defined	define	VERB
bracis-28347	114	6	in	in	ADP
bracis-28347	114	7	this	this	DET
bracis-28347	114	8	work	work	NOUN
bracis-28347	114	9	that	that	PRON
bracis-28347	114	10	the	the	DET
bracis-28347	114	11	minimum	minimum	ADJ
bracis-28347	114	12	cycle	cycle	NOUN
bracis-28347	114	13	size	size	NOUN
bracis-28347	114	14	k	k	PROPN
bracis-28347	114	15	is	be	AUX
bracis-28347	114	16	equal	equal	ADJ
bracis-28347	114	17	to	to	ADP
bracis-28347	114	18	3	3	NUM
bracis-28347	114	19	,	,	PUNCT
bracis-28347	114	20	as	as	SCONJ
bracis-28347	114	21	such	such	ADJ
bracis-28347	114	22	variation	variation	NOUN
bracis-28347	114	23	did	do	AUX
bracis-28347	114	24	not	not	PART
bracis-28347	114	25	present	present	VERB
bracis-28347	114	26	a	a	DET
bracis-28347	114	27	significant	significant	ADJ
bracis-28347	114	28	change	change	NOUN
bracis-28347	114	29	in	in	ADP
bracis-28347	114	30	the	the	DET
bracis-28347	114	31	final	final	ADJ
bracis-28347	114	32	results	result	NOUN
bracis-28347	114	33	of	of	ADP
bracis-28347	114	34	the	the	DET
bracis-28347	114	35	paths	path	NOUN
bracis-28347	114	36	found	find	VERB
bracis-28347	114	37	.	.	PUNCT
bracis-28347	115	1	note	note	VERB
bracis-28347	115	2	that	that	SCONJ
bracis-28347	115	3	the	the	DET
bracis-28347	115	4	cactus	cactus	NOUN
bracis-28347	115	5	-	-	PUNCT
bracis-28347	115	6	graph	graph	NOUN
bracis-28347	115	7	algorithm	algorithm	NOUN
bracis-28347	115	8	is	be	AUX
bracis-28347	115	9	linear	linear	ADJ
bracis-28347	115	10	,	,	PUNCT
bracis-28347	115	11	and	and	CCONJ
bracis-28347	115	12	at	at	ADP
bracis-28347	115	13	each	each	DET
bracis-28347	115	14	step	step	NOUN
bracis-28347	115	15	of	of	ADP
bracis-28347	115	16	the	the	DET
bracis-28347	115	17	algorithm	algorithm	NOUN
bracis-28347	115	18	either	either	CCONJ
bracis-28347	115	19	a	a	DET
bracis-28347	115	20	cycle	cycle	NOUN
bracis-28347	115	21	or	or	CCONJ
bracis-28347	115	22	a	a	DET
bracis-28347	115	23	vertex	vertex	NOUN
bracis-28347	115	24	is	be	AUX
bracis-28347	115	25	extracted	extract	VERB
bracis-28347	115	26	from	from	ADP
bracis-28347	115	27	g	g	ADP
bracis-28347	115	28	which	which	PRON
bracis-28347	115	29	in	in	ADP
bracis-28347	115	30	turn	turn	NOUN
bracis-28347	115	31	is	be	AUX
bracis-28347	115	32	connected	connect	VERB
bracis-28347	115	33	to	to	ADP
bracis-28347	115	34	another	another	DET
bracis-28347	115	35	cycle	cycle	NOUN
bracis-28347	115	36	or	or	CCONJ
bracis-28347	115	37	another	another	DET
bracis-28347	115	38	vertex	vertex	NOUN
bracis-28347	115	39	,	,	PUNCT
bracis-28347	115	40	maintaining	maintain	VERB
bracis-28347	115	41	the	the	DET
bracis-28347	115	42	properties	property	NOUN
bracis-28347	115	43	of	of	ADP
bracis-28347	115	44	a	a	DET
bracis-28347	115	45	cactus	cactus	NOUN
bracis-28347	115	46	graph	graph	NOUN
bracis-28347	115	47	.	.	PUNCT
bracis-28347	116	1	fig	fig	NOUN
bracis-28347	116	2	.	.	PUNCT
bracis-28347	117	1	2	2	NUM
bracis-28347	117	2	.	.	X
bracis-28347	117	3	example	example	NOUN
bracis-28347	117	4	of	of	ADP
bracis-28347	117	5	transforming	transform	VERB
bracis-28347	117	6	g	g	NOUN
bracis-28347	117	7	into	into	ADP
bracis-28347	117	8	\(a_k\	\(a_k\	NOUN
bracis-28347	117	9	)	)	PUNCT
bracis-28347	117	10	for	for	ADP
bracis-28347	117	11	\(k	\(k	NOUN
bracis-28347	117	12	\ge	\ge	PROPN
bracis-28347	117	13	3\	3\	NUM
bracis-28347	117	14	)	)	PUNCT
bracis-28347	117	15	full	full	ADJ
bracis-28347	117	16	size	size	NOUN
bracis-28347	117	17	image	image	NOUN
bracis-28347	117	18	4.2	4.2	NUM
bracis-28347	117	19	labelling	labelling	NOUN
bracis-28347	117	20	algorithm	algorithm	NOUN
bracis-28347	117	21	definition	definition	NOUN
bracis-28347	117	22	1	1	NUM
bracis-28347	117	23	given	give	VERB
bracis-28347	117	24	a	a	DET
bracis-28347	117	25	vertex	vertex	NOUN
bracis-28347	117	26	u	u	NOUN
bracis-28347	117	27	in	in	ADP
bracis-28347	117	28	a	a	DET
bracis-28347	117	29	cactus	cactus	NOUN
bracis-28347	117	30	graph	graph	NOUN
bracis-28347	117	31	g	g	NOUN
bracis-28347	117	32	that	that	PRON
bracis-28347	117	33	is	be	AUX
bracis-28347	117	34	root	root	NOUN
bracis-28347	117	35	,	,	PUNCT
bracis-28347	117	36	the	the	DET
bracis-28347	117	37	children	child	NOUN
bracis-28347	117	38	of	of	ADP
bracis-28347	117	39	u	u	NOUN
bracis-28347	117	40	are	be	AUX
bracis-28347	117	41	all	all	ADV
bracis-28347	117	42	vertices	vertex	NOUN
bracis-28347	117	43	adjacent	adjacent	ADJ
bracis-28347	117	44	to	to	ADP
bracis-28347	117	45	u	u	PRON
bracis-28347	117	46	or	or	CCONJ
bracis-28347	117	47	that	that	PRON
bracis-28347	117	48	are	be	AUX
bracis-28347	117	49	in	in	ADP
bracis-28347	117	50	a	a	DET
bracis-28347	117	51	cycle	cycle	NOUN
bracis-28347	117	52	that	that	PRON
bracis-28347	117	53	contains	contain	VERB
bracis-28347	117	54	u.	u.	NOUN
bracis-28347	117	55	definition	definition	NOUN
bracis-28347	117	56	2	2	NUM
bracis-28347	117	57	given	give	VERB
bracis-28347	117	58	a	a	DET
bracis-28347	117	59	cactus	cactus	NOUN
bracis-28347	117	60	graph	graph	NOUN
bracis-28347	117	61	g	g	NOUN
bracis-28347	117	62	and	and	CCONJ
bracis-28347	117	63	a	a	DET
bracis-28347	117	64	vertex	vertex	NOUN
bracis-28347	117	65	\(u	\(u	ADJ
bracis-28347	117	66	\in	\in	PROPN
bracis-28347	117	67	v(g)\	v(g)\	PROPN
bracis-28347	117	68	)	)	PUNCT
bracis-28347	117	69	,	,	PUNCT
bracis-28347	117	70	\(f^u\	\(f^u\	NOUN
bracis-28347	117	71	)	)	PUNCT
bracis-28347	117	72	denotes	denote	VERB
bracis-28347	117	73	the	the	DET
bracis-28347	117	74	set	set	NOUN
bracis-28347	117	75	of	of	ADP
bracis-28347	117	76	all	all	DET
bracis-28347	117	77	vertices	vertex	NOUN
bracis-28347	117	78	that	that	PRON
bracis-28347	117	79	are	be	AUX
bracis-28347	117	80	children	child	NOUN
bracis-28347	117	81	of	of	ADP
bracis-28347	117	82	u	u	NOUN
bracis-28347	117	83	,	,	PUNCT
bracis-28347	117	84	and	and	CCONJ
bracis-28347	117	85	\(h^u\subseteq	\(h^u\subseteq	ADV
bracis-28347	117	86	f^u\	f^u\	ADJ
bracis-28347	117	87	)	)	PUNCT
bracis-28347	117	88	denotes	denote	VERB
bracis-28347	117	89	the	the	DET
bracis-28347	117	90	subset	subset	NOUN
bracis-28347	117	91	of	of	ADP
bracis-28347	117	92	\(f^u\	\(f^u\	NOUN
bracis-28347	117	93	)	)	PUNCT
bracis-28347	117	94	consisting	consist	VERB
bracis-28347	117	95	only	only	ADV
bracis-28347	117	96	of	of	ADP
bracis-28347	117	97	the	the	DET
bracis-28347	117	98	children	child	NOUN
bracis-28347	117	99	of	of	ADP
bracis-28347	117	100	u	u	PRON
bracis-28347	117	101	that	that	PRON
bracis-28347	117	102	belong	belong	VERB
bracis-28347	117	103	to	to	ADP
bracis-28347	117	104	some	some	DET
bracis-28347	117	105	cycle	cycle	NOUN
bracis-28347	117	106	containing	contain	VERB
bracis-28347	117	107	u.	u.	PROPN
bracis-28347	117	108	definition	definition	NOUN
bracis-28347	117	109	3	3	NUM
bracis-28347	117	110	a	a	DET
bracis-28347	117	111	vertex	vertex	NOUN
bracis-28347	117	112	u	u	NOUN
bracis-28347	117	113	is	be	AUX
bracis-28347	117	114	a	a	DET
bracis-28347	117	115	bridge	bridge	NOUN
bracis-28347	117	116	vertex	vertex	NOUN
bracis-28347	117	117	if	if	SCONJ
bracis-28347	117	118	u	u	NOUN
bracis-28347	117	119	has	have	VERB
bracis-28347	117	120	degree	degree	NOUN
bracis-28347	117	121	two	two	NUM
bracis-28347	117	122	,	,	PUNCT
bracis-28347	117	123	belongs	belong	VERB
bracis-28347	117	124	to	to	ADP
bracis-28347	117	125	a	a	DET
bracis-28347	117	126	cycle	cycle	NOUN
bracis-28347	117	127	,	,	PUNCT
bracis-28347	117	128	and	and	CCONJ
bracis-28347	117	129	is	be	AUX
bracis-28347	117	130	the	the	DET
bracis-28347	117	131	child	child	NOUN
bracis-28347	117	132	of	of	ADP
bracis-28347	117	133	some	some	DET
bracis-28347	117	134	other	other	ADJ
bracis-28347	117	135	visited	visit	VERB
bracis-28347	117	136	vertex	vertex	NOUN
bracis-28347	117	137	.	.	PUNCT
bracis-28347	118	1	definition	definition	NOUN
bracis-28347	118	2	4	4	NUM
bracis-28347	118	3	a	a	DET
bracis-28347	118	4	vertex	vertex	NOUN
bracis-28347	118	5	\(u'\	\(u'\	PROPN
bracis-28347	118	6	)	)	PUNCT
bracis-28347	118	7	,	,	PUNCT
bracis-28347	118	8	child	child	NOUN
bracis-28347	118	9	of	of	ADP
bracis-28347	118	10	a	a	DET
bracis-28347	118	11	root	root	NOUN
bracis-28347	118	12	u	u	NOUN
bracis-28347	118	13	,	,	PUNCT
bracis-28347	118	14	has	have	VERB
bracis-28347	118	15	no	no	DET
bracis-28347	118	16	children	child	NOUN
bracis-28347	118	17	if	if	SCONJ
bracis-28347	118	18	\(u'\	\(u'\	PROPN
bracis-28347	118	19	)	)	PUNCT
bracis-28347	118	20	is	be	AUX
bracis-28347	118	21	a	a	DET
bracis-28347	118	22	bridge	bridge	NOUN
bracis-28347	118	23	vertex	vertex	NOUN
bracis-28347	118	24	or	or	CCONJ
bracis-28347	118	25	a	a	DET
bracis-28347	118	26	leaf	leaf	NOUN
bracis-28347	118	27	vertex	vertex	NOUN
bracis-28347	118	28	.	.	PUNCT
bracis-28347	119	1	the	the	DET
bracis-28347	119	2	fig	fig	NOUN
bracis-28347	119	3	.	.	PUNCT
bracis-28347	119	4	 	 	SPACE
bracis-28347	119	5	3	3	NUM
bracis-28347	119	6	demonstrates	demonstrate	VERB
bracis-28347	119	7	a	a	DET
bracis-28347	119	8	cactus	cactus	NOUN
bracis-28347	119	9	graph	graph	NOUN
bracis-28347	119	10	rooted	root	VERB
bracis-28347	119	11	in	in	ADP
bracis-28347	119	12	u	u	NOUN
bracis-28347	119	13	,	,	PUNCT
bracis-28347	119	14	and	and	CCONJ
bracis-28347	119	15	presents	present	VERB
bracis-28347	119	16	an	an	DET
bracis-28347	119	17	example	example	NOUN
bracis-28347	119	18	of	of	ADP
bracis-28347	119	19	the	the	DET
bracis-28347	119	20	formation	formation	NOUN
bracis-28347	119	21	of	of	ADP
bracis-28347	119	22	the	the	DET
bracis-28347	119	23	sets	set	NOUN
bracis-28347	119	24	\(f^u\	\(f^u\	NOUN
bracis-28347	119	25	)	)	PUNCT
bracis-28347	119	26	and	and	CCONJ
bracis-28347	119	27	\(h^u\	\(h^u\	NOUN
bracis-28347	119	28	)	)	PUNCT
bracis-28347	119	29	.	.	PUNCT
bracis-28347	120	1	in	in	ADP
bracis-28347	120	2	the	the	DET
bracis-28347	120	3	figure	figure	NOUN
bracis-28347	120	4	,	,	PUNCT
bracis-28347	120	5	\(f^u\	\(f^u\	NOUN
bracis-28347	120	6	)	)	PUNCT
bracis-28347	120	7	is	be	AUX
bracis-28347	120	8	highlighted	highlight	VERB
bracis-28347	120	9	by	by	ADP
bracis-28347	120	10	the	the	DET
bracis-28347	120	11	red	red	ADJ
bracis-28347	120	12	line	line	NOUN
bracis-28347	120	13	and	and	CCONJ
bracis-28347	120	14	,	,	PUNCT
bracis-28347	120	15	in	in	ADP
bracis-28347	120	16	this	this	DET
bracis-28347	120	17	example	example	NOUN
bracis-28347	120	18	,	,	PUNCT
bracis-28347	120	19	is	be	AUX
bracis-28347	120	20	formed	form	VERB
bracis-28347	120	21	by	by	ADP
bracis-28347	120	22	the	the	DET
bracis-28347	120	23	vertices	vertex	NOUN
bracis-28347	120	24	\(f^u	\(f^u	PROPN
bracis-28347	120	25	=	=	SYM
bracis-28347	120	26	v_1	v_1	PROPN
bracis-28347	120	27	,	,	PUNCT
bracis-28347	120	28	v_2	v_2	PROPN
bracis-28347	120	29	,	,	PUNCT
bracis-28347	120	30	v_3	v_3	PROPN
bracis-28347	120	31	,	,	PUNCT
bracis-28347	120	32	v_4	v_4	ADJ
bracis-28347	120	33	,	,	PUNCT
bracis-28347	120	34	v_5	v_5	ADP
bracis-28347	120	35	,	,	PUNCT
bracis-28347	120	36	v_6	v_6	PROPN
bracis-28347	120	37	,	,	PUNCT
bracis-28347	120	38	v_7\	v_7\	PROPN
bracis-28347	120	39	)	)	PUNCT
bracis-28347	120	40	,	,	PUNCT
bracis-28347	120	41	while	while	SCONJ
bracis-28347	120	42	\(h^u\	\(h^u\	NOUN
bracis-28347	120	43	)	)	PUNCT
bracis-28347	120	44	is	be	AUX
bracis-28347	120	45	highlighted	highlight	VERB
bracis-28347	120	46	by	by	ADP
bracis-28347	120	47	the	the	DET
bracis-28347	120	48	blue	blue	ADJ
bracis-28347	120	49	line	line	NOUN
bracis-28347	120	50	and	and	CCONJ
bracis-28347	120	51	,	,	PUNCT
bracis-28347	120	52	in	in	ADP
bracis-28347	120	53	this	this	DET
bracis-28347	120	54	example	example	NOUN
bracis-28347	120	55	,	,	PUNCT
bracis-28347	120	56	is	be	AUX
bracis-28347	120	57	formed	form	VERB
bracis-28347	120	58	by	by	ADP
bracis-28347	120	59	the	the	DET
bracis-28347	120	60	vertices	vertex	NOUN
bracis-28347	120	61	\(h^u	\(h^u	PROPN
bracis-28347	120	62	=	=	SYM
bracis-28347	120	63	v_3	v_3	PROPN
bracis-28347	120	64	,	,	PUNCT
bracis-28347	120	65	v_4	v_4	ADJ
bracis-28347	120	66	,	,	PUNCT
bracis-28347	120	67	v_5	v_5	ADP
bracis-28347	120	68	,	,	PUNCT
bracis-28347	120	69	v_6	v_6	PROPN
bracis-28347	120	70	,	,	PUNCT
bracis-28347	120	71	v_7\	v_7\	PROPN
bracis-28347	120	72	)	)	PUNCT
bracis-28347	120	73	.	.	PUNCT
bracis-28347	121	1	fig	fig	NOUN
bracis-28347	121	2	.	.	PUNCT
bracis-28347	122	1	3	3	X
bracis-28347	122	2	.	.	X
bracis-28347	122	3	a	a	DET
bracis-28347	122	4	rooted	rooted	ADJ
bracis-28347	122	5	cactus	cactus	NOUN
bracis-28347	122	6	graph	graph	NOUN
bracis-28347	122	7	at	at	ADP
bracis-28347	122	8	u.	u.	PROPN
bracis-28347	122	9	full	full	ADJ
bracis-28347	122	10	size	size	NOUN
bracis-28347	122	11	image	image	NOUN
bracis-28347	122	12	step	step	NOUN
bracis-28347	122	13	of	of	ADP
bracis-28347	122	14	calculating	calculate	VERB
bracis-28347	122	15	the	the	DET
bracis-28347	122	16	vertex	vertex	NOUN
bracis-28347	122	17	labels	label	NOUN
bracis-28347	122	18	of	of	ADP
bracis-28347	122	19	a	a	DET
bracis-28347	122	20	cactus	cactus	NOUN
bracis-28347	122	21	graph	graph	NOUN
bracis-28347	122	22	:	:	PUNCT
bracis-28347	122	23	by	by	ADP
bracis-28347	122	24	associating	associate	VERB
bracis-28347	122	25	an	an	DET
bracis-28347	122	26	integer	integer	NOUN
bracis-28347	122	27	value	value	NOUN
bracis-28347	122	28	to	to	ADP
bracis-28347	122	29	each	each	DET
bracis-28347	122	30	vertex	vertex	NOUN
bracis-28347	122	31	of	of	ADP
bracis-28347	122	32	a	a	DET
bracis-28347	122	33	cactus	cactus	NOUN
bracis-28347	122	34	graph	graph	NOUN
bracis-28347	122	35	,	,	PUNCT
bracis-28347	122	36	one	one	NOUN
bracis-28347	122	37	obtains	obtain	VERB
bracis-28347	122	38	a	a	DET
bracis-28347	122	39	labeled	label	VERB
bracis-28347	122	40	cactus	cactus	NOUN
bracis-28347	122	41	graph	graph	NOUN
bracis-28347	122	42	.	.	PUNCT
bracis-28347	123	1	in	in	ADP
bracis-28347	123	2	this	this	DET
bracis-28347	123	3	algorithm	algorithm	NOUN
bracis-28347	123	4	,	,	PUNCT
bracis-28347	123	5	two	two	NUM
bracis-28347	123	6	labels	label	NOUN
bracis-28347	123	7	are	be	AUX
bracis-28347	123	8	associated	associate	VERB
bracis-28347	123	9	with	with	ADP
bracis-28347	123	10	each	each	DET
bracis-28347	123	11	vertex	vertex	NOUN
bracis-28347	123	12	\(u	\(u	NOUN
bracis-28347	123	13	\in	\in	PROPN
bracis-28347	123	14	v\	v\	NOUN
bracis-28347	123	15	):	):	PUNCT
bracis-28347	123	16	the	the	DET
bracis-28347	123	17	partial	partial	ADJ
bracis-28347	123	18	label	label	NOUN
bracis-28347	123	19	and	and	CCONJ
bracis-28347	123	20	the	the	DET
bracis-28347	123	21	total	total	ADJ
bracis-28347	123	22	label	label	NOUN
bracis-28347	123	23	,	,	PUNCT
bracis-28347	123	24	both	both	PRON
bracis-28347	123	25	defined	define	VERB
bracis-28347	123	26	below	below	ADV
bracis-28347	123	27	.	.	PUNCT
bracis-28347	124	1	definition	definition	NOUN
bracis-28347	124	2	5	5	NUM
bracis-28347	124	3	the	the	DET
bracis-28347	124	4	value	value	NOUN
bracis-28347	124	5	of	of	ADP
bracis-28347	124	6	the	the	DET
bracis-28347	124	7	partial	partial	ADJ
bracis-28347	124	8	label	label	NOUN
bracis-28347	124	9	of	of	ADP
bracis-28347	124	10	u	u	NOUN
bracis-28347	124	11	(	(	PUNCT
bracis-28347	124	12	\(r_p(u)\	\(r_p(u)\	NUM
bracis-28347	124	13	)	)	PUNCT
bracis-28347	124	14	)	)	PUNCT
bracis-28347	124	15	represents	represent	VERB
bracis-28347	124	16	the	the	DET
bracis-28347	124	17	largest	large	ADJ
bracis-28347	124	18	number	number	NOUN
bracis-28347	124	19	of	of	ADP
bracis-28347	124	20	colors	color	NOUN
bracis-28347	124	21	on	on	ADP
bracis-28347	124	22	a	a	DET
bracis-28347	124	23	path	path	NOUN
bracis-28347	124	24	in	in	ADP
bracis-28347	124	25	a	a	DET
bracis-28347	124	26	cactus	cactus	NOUN
bracis-28347	124	27	subgraph	subgraph	NOUN
bracis-28347	124	28	rooted	root	VERB
bracis-28347	124	29	at	at	ADP
bracis-28347	124	30	u.	u.	PROPN
bracis-28347	124	31	definition	definition	NOUN
bracis-28347	124	32	6	6	NUM
bracis-28347	124	33	the	the	DET
bracis-28347	124	34	value	value	NOUN
bracis-28347	124	35	of	of	ADP
bracis-28347	124	36	the	the	DET
bracis-28347	124	37	total	total	ADJ
bracis-28347	124	38	label	label	NOUN
bracis-28347	124	39	of	of	ADP
bracis-28347	124	40	u	u	NOUN
bracis-28347	124	41	(	(	PUNCT
bracis-28347	124	42	\(r_t(u)\	\(r_t(u)\	NOUN
bracis-28347	124	43	)	)	PUNCT
bracis-28347	124	44	)	)	PUNCT
bracis-28347	124	45	represents	represent	VERB
bracis-28347	124	46	the	the	DET
bracis-28347	124	47	largest	large	ADJ
bracis-28347	124	48	number	number	NOUN
bracis-28347	124	49	of	of	ADP
bracis-28347	124	50	colors	color	NOUN
bracis-28347	124	51	on	on	ADP
bracis-28347	124	52	a	a	DET
bracis-28347	124	53	path	path	NOUN
bracis-28347	124	54	that	that	PRON
bracis-28347	124	55	contains	contain	VERB
bracis-28347	124	56	u	u	NOUN
bracis-28347	124	57	and	and	CCONJ
bracis-28347	124	58	is	be	AUX
bracis-28347	124	59	contained	contain	VERB
bracis-28347	124	60	in	in	ADP
bracis-28347	124	61	cactus	cactus	NOUN
bracis-28347	124	62	subgraphs	subgraph	NOUN
bracis-28347	124	63	rooted	root	VERB
bracis-28347	124	64	at	at	ADP
bracis-28347	124	65	u.	u.	PROPN
bracis-28347	124	66	algorithm	algorithm	PROPN
bracis-28347	124	67	1	1	NUM
bracis-28347	124	68	label	label	NOUN
bracis-28347	124	69	-	-	PUNCT
bracis-28347	124	70	calculation	calculation	NOUN
bracis-28347	124	71	full	full	ADJ
bracis-28347	124	72	size	size	NOUN
bracis-28347	124	73	image	image	NOUN
bracis-28347	124	74	to	to	PART
bracis-28347	124	75	compute	compute	VERB
bracis-28347	124	76	the	the	DET
bracis-28347	124	77	label	label	NOUN
bracis-28347	124	78	of	of	ADP
bracis-28347	124	79	the	the	DET
bracis-28347	124	80	vertices	vertex	NOUN
bracis-28347	124	81	of	of	ADP
bracis-28347	124	82	the	the	DET
bracis-28347	124	83	cactus	cactus	NOUN
bracis-28347	124	84	graph	graph	NOUN
bracis-28347	124	85	,	,	PUNCT
bracis-28347	124	86	each	each	DET
bracis-28347	124	87	vertex	vertex	NOUN
bracis-28347	124	88	\(u	\(u	ADJ
bracis-28347	124	89	\in	\in	PROPN
bracis-28347	124	90	v\	v\	NOUN
bracis-28347	124	91	)	)	PUNCT
bracis-28347	124	92	receives	receive	VERB
bracis-28347	124	93	a	a	DET
bracis-28347	124	94	color	color	NOUN
bracis-28347	124	95	list	list	NOUN
bracis-28347	124	96	l(u	l(u	PROPN
bracis-28347	124	97	)	)	PUNCT
bracis-28347	124	98	that	that	PRON
bracis-28347	124	99	will	will	AUX
bracis-28347	124	100	initially	initially	ADV
bracis-28347	124	101	contain	contain	VERB
bracis-28347	124	102	the	the	DET
bracis-28347	124	103	color	color	NOUN
bracis-28347	124	104	of	of	ADP
bracis-28347	124	105	u.	u.	NOUN
bracis-28347	124	106	this	this	DET
bracis-28347	124	107	list	list	NOUN
bracis-28347	124	108	l	l	NOUN
bracis-28347	124	109	,	,	PUNCT
bracis-28347	124	110	after	after	ADP
bracis-28347	124	111	execution	execution	NOUN
bracis-28347	124	112	of	of	ADP
bracis-28347	124	113	the	the	DET
bracis-28347	124	114	algorithm	algorithm	NOUN
bracis-28347	124	115	,	,	PUNCT
bracis-28347	124	116	will	will	AUX
bracis-28347	124	117	contain	contain	VERB
bracis-28347	124	118	the	the	DET
bracis-28347	124	119	set	set	NOUN
bracis-28347	124	120	of	of	ADP
bracis-28347	124	121	colors	color	NOUN
bracis-28347	124	122	of	of	ADP
bracis-28347	124	123	the	the	DET
bracis-28347	124	124	vertices	vertex	NOUN
bracis-28347	124	125	of	of	ADP
bracis-28347	124	126	a	a	DET
bracis-28347	124	127	path	path	NOUN
bracis-28347	124	128	of	of	ADP
bracis-28347	124	129	a	a	DET
bracis-28347	124	130	subgraph	subgraph	NOUN
bracis-28347	124	131	with	with	ADP
bracis-28347	124	132	a	a	DET
bracis-28347	124	133	root	root	NOUN
bracis-28347	124	134	at	at	ADP
bracis-28347	124	135	u	u	NOUN
bracis-28347	124	136	that	that	PRON
bracis-28347	124	137	contains	contain	VERB
bracis-28347	124	138	the	the	DET
bracis-28347	124	139	greatest	great	ADJ
bracis-28347	124	140	number	number	NOUN
bracis-28347	124	141	of	of	ADP
bracis-28347	124	142	colors	color	NOUN
bracis-28347	124	143	.	.	PUNCT
bracis-28347	125	1	the	the	DET
bracis-28347	125	2	label	label	NOUN
bracis-28347	125	3	of	of	ADP
bracis-28347	125	4	each	each	DET
bracis-28347	125	5	vertex	vertex	NOUN
bracis-28347	125	6	,	,	PUNCT
bracis-28347	125	7	except	except	SCONJ
bracis-28347	125	8	the	the	DET
bracis-28347	125	9	leaf	leaf	NOUN
bracis-28347	125	10	and	and	CCONJ
bracis-28347	125	11	bridge	bridge	NOUN
bracis-28347	125	12	vertices	vertex	NOUN
bracis-28347	125	13	which	which	PRON
bracis-28347	125	14	have	have	VERB
bracis-28347	125	15	labels	label	NOUN
bracis-28347	125	16	\(=	\(=	ADP
bracis-28347	125	17	1\	1\	NUM
bracis-28347	125	18	)	)	PUNCT
bracis-28347	125	19	,	,	PUNCT
bracis-28347	125	20	is	be	AUX
bracis-28347	125	21	calculated	calculate	VERB
bracis-28347	125	22	based	base	VERB
bracis-28347	125	23	on	on	ADP
bracis-28347	125	24	the	the	DET
bracis-28347	125	25	color	color	NOUN
bracis-28347	125	26	lists	list	NOUN
bracis-28347	125	27	of	of	ADP
bracis-28347	125	28	its	its	PRON
bracis-28347	125	29	children	child	NOUN
bracis-28347	125	30	.	.	PUNCT
bracis-28347	126	1	note	note	VERB
bracis-28347	126	2	that	that	SCONJ
bracis-28347	126	3	the	the	DET
bracis-28347	126	4	label	label	NOUN
bracis-28347	126	5	-	-	PUNCT
bracis-28347	126	6	calculation	calculation	NOUN
bracis-28347	126	7	algorithm	algorithm	NOUN
bracis-28347	126	8	labels	label	VERB
bracis-28347	126	9	either	either	CCONJ
bracis-28347	126	10	leaf	leaf	NOUN
bracis-28347	126	11	-	-	PUNCT
bracis-28347	126	12	type	type	NOUN
bracis-28347	126	13	or	or	CCONJ
bracis-28347	126	14	bridge	bridge	NOUN
bracis-28347	126	15	-	-	PUNCT
bracis-28347	126	16	type	type	NOUN
bracis-28347	126	17	vertices	vertex	NOUN
bracis-28347	126	18	first	first	ADV
bracis-28347	126	19	,	,	PUNCT
bracis-28347	126	20	and	and	CCONJ
bracis-28347	126	21	so	so	ADV
bracis-28347	126	22	on	on	ADV
bracis-28347	126	23	until	until	SCONJ
bracis-28347	126	24	it	it	PRON
bracis-28347	126	25	reaches	reach	VERB
bracis-28347	126	26	the	the	DET
bracis-28347	126	27	root	root	NOUN
bracis-28347	126	28	.	.	PUNCT
bracis-28347	127	1	the	the	DET
bracis-28347	127	2	algorithm	algorithm	NOUN
bracis-28347	127	3	label	label	NOUN
bracis-28347	127	4	-	-	PUNCT
bracis-28347	127	5	calculation	calculation	NOUN
bracis-28347	127	6	is	be	AUX
bracis-28347	127	7	executed	execute	VERB
bracis-28347	127	8	for	for	ADP
bracis-28347	127	9	all	all	DET
bracis-28347	127	10	vertices	vertex	NOUN
bracis-28347	127	11	of	of	ADP
bracis-28347	127	12	the	the	DET
bracis-28347	127	13	set	set	VERB
bracis-28347	127	14	\(f^{u}\	\(f^{u}\	NOUN
bracis-28347	127	15	)	)	PUNCT
bracis-28347	127	16	,	,	PUNCT
bracis-28347	127	17	children	child	NOUN
bracis-28347	127	18	of	of	ADP
bracis-28347	127	19	the	the	DET
bracis-28347	127	20	root	root	NOUN
bracis-28347	127	21	u.	u.	VERB
bracis-28347	127	22	the	the	DET
bracis-28347	127	23	vertex	vertex	NOUN
bracis-28347	127	24	label	label	NOUN
bracis-28347	127	25	u	u	NOUN
bracis-28347	127	26	is	be	AUX
bracis-28347	127	27	calculated	calculate	VERB
bracis-28347	127	28	only	only	ADV
bracis-28347	127	29	after	after	ADV
bracis-28347	127	30	all	all	DET
bracis-28347	127	31	vertices	vertex	NOUN
bracis-28347	127	32	in	in	ADP
bracis-28347	127	33	\(f^{u}\	\(f^{u}\	NOUN
bracis-28347	127	34	)	)	PUNCT
bracis-28347	127	35	already	already	ADV
bracis-28347	127	36	have	have	VERB
bracis-28347	127	37	a	a	DET
bracis-28347	127	38	label	label	NOUN
bracis-28347	127	39	.	.	PUNCT
bracis-28347	128	1	it	it	PRON
bracis-28347	128	2	is	be	AUX
bracis-28347	128	3	easy	easy	ADJ
bracis-28347	128	4	to	to	PART
bracis-28347	128	5	see	see	VERB
bracis-28347	128	6	that	that	SCONJ
bracis-28347	128	7	the	the	DET
bracis-28347	128	8	algorithm	algorithm	NOUN
bracis-28347	128	9	can	can	AUX
bracis-28347	128	10	be	be	AUX
bracis-28347	128	11	adapted	adapt	VERB
bracis-28347	128	12	to	to	PART
bracis-28347	128	13	return	return	VERB
bracis-28347	128	14	the	the	DET
bracis-28347	128	15	vertices	vertex	NOUN
bracis-28347	128	16	of	of	ADP
bracis-28347	128	17	the	the	DET
bracis-28347	128	18	best	good	ADJ
bracis-28347	128	19	path	path	NOUN
bracis-28347	128	20	found	find	VERB
bracis-28347	128	21	in	in	ADP
bracis-28347	128	22	linear	linear	ADJ
bracis-28347	128	23	time	time	NOUN
bracis-28347	128	24	.	.	PUNCT
bracis-28347	129	1	4.3	4.3	NUM
bracis-28347	129	2	tropical	tropical	ADJ
bracis-28347	129	3	-	-	PUNCT
bracis-28347	129	4	cactus	cactus	NOUN
bracis-28347	129	5	algorithm	algorithm	NOUN
bracis-28347	129	6	given	give	VERB
bracis-28347	129	7	any	any	DET
bracis-28347	129	8	vertex	vertex	NOUN
bracis-28347	129	9	u	u	NOUN
bracis-28347	129	10	defined	define	VERB
bracis-28347	129	11	as	as	ADP
bracis-28347	129	12	a	a	DET
bracis-28347	129	13	root	root	NOUN
bracis-28347	129	14	of	of	ADP
bracis-28347	129	15	g	g	NOUN
bracis-28347	129	16	,	,	PUNCT
bracis-28347	129	17	the	the	DET
bracis-28347	129	18	main	main	ADJ
bracis-28347	129	19	tropical	tropical	ADJ
bracis-28347	129	20	-	-	PUNCT
bracis-28347	129	21	cactus	cactus	NOUN
bracis-28347	129	22	algorithm	algorithm	NOUN
bracis-28347	129	23	uses	use	VERB
bracis-28347	129	24	the	the	DET
bracis-28347	129	25	auxiliary	auxiliary	ADJ
bracis-28347	129	26	label	label	NOUN
bracis-28347	129	27	-	-	PUNCT
bracis-28347	129	28	calculation	calculation	NOUN
bracis-28347	129	29	algorithm	algorithm	NOUN
bracis-28347	129	30	to	to	PART
bracis-28347	129	31	label	label	VERB
bracis-28347	129	32	all	all	DET
bracis-28347	129	33	vertices	vertex	NOUN
bracis-28347	129	34	of	of	ADP
bracis-28347	129	35	the	the	DET
bracis-28347	129	36	cactus	cactus	NOUN
bracis-28347	129	37	graph	graph	NOUN
bracis-28347	129	38	g.	g.	NOUN
bracis-28347	129	39	for	for	ADP
bracis-28347	129	40	each	each	DET
bracis-28347	129	41	root	root	NOUN
bracis-28347	129	42	\(u'\ne	\(u'\ne	ADV
bracis-28347	129	43	u\	u\	NOUN
bracis-28347	129	44	)	)	PUNCT
bracis-28347	129	45	,	,	PUNCT
bracis-28347	129	46	the	the	DET
bracis-28347	129	47	tropical	tropical	ADJ
bracis-28347	129	48	-	-	PUNCT
bracis-28347	129	49	cactus	cactus	NOUN
bracis-28347	129	50	algorithm	algorithm	NOUN
bracis-28347	129	51	is	be	AUX
bracis-28347	129	52	run	run	VERB
bracis-28347	129	53	,	,	PUNCT
bracis-28347	129	54	and	and	CCONJ
bracis-28347	129	55	the	the	DET
bracis-28347	129	56	vertices	vertex	NOUN
bracis-28347	129	57	of	of	ADP
bracis-28347	129	58	g	g	NOUN
bracis-28347	129	59	are	be	AUX
bracis-28347	129	60	given	give	VERB
bracis-28347	129	61	a	a	DET
bracis-28347	129	62	label	label	NOUN
bracis-28347	129	63	.	.	PUNCT
bracis-28347	130	1	in	in	ADP
bracis-28347	130	2	short	short	ADJ
bracis-28347	130	3	,	,	PUNCT
bracis-28347	130	4	the	the	DET
bracis-28347	130	5	tropical	tropical	ADJ
bracis-28347	130	6	-	-	PUNCT
bracis-28347	130	7	cactus	cactus	NOUN
bracis-28347	130	8	algorithm	algorithm	NOUN
bracis-28347	130	9	returns	return	VERB
bracis-28347	130	10	the	the	DET
bracis-28347	130	11	largest	large	ADJ
bracis-28347	130	12	found	find	VERB
bracis-28347	130	13	value	value	NOUN
bracis-28347	130	14	of	of	ADP
bracis-28347	130	15	the	the	DET
bracis-28347	130	16	labels	label	NOUN
bracis-28347	130	17	\(r_t(u)\	\(r_t(u)\	NOUN
bracis-28347	130	18	)	)	PUNCT
bracis-28347	130	19	that	that	PRON
bracis-28347	130	20	is	be	AUX
bracis-28347	130	21	calculated	calculate	VERB
bracis-28347	130	22	for	for	ADP
bracis-28347	130	23	each	each	PRON
bracis-28347	130	24	\(u'\in	\(u'\in	ADJ
bracis-28347	130	25	v\	v\	NOUN
bracis-28347	130	26	)	)	PUNCT
bracis-28347	130	27	possible	possible	ADJ
bracis-28347	130	28	root	root	NOUN
bracis-28347	130	29	of	of	ADP
bracis-28347	130	30	g.	g.	NOUN
bracis-28347	130	31	by	by	ADP
bracis-28347	130	32	the	the	DET
bracis-28347	130	33	definition	definition	NOUN
bracis-28347	130	34	of	of	ADP
bracis-28347	130	35	\(r_t(u)\	\(r_t(u)\	PROPN
bracis-28347	130	36	)	)	PUNCT
bracis-28347	130	37	,	,	PUNCT
bracis-28347	130	38	this	this	PRON
bracis-28347	130	39	is	be	AUX
bracis-28347	130	40	equivalent	equivalent	ADJ
bracis-28347	130	41	to	to	ADP
bracis-28347	130	42	the	the	DET
bracis-28347	130	43	largest	large	ADJ
bracis-28347	130	44	number	number	NOUN
bracis-28347	130	45	of	of	ADP
bracis-28347	130	46	colors	color	NOUN
bracis-28347	130	47	of	of	ADP
bracis-28347	130	48	a	a	DET
bracis-28347	130	49	found	find	VERB
bracis-28347	130	50	path	path	NOUN
bracis-28347	130	51	that	that	PRON
bracis-28347	130	52	passes	pass	VERB
bracis-28347	130	53	through	through	ADP
bracis-28347	130	54	u.	u.	PROPN
bracis-28347	130	55	algorithm	algorithm	PROPN
bracis-28347	130	56	2	2	NUM
bracis-28347	130	57	tropical	tropical	ADJ
bracis-28347	130	58	-	-	PUNCT
bracis-28347	130	59	cactus	cactus	NOUN
bracis-28347	130	60	full	full	ADJ
bracis-28347	130	61	size	size	NOUN
bracis-28347	130	62	image	image	NOUN
bracis-28347	130	63	the	the	DET
bracis-28347	130	64	following	follow	VERB
bracis-28347	130	65	result	result	NOUN
bracis-28347	130	66	shows	show	VERB
bracis-28347	130	67	the	the	DET
bracis-28347	130	68	complexity	complexity	NOUN
bracis-28347	130	69	of	of	ADP
bracis-28347	130	70	the	the	DET
bracis-28347	130	71	tropical	tropical	ADJ
bracis-28347	130	72	-	-	PUNCT
bracis-28347	130	73	cactus	cactus	NOUN
bracis-28347	130	74	algorithm	algorithm	NOUN
bracis-28347	130	75	.	.	PUNCT
bracis-28347	131	1	the	the	DET
bracis-28347	131	2	idea	idea	NOUN
bracis-28347	131	3	in	in	ADP
bracis-28347	131	4	this	this	DET
bracis-28347	131	5	context	context	NOUN
bracis-28347	131	6	is	be	AUX
bracis-28347	131	7	to	to	PART
bracis-28347	131	8	show	show	VERB
bracis-28347	131	9	that	that	SCONJ
bracis-28347	131	10	the	the	DET
bracis-28347	131	11	execution	execution	NOUN
bracis-28347	131	12	of	of	ADP
bracis-28347	131	13	the	the	DET
bracis-28347	131	14	algorithm	algorithm	NOUN
bracis-28347	131	15	takes	take	VERB
bracis-28347	131	16	polynomial	polynomial	ADJ
bracis-28347	131	17	time	time	NOUN
bracis-28347	131	18	.	.	PUNCT
bracis-28347	132	1	lemma	lemma	PROPN
bracis-28347	132	2	1	1	NUM
bracis-28347	132	3	the	the	DET
bracis-28347	132	4	label	label	NOUN
bracis-28347	132	5	-	-	PUNCT
bracis-28347	132	6	calculation	calculation	NOUN
bracis-28347	132	7	algorithm	algorithm	NOUN
bracis-28347	132	8	runs	run	VERB
bracis-28347	132	9	in	in	ADP
bracis-28347	132	10	linear	linear	ADJ
bracis-28347	132	11	time	time	NOUN
bracis-28347	132	12	\(\vartheta	\(\vartheta	ADJ
bracis-28347	132	13	\left	\left	PROPN
bracis-28347	132	14	(	(	PUNCT
bracis-28347	132	15	\left|	\left|	NOUN
bracis-28347	132	16	v\left	v\left	NOUN
bracis-28347	132	17	(	(	PUNCT
bracis-28347	132	18	g	g	PROPN
bracis-28347	132	19	\right	\right	PROPN
bracis-28347	132	20	)	)	PUNCT
bracis-28347	132	21	\right|	\right|	NOUN
bracis-28347	132	22	\right	\right	PROPN
bracis-28347	132	23	)	)	PUNCT
bracis-28347	132	24	\	\	NOUN
bracis-28347	132	25	)	)	PUNCT
bracis-28347	132	26	.	.	PUNCT
bracis-28347	133	1	proof	proof	NOUN
bracis-28347	133	2	the	the	DET
bracis-28347	133	3	algorithm	algorithm	NOUN
bracis-28347	133	4	is	be	AUX
bracis-28347	133	5	initially	initially	ADV
bracis-28347	133	6	run	run	VERB
bracis-28347	133	7	for	for	ADP
bracis-28347	133	8	the	the	DET
bracis-28347	133	9	root	root	NOUN
bracis-28347	133	10	vertex	vertex	NOUN
bracis-28347	133	11	u.	u.	NOUN
bracis-28347	133	12	in	in	ADP
bracis-28347	133	13	line	line	NOUN
bracis-28347	133	14	4	4	NUM
bracis-28347	133	15	,	,	PUNCT
bracis-28347	133	16	the	the	DET
bracis-28347	133	17	algorithm	algorithm	NOUN
bracis-28347	133	18	is	be	AUX
bracis-28347	133	19	called	call	VERB
bracis-28347	133	20	recursively	recursively	ADV
bracis-28347	133	21	for	for	ADP
bracis-28347	133	22	each	each	DET
bracis-28347	133	23	child	child	NOUN
bracis-28347	133	24	\(u'\	\(u'\	PROPN
bracis-28347	133	25	)	)	PUNCT
bracis-28347	133	26	of	of	ADP
bracis-28347	133	27	u	u	PROPN
bracis-28347	133	28	,	,	PUNCT
bracis-28347	133	29	which	which	PRON
bracis-28347	133	30	will	will	AUX
bracis-28347	133	31	either	either	CCONJ
bracis-28347	133	32	be	be	AUX
bracis-28347	133	33	a	a	DET
bracis-28347	133	34	bridge	bridge	NOUN
bracis-28347	133	35	or	or	CCONJ
bracis-28347	133	36	a	a	DET
bracis-28347	133	37	leaf	leaf	NOUN
bracis-28347	133	38	,	,	PUNCT
bracis-28347	133	39	or	or	CCONJ
bracis-28347	133	40	there	there	PRON
bracis-28347	133	41	will	will	AUX
bracis-28347	133	42	be	be	AUX
bracis-28347	133	43	a	a	DET
bracis-28347	133	44	cactus	cactus	NOUN
bracis-28347	133	45	subgraph	subgraph	NOUN
bracis-28347	133	46	rooted	root	VERB
bracis-28347	133	47	in	in	ADP
bracis-28347	133	48	\(u'\	\(u'\	PROPN
bracis-28347	133	49	)	)	PUNCT
bracis-28347	133	50	,	,	PUNCT
bracis-28347	133	51	of	of	ADP
bracis-28347	133	52	which	which	PRON
bracis-28347	133	53	u	u	NOUN
bracis-28347	133	54	is	be	AUX
bracis-28347	133	55	no	no	ADV
bracis-28347	133	56	longer	long	ADJ
bracis-28347	133	57	part	part	NOUN
bracis-28347	133	58	,	,	PUNCT
bracis-28347	133	59	thus	thus	ADV
bracis-28347	133	60	the	the	DET
bracis-28347	133	61	total	total	ADJ
bracis-28347	133	62	number	number	NOUN
bracis-28347	133	63	of	of	ADP
bracis-28347	133	64	recursive	recursive	ADJ
bracis-28347	133	65	calls	call	NOUN
bracis-28347	133	66	of	of	ADP
bracis-28347	133	67	the	the	DET
bracis-28347	133	68	algorithm	algorithm	NOUN
bracis-28347	133	69	is	be	AUX
bracis-28347	133	70	the	the	DET
bracis-28347	133	71	number	number	NOUN
bracis-28347	133	72	of	of	ADP
bracis-28347	133	73	vertices	vertex	NOUN
bracis-28347	133	74	in	in	ADP
bracis-28347	133	75	the	the	DET
bracis-28347	133	76	graph	graph	NOUN
bracis-28347	133	77	.	.	PUNCT
bracis-28347	134	1	additionally	additionally	ADV
bracis-28347	134	2	,	,	PUNCT
bracis-28347	134	3	note	note	VERB
bracis-28347	134	4	that	that	SCONJ
bracis-28347	134	5	the	the	DET
bracis-28347	134	6	operations	operation	NOUN
bracis-28347	134	7	in	in	ADP
bracis-28347	134	8	lines	line	NOUN
bracis-28347	134	9	1	1	NUM
bracis-28347	134	10	and	and	CCONJ
bracis-28347	134	11	2	2	NUM
bracis-28347	134	12	and	and	CCONJ
bracis-28347	134	13	lines	line	NOUN
bracis-28347	134	14	6–18	6–18	NUM
bracis-28347	134	15	take	take	NOUN
bracis-28347	134	16	o(1	o(1	NOUN
bracis-28347	134	17	)	)	PUNCT
bracis-28347	134	18	time	time	NOUN
bracis-28347	134	19	,	,	PUNCT
bracis-28347	134	20	which	which	PRON
bracis-28347	134	21	shows	show	VERB
bracis-28347	134	22	that	that	SCONJ
bracis-28347	134	23	the	the	DET
bracis-28347	134	24	algorithm	algorithm	NOUN
bracis-28347	134	25	has	have	VERB
bracis-28347	134	26	linear	linear	ADJ
bracis-28347	134	27	complexity	complexity	NOUN
bracis-28347	134	28	in	in	ADP
bracis-28347	134	29	input	input	NOUN
bracis-28347	134	30	size	size	NOUN
bracis-28347	134	31	.	.	PUNCT
bracis-28347	135	1	proposition	proposition	NOUN
bracis-28347	135	2	1	1	NUM
bracis-28347	135	3	the	the	DET
bracis-28347	135	4	tropical	tropical	ADJ
bracis-28347	135	5	-	-	PUNCT
bracis-28347	135	6	cactus	cactus	NOUN
bracis-28347	135	7	algorithm	algorithm	NOUN
bracis-28347	135	8	runs	run	VERB
bracis-28347	135	9	in	in	ADP
bracis-28347	135	10	polynomial	polynomial	ADJ
bracis-28347	135	11	time	time	NOUN
bracis-28347	135	12	\(\vartheta	\(\vartheta	ADJ
bracis-28347	135	13	\left	\left	PROPN
bracis-28347	135	14	(	(	PUNCT
bracis-28347	135	15	\left|	\left|	NOUN
bracis-28347	135	16	v\left	v\left	NOUN
bracis-28347	135	17	(	(	PUNCT
bracis-28347	135	18	g	g	NOUN
bracis-28347	135	19	\right	\right	PROPN
bracis-28347	135	20	)	)	PUNCT
bracis-28347	135	21	\right|	\right|	NOUN
bracis-28347	135	22	^2	^2	PUNCT
bracis-28347	135	23	\right	\right	NOUN
bracis-28347	135	24	)	)	PUNCT
bracis-28347	135	25	\	\	NOUN
bracis-28347	135	26	)	)	PUNCT
bracis-28347	135	27	proof	proof	NOUN
bracis-28347	135	28	note	note	VERB
bracis-28347	135	29	that	that	SCONJ
bracis-28347	135	30	the	the	DET
bracis-28347	135	31	tropical	tropical	ADJ
bracis-28347	135	32	-	-	PUNCT
bracis-28347	135	33	cactus	cactus	NOUN
bracis-28347	135	34	algorithm	algorithm	NOUN
bracis-28347	135	35	makes	make	VERB
bracis-28347	135	36	\(\left|	\(\left|	NOUN
bracis-28347	135	37	v\left	v\left	NOUN
bracis-28347	135	38	(	(	PUNCT
bracis-28347	135	39	g	g	PROPN
bracis-28347	135	40	\right	\right	PROPN
bracis-28347	135	41	)	)	PUNCT
bracis-28347	135	42	\right|	\right|	PROPN
bracis-28347	135	43	\	\	PROPN
bracis-28347	135	44	)	)	PUNCT
bracis-28347	135	45	calls	call	VERB
bracis-28347	135	46	to	to	ADP
bracis-28347	135	47	the	the	DET
bracis-28347	135	48	label	label	NOUN
bracis-28347	135	49	-	-	PUNCT
bracis-28347	135	50	calculation	calculation	NOUN
bracis-28347	135	51	algorithm	algorithm	NOUN
bracis-28347	135	52	,	,	PUNCT
bracis-28347	135	53	one	one	NUM
bracis-28347	135	54	call	call	NOUN
bracis-28347	135	55	for	for	ADP
bracis-28347	135	56	each	each	DET
bracis-28347	135	57	vertex	vertex	NOUN
bracis-28347	135	58	that	that	PRON
bracis-28347	135	59	will	will	AUX
bracis-28347	135	60	be	be	AUX
bracis-28347	135	61	taken	take	VERB
bracis-28347	135	62	as	as	ADP
bracis-28347	135	63	the	the	DET
bracis-28347	135	64	root	root	NOUN
bracis-28347	135	65	of	of	ADP
bracis-28347	135	66	the	the	DET
bracis-28347	135	67	graph	graph	NOUN
bracis-28347	135	68	.	.	PUNCT
bracis-28347	136	1	by	by	ADP
bracis-28347	136	2	the	the	DET
bracis-28347	136	3	lemma	lemma	PROPN
bracis-28347	136	4	 	 	SPACE
bracis-28347	136	5	1	1	NUM
bracis-28347	136	6	,	,	PUNCT
bracis-28347	136	7	the	the	DET
bracis-28347	136	8	label	label	NOUN
bracis-28347	136	9	-	-	PUNCT
bracis-28347	136	10	calculation	calculation	NOUN
bracis-28347	136	11	algorithm	algorithm	NOUN
bracis-28347	136	12	runs	run	VERB
bracis-28347	136	13	on	on	ADP
bracis-28347	136	14	\(\vartheta	\(\vartheta	ADJ
bracis-28347	136	15	\left	\left	PROPN
bracis-28347	136	16	(	(	PUNCT
bracis-28347	136	17	\left|	\left|	NOUN
bracis-28347	136	18	v\left	v\left	NOUN
bracis-28347	136	19	(	(	PUNCT
bracis-28347	136	20	g	g	PROPN
bracis-28347	136	21	\right	\right	PROPN
bracis-28347	136	22	)	)	PUNCT
bracis-28347	136	23	\right|	\right|	NOUN
bracis-28347	136	24	\right	\right	PROPN
bracis-28347	136	25	)	)	PUNCT
bracis-28347	136	26	\	\	NOUN
bracis-28347	136	27	)	)	PUNCT
bracis-28347	136	28	and	and	CCONJ
bracis-28347	136	29	therefore	therefore	ADV
bracis-28347	136	30	the	the	DET
bracis-28347	136	31	result	result	NOUN
bracis-28347	136	32	follows	follow	VERB
bracis-28347	136	33	.	.	PUNCT
bracis-28347	137	1	5	5	NUM
bracis-28347	137	2	experimental	experimental	ADJ
bracis-28347	137	3	results	result	NOUN
bracis-28347	137	4	this	this	DET
bracis-28347	137	5	section	section	NOUN
bracis-28347	137	6	presents	present	VERB
bracis-28347	137	7	an	an	DET
bracis-28347	137	8	analysis	analysis	NOUN
bracis-28347	137	9	of	of	ADP
bracis-28347	137	10	the	the	DET
bracis-28347	137	11	experimental	experimental	ADJ
bracis-28347	137	12	results	result	NOUN
bracis-28347	137	13	performed	perform	VERB
bracis-28347	137	14	in	in	ADP
bracis-28347	137	15	this	this	DET
bracis-28347	137	16	work	work	NOUN
bracis-28347	137	17	.	.	PUNCT
bracis-28347	138	1	in	in	ADP
bracis-28347	138	2	general	general	ADJ
bracis-28347	138	3	terms	term	NOUN
bracis-28347	138	4	,	,	PUNCT
bracis-28347	138	5	the	the	DET
bracis-28347	138	6	performance	performance	NOUN
bracis-28347	138	7	of	of	ADP
bracis-28347	138	8	the	the	DET
bracis-28347	138	9	heuristic	heuristic	ADJ
bracis-28347	138	10	algorithm	algorithm	NOUN
bracis-28347	138	11	was	be	AUX
bracis-28347	138	12	evaluated	evaluate	VERB
bracis-28347	138	13	in	in	ADP
bracis-28347	138	14	relation	relation	NOUN
bracis-28347	138	15	to	to	ADP
bracis-28347	138	16	the	the	DET
bracis-28347	138	17	integer	integer	NOUN
bracis-28347	138	18	linear	linear	PROPN
bracis-28347	138	19	programming	programming	NOUN
bracis-28347	138	20	model	model	NOUN
bracis-28347	138	21	for	for	ADP
bracis-28347	138	22	mtpp	mtpp	PROPN
bracis-28347	138	23	in	in	ADP
bracis-28347	138	24	general	general	ADJ
bracis-28347	138	25	graphs	graph	NOUN
bracis-28347	138	26	,	,	PUNCT
bracis-28347	138	27	and	and	CCONJ
bracis-28347	138	28	in	in	ADP
bracis-28347	138	29	cactus	cactus	NOUN
bracis-28347	138	30	graphs	graph	NOUN
bracis-28347	138	31	.	.	PUNCT
bracis-28347	139	1	although	although	SCONJ
bracis-28347	139	2	the	the	DET
bracis-28347	139	3	problem	problem	NOUN
bracis-28347	139	4	is	be	AUX
bracis-28347	139	5	np	np	INTJ
bracis-28347	139	6	-	-	ADJ
bracis-28347	139	7	hard	hard	ADJ
bracis-28347	139	8	in	in	ADP
bracis-28347	139	9	all	all	DET
bracis-28347	139	10	these	these	DET
bracis-28347	139	11	classes	class	NOUN
bracis-28347	139	12	,	,	PUNCT
bracis-28347	139	13	the	the	DET
bracis-28347	139	14	idea	idea	NOUN
bracis-28347	139	15	was	be	AUX
bracis-28347	139	16	to	to	PART
bracis-28347	139	17	obtain	obtain	VERB
bracis-28347	139	18	the	the	DET
bracis-28347	139	19	optimal	optimal	ADJ
bracis-28347	139	20	solution	solution	NOUN
bracis-28347	139	21	for	for	ADP
bracis-28347	139	22	instances	instance	NOUN
bracis-28347	139	23	of	of	ADP
bracis-28347	139	24	various	various	ADJ
bracis-28347	139	25	dimensions	dimension	NOUN
bracis-28347	139	26	,	,	PUNCT
bracis-28347	139	27	in	in	ADP
bracis-28347	139	28	terms	term	NOUN
bracis-28347	139	29	of	of	ADP
bracis-28347	139	30	number	number	NOUN
bracis-28347	139	31	of	of	ADP
bracis-28347	139	32	vertices	vertex	NOUN
bracis-28347	139	33	,	,	PUNCT
bracis-28347	139	34	edges	edge	NOUN
bracis-28347	139	35	,	,	PUNCT
bracis-28347	139	36	and	and	CCONJ
bracis-28347	139	37	colors	color	NOUN
bracis-28347	139	38	,	,	PUNCT
bracis-28347	139	39	and	and	CCONJ
bracis-28347	139	40	compare	compare	VERB
bracis-28347	139	41	it	it	PRON
bracis-28347	139	42	with	with	ADP
bracis-28347	139	43	the	the	DET
bracis-28347	139	44	result	result	NOUN
bracis-28347	139	45	of	of	ADP
bracis-28347	139	46	the	the	DET
bracis-28347	139	47	heuristic	heuristic	ADJ
bracis-28347	139	48	algorithm	algorithm	NOUN
bracis-28347	139	49	for	for	ADP
bracis-28347	139	50	this	this	DET
bracis-28347	139	51	same	same	ADJ
bracis-28347	139	52	set	set	NOUN
bracis-28347	139	53	of	of	ADP
bracis-28347	139	54	instances	instance	NOUN
bracis-28347	139	55	.	.	PUNCT
bracis-28347	140	1	for	for	ADP
bracis-28347	140	2	this	this	DET
bracis-28347	140	3	purpose	purpose	NOUN
bracis-28347	140	4	,	,	PUNCT
bracis-28347	140	5	instances	instance	NOUN
bracis-28347	140	6	were	be	AUX
bracis-28347	140	7	generated	generate	VERB
bracis-28347	140	8	randomly	randomly	ADV
bracis-28347	140	9	and	and	CCONJ
bracis-28347	140	10	also	also	ADV
bracis-28347	140	11	obtained	obtain	VERB
bracis-28347	140	12	from	from	ADP
bracis-28347	140	13	real	real	ADJ
bracis-28347	140	14	-	-	PUNCT
bracis-28347	140	15	world	world	NOUN
bracis-28347	140	16	data	data	NOUN
bracis-28347	140	17	sets	set	NOUN
bracis-28347	140	18	.	.	PUNCT
bracis-28347	141	1	implementation	implementation	NOUN
bracis-28347	141	2	details	detail	NOUN
bracis-28347	141	3	.	.	PUNCT
bracis-28347	142	1	the	the	DET
bracis-28347	142	2	computational	computational	ADJ
bracis-28347	142	3	experiments	experiment	NOUN
bracis-28347	142	4	were	be	AUX
bracis-28347	142	5	carried	carry	VERB
bracis-28347	142	6	out	out	ADP
bracis-28347	142	7	on	on	ADP
bracis-28347	142	8	a	a	DET
bracis-28347	142	9	pc	pc	NOUN
bracis-28347	142	10	with	with	ADP
bracis-28347	142	11	the	the	DET
bracis-28347	142	12	following	follow	VERB
bracis-28347	142	13	specifications	specification	NOUN
bracis-28347	142	14	:	:	PUNCT
bracis-28347	142	15	intel(r	intel(r	PROPN
bracis-28347	142	16	)	)	PUNCT
bracis-28347	142	17	core	core	NOUN
bracis-28347	142	18	(	(	PUNCT
bracis-28347	142	19	tm	tm	NOUN
bracis-28347	142	20	)	)	PUNCT
bracis-28347	142	21	i7	i7	ADJ
bracis-28347	142	22	-	-	PUNCT
bracis-28347	142	23	8550u	8550u	NOUN
bracis-28347	142	24	cpu	cpu	NOUN
bracis-28347	142	25	1.99	1.99	NUM
bracis-28347	142	26	 	 	SPACE
bracis-28347	142	27	ghz	ghz	NOUN
bracis-28347	142	28	processor	processor	NOUN
bracis-28347	142	29	,	,	PUNCT
bracis-28347	142	30	8	8	NUM
bracis-28347	142	31	 	 	SPACE
bracis-28347	142	32	gb	gb	NOUN
bracis-28347	142	33	of	of	ADP
bracis-28347	142	34	ram	ram	NOUN
bracis-28347	142	35	,	,	PUNCT
bracis-28347	142	36	and	and	CCONJ
bracis-28347	142	37	windows	window	VERB
bracis-28347	142	38	10	10	NUM
bracis-28347	142	39	home	home	NOUN
bracis-28347	142	40	operating	operating	NOUN
bracis-28347	142	41	system	system	NOUN
bracis-28347	142	42	version	version	NOUN
bracis-28347	142	43	20h2	20h2	NUM
bracis-28347	142	44	.	.	PUNCT
bracis-28347	143	1	for	for	ADP
bracis-28347	143	2	the	the	DET
bracis-28347	143	3	implementation	implementation	NOUN
bracis-28347	143	4	of	of	ADP
bracis-28347	143	5	the	the	DET
bracis-28347	143	6	lp	lp	PROPN
bracis-28347	143	7	models	model	NOUN
bracis-28347	143	8	,	,	PUNCT
bracis-28347	143	9	the	the	DET
bracis-28347	143	10	commercial	commercial	ADJ
bracis-28347	143	11	optimization	optimization	NOUN
bracis-28347	143	12	software	software	NOUN
bracis-28347	143	13	gurobi	gurobi	NOUN
bracis-28347	143	14	optimizer	optimizer	NOUN
bracis-28347	143	15	version	version	NOUN
bracis-28347	143	16	9.5.0	9.5.0	NUM
bracis-28347	143	17	was	be	AUX
bracis-28347	143	18	used	use	VERB
bracis-28347	143	19	.	.	PUNCT
bracis-28347	144	1	the	the	DET
bracis-28347	144	2	gurobi	gurobi	PROPN
bracis-28347	144	3	parameters	parameter	NOUN
bracis-28347	144	4	were	be	AUX
bracis-28347	144	5	configured	configure	VERB
bracis-28347	144	6	with	with	ADP
bracis-28347	144	7	their	their	PRON
bracis-28347	144	8	respective	respective	ADJ
bracis-28347	144	9	default	default	NOUN
bracis-28347	144	10	values	value	NOUN
bracis-28347	144	11	.	.	PUNCT
bracis-28347	145	1	to	to	PART
bracis-28347	145	2	consolidate	consolidate	VERB
bracis-28347	145	3	the	the	DET
bracis-28347	145	4	results	result	NOUN
bracis-28347	145	5	,	,	PUNCT
bracis-28347	145	6	all	all	DET
bracis-28347	145	7	instances	instance	NOUN
bracis-28347	145	8	were	be	AUX
bracis-28347	145	9	run	run	VERB
bracis-28347	145	10	10	10	NUM
bracis-28347	145	11	times	time	NOUN
bracis-28347	145	12	,	,	PUNCT
bracis-28347	145	13	and	and	CCONJ
bracis-28347	145	14	the	the	DET
bracis-28347	145	15	final	final	ADJ
bracis-28347	145	16	results	result	NOUN
bracis-28347	145	17	of	of	ADP
bracis-28347	145	18	each	each	DET
bracis-28347	145	19	instance	instance	NOUN
bracis-28347	145	20	were	be	AUX
bracis-28347	145	21	defined	define	VERB
bracis-28347	145	22	by	by	ADP
bracis-28347	145	23	the	the	DET
bracis-28347	145	24	average	average	NOUN
bracis-28347	145	25	of	of	ADP
bracis-28347	145	26	the	the	DET
bracis-28347	145	27	valid	valid	ADJ
bracis-28347	145	28	results	result	NOUN
bracis-28347	145	29	.	.	PUNCT
bracis-28347	146	1	benchmark	benchmark	ADJ
bracis-28347	146	2	instances	instance	NOUN
bracis-28347	146	3	.	.	PUNCT
bracis-28347	147	1	real	real	ADJ
bracis-28347	147	2	-	-	PUNCT
bracis-28347	147	3	world	world	NOUN
bracis-28347	147	4	instances	instance	NOUN
bracis-28347	147	5	were	be	AUX
bracis-28347	147	6	obtained	obtain	VERB
bracis-28347	147	7	from	from	ADP
bracis-28347	147	8	a	a	DET
bracis-28347	147	9	dataset	dataset	ADJ
bracis-28347	147	10	repository	repository	NOUN
bracis-28347	147	11	[	[	X
bracis-28347	147	12	8	8	NUM
bracis-28347	147	13	]	]	PUNCT
bracis-28347	147	14	.	.	PUNCT
bracis-28347	148	1	in	in	ADP
bracis-28347	148	2	some	some	DET
bracis-28347	148	3	instances	instance	NOUN
bracis-28347	148	4	,	,	PUNCT
bracis-28347	148	5	adaptations	adaptation	NOUN
bracis-28347	148	6	were	be	AUX
bracis-28347	148	7	necessary	necessary	ADJ
bracis-28347	148	8	due	due	ADP
bracis-28347	148	9	to	to	ADP
bracis-28347	148	10	the	the	DET
bracis-28347	148	11	different	different	ADJ
bracis-28347	148	12	characteristics	characteristic	NOUN
bracis-28347	148	13	of	of	ADP
bracis-28347	148	14	the	the	DET
bracis-28347	148	15	networks	network	NOUN
bracis-28347	148	16	in	in	ADP
bracis-28347	148	17	relation	relation	NOUN
bracis-28347	148	18	to	to	ADP
bracis-28347	148	19	the	the	DET
bracis-28347	148	20	problem	problem	NOUN
bracis-28347	148	21	studied	study	VERB
bracis-28347	148	22	.	.	PUNCT
bracis-28347	149	1	the	the	DET
bracis-28347	149	2	adaptations	adaptation	NOUN
bracis-28347	149	3	included	include	VERB
bracis-28347	149	4	removing	remove	VERB
bracis-28347	149	5	isolated	isolate	VERB
bracis-28347	149	6	vertices	vertex	NOUN
bracis-28347	149	7	,	,	PUNCT
bracis-28347	149	8	parallel	parallel	ADJ
bracis-28347	149	9	edges	edge	NOUN
bracis-28347	149	10	,	,	PUNCT
bracis-28347	149	11	and	and	CCONJ
bracis-28347	149	12	loops	loop	NOUN
bracis-28347	149	13	.	.	PUNCT
bracis-28347	150	1	to	to	PART
bracis-28347	150	2	study	study	VERB
bracis-28347	150	3	the	the	DET
bracis-28347	150	4	impact	impact	NOUN
bracis-28347	150	5	of	of	ADP
bracis-28347	150	6	varying	vary	VERB
bracis-28347	150	7	the	the	DET
bracis-28347	150	8	number	number	NOUN
bracis-28347	150	9	of	of	ADP
bracis-28347	150	10	colors	color	NOUN
bracis-28347	150	11	in	in	ADP
bracis-28347	150	12	an	an	DET
bracis-28347	150	13	instance	instance	NOUN
bracis-28347	150	14	,	,	PUNCT
bracis-28347	150	15	three	three	NUM
bracis-28347	150	16	random	random	ADJ
bracis-28347	150	17	colorings	coloring	NOUN
bracis-28347	150	18	were	be	AUX
bracis-28347	150	19	set	set	VERB
bracis-28347	150	20	for	for	ADP
bracis-28347	150	21	all	all	DET
bracis-28347	150	22	networks	network	NOUN
bracis-28347	150	23	that	that	PRON
bracis-28347	150	24	did	do	AUX
bracis-28347	150	25	not	not	PART
bracis-28347	150	26	have	have	VERB
bracis-28347	150	27	a	a	DET
bracis-28347	150	28	previous	previous	ADJ
bracis-28347	150	29	coloring	coloring	NOUN
bracis-28347	150	30	.	.	PUNCT
bracis-28347	151	1	to	to	PART
bracis-28347	151	2	explore	explore	VERB
bracis-28347	151	3	the	the	DET
bracis-28347	151	4	behavior	behavior	NOUN
bracis-28347	151	5	of	of	ADP
bracis-28347	151	6	both	both	CCONJ
bracis-28347	151	7	the	the	DET
bracis-28347	151	8	heuristic	heuristic	ADJ
bracis-28347	151	9	algorithm	algorithm	NOUN
bracis-28347	151	10	and	and	CCONJ
bracis-28347	151	11	the	the	DET
bracis-28347	151	12	ilp	ilp	ADJ
bracis-28347	151	13	model	model	NOUN
bracis-28347	151	14	in	in	ADP
bracis-28347	151	15	terms	term	NOUN
bracis-28347	151	16	of	of	ADP
bracis-28347	151	17	the	the	DET
bracis-28347	151	18	number	number	NOUN
bracis-28347	151	19	of	of	ADP
bracis-28347	151	20	vertices	vertex	NOUN
bracis-28347	151	21	,	,	PUNCT
bracis-28347	151	22	edges	edge	NOUN
bracis-28347	151	23	,	,	PUNCT
bracis-28347	151	24	and	and	CCONJ
bracis-28347	151	25	colors	color	NOUN
bracis-28347	151	26	,	,	PUNCT
bracis-28347	151	27	random	random	ADJ
bracis-28347	151	28	graphs	graph	NOUN
bracis-28347	151	29	were	be	AUX
bracis-28347	151	30	generated	generate	VERB
bracis-28347	151	31	.	.	PUNCT
bracis-28347	152	1	for	for	ADP
bracis-28347	152	2	each	each	DET
bracis-28347	152	3	n	n	PRON
bracis-28347	152	4	vertices	vertex	NOUN
bracis-28347	152	5	,	,	PUNCT
bracis-28347	152	6	instances	instance	NOUN
bracis-28347	152	7	were	be	AUX
bracis-28347	152	8	generated	generate	VERB
bracis-28347	152	9	with	with	ADP
bracis-28347	152	10	the	the	DET
bracis-28347	152	11	following	follow	VERB
bracis-28347	152	12	variations	variation	NOUN
bracis-28347	152	13	in	in	ADP
bracis-28347	152	14	the	the	DET
bracis-28347	152	15	number	number	NOUN
bracis-28347	152	16	of	of	ADP
bracis-28347	152	17	edges	edge	NOUN
bracis-28347	152	18	:	:	PUNCT
bracis-28347	152	19	\(n	\(n	NOUN
bracis-28347	152	20	+	+	CCONJ
bracis-28347	152	21	(	(	PUNCT
bracis-28347	152	22	n/10)\	n/10)\	ADJ
bracis-28347	152	23	)	)	PUNCT
bracis-28347	152	24	,	,	PUNCT
bracis-28347	152	25	2n	2n	NUM
bracis-28347	152	26	,	,	PUNCT
bracis-28347	152	27	\((n*(n-1))/4\	\((n*(n-1))/4\	NOUN
bracis-28347	152	28	)	)	PUNCT
bracis-28347	152	29	,	,	PUNCT
bracis-28347	152	30	and	and	CCONJ
bracis-28347	152	31	\((n*(n-1))/3\	\((n*(n-1))/3\	NOUN
bracis-28347	152	32	)	)	PUNCT
bracis-28347	152	33	.	.	PUNCT
bracis-28347	153	1	additionally	additionally	ADV
bracis-28347	153	2	,	,	PUNCT
bracis-28347	153	3	for	for	ADP
bracis-28347	153	4	each	each	DET
bracis-28347	153	5	number	number	NOUN
bracis-28347	153	6	of	of	ADP
bracis-28347	153	7	vertices	vertex	NOUN
bracis-28347	153	8	,	,	PUNCT
bracis-28347	153	9	three	three	NUM
bracis-28347	153	10	variations	variation	NOUN
bracis-28347	153	11	in	in	ADP
bracis-28347	153	12	the	the	DET
bracis-28347	153	13	number	number	NOUN
bracis-28347	153	14	of	of	ADP
bracis-28347	153	15	colors	color	NOUN
bracis-28347	153	16	were	be	AUX
bracis-28347	153	17	generated	generate	VERB
bracis-28347	153	18	,	,	PUNCT
bracis-28347	153	19	representing	represent	VERB
bracis-28347	153	20	10	10	NUM
bracis-28347	153	21	%	%	NOUN
bracis-28347	153	22	,	,	PUNCT
bracis-28347	153	23	50	50	NUM
bracis-28347	153	24	%	%	NOUN
bracis-28347	153	25	,	,	PUNCT
bracis-28347	153	26	and	and	CCONJ
bracis-28347	153	27	90	90	NUM
bracis-28347	153	28	%	%	NOUN
bracis-28347	153	29	of	of	ADP
bracis-28347	153	30	the	the	DET
bracis-28347	153	31	total	total	ADJ
bracis-28347	153	32	number	number	NOUN
bracis-28347	153	33	of	of	ADP
bracis-28347	153	34	vertices	vertex	NOUN
bracis-28347	153	35	.	.	PUNCT
bracis-28347	154	1	it	it	PRON
bracis-28347	154	2	was	be	AUX
bracis-28347	154	3	noted	note	VERB
bracis-28347	154	4	that	that	SCONJ
bracis-28347	154	5	the	the	DET
bracis-28347	154	6	ilp	ilp	ADJ
bracis-28347	154	7	model	model	NOUN
bracis-28347	154	8	exhibited	exhibit	VERB
bracis-28347	154	9	performance	performance	NOUN
bracis-28347	154	10	limitations	limitation	NOUN
bracis-28347	154	11	in	in	ADP
bracis-28347	154	12	instances	instance	NOUN
bracis-28347	154	13	with	with	ADP
bracis-28347	154	14	around	around	ADP
bracis-28347	154	15	800	800	NUM
bracis-28347	154	16	vertices	vertex	NOUN
bracis-28347	154	17	,	,	PUNCT
bracis-28347	154	18	although	although	SCONJ
bracis-28347	154	19	,	,	PUNCT
bracis-28347	154	20	an	an	DET
bracis-28347	154	21	optimal	optimal	ADJ
bracis-28347	154	22	integer	integer	NOUN
bracis-28347	154	23	solution	solution	NOUN
bracis-28347	154	24	was	be	AUX
bracis-28347	154	25	obtained	obtain	VERB
bracis-28347	154	26	for	for	ADP
bracis-28347	154	27	isolated	isolated	ADJ
bracis-28347	154	28	instances	instance	NOUN
bracis-28347	154	29	with	with	ADP
bracis-28347	154	30	more	more	ADJ
bracis-28347	154	31	than	than	ADP
bracis-28347	154	32	1200	1200	NUM
bracis-28347	154	33	vertices	vertex	NOUN
bracis-28347	154	34	.	.	PUNCT
bracis-28347	155	1	therefore	therefore	ADV
bracis-28347	155	2	,	,	PUNCT
bracis-28347	155	3	for	for	ADP
bracis-28347	155	4	comparative	comparative	ADJ
bracis-28347	155	5	purposes	purpose	NOUN
bracis-28347	155	6	,	,	PUNCT
bracis-28347	155	7	instances	instance	NOUN
bracis-28347	155	8	with	with	ADP
bracis-28347	155	9	200	200	NUM
bracis-28347	155	10	,	,	PUNCT
bracis-28347	155	11	400	400	NUM
bracis-28347	155	12	,	,	PUNCT
bracis-28347	155	13	600	600	NUM
bracis-28347	155	14	,	,	PUNCT
bracis-28347	155	15	and	and	CCONJ
bracis-28347	155	16	800	800	NUM
bracis-28347	155	17	vertices	vertex	NOUN
bracis-28347	155	18	were	be	AUX
bracis-28347	155	19	considered	consider	VERB
bracis-28347	155	20	.	.	PUNCT
bracis-28347	156	1	forty	forty	NUM
bracis-28347	156	2	-	-	PUNCT
bracis-28347	156	3	eight	eight	NUM
bracis-28347	156	4	random	random	ADJ
bracis-28347	156	5	instances	instance	NOUN
bracis-28347	156	6	will	will	AUX
bracis-28347	156	7	be	be	AUX
bracis-28347	156	8	presented	present	VERB
bracis-28347	156	9	in	in	ADP
bracis-28347	156	10	this	this	DET
bracis-28347	156	11	analysis	analysis	NOUN
bracis-28347	156	12	,	,	PUNCT
bracis-28347	156	13	which	which	PRON
bracis-28347	156	14	are	be	AUX
bracis-28347	156	15	identified	identify	VERB
bracis-28347	156	16	in	in	ADP
bracis-28347	156	17	the	the	DET
bracis-28347	156	18	tables	table	NOUN
bracis-28347	156	19	 	 	SPACE
bracis-28347	156	20	2	2	NUM
bracis-28347	156	21	and	and	CCONJ
bracis-28347	156	22	3	3	NUM
bracis-28347	156	23	.	.	PUNCT
bracis-28347	157	1	the	the	DET
bracis-28347	157	2	tables	table	NOUN
bracis-28347	157	3	use	use	VERB
bracis-28347	157	4	an	an	DET
bracis-28347	157	5	index	index	NOUN
bracis-28347	157	6	for	for	ADP
bracis-28347	157	7	each	each	DET
bracis-28347	157	8	variation	variation	NOUN
bracis-28347	157	9	in	in	ADP
bracis-28347	157	10	the	the	DET
bracis-28347	157	11	number	number	NOUN
bracis-28347	157	12	of	of	ADP
bracis-28347	157	13	vertices	vertex	NOUN
bracis-28347	157	14	,	,	PUNCT
bracis-28347	157	15	colors	color	NOUN
bracis-28347	157	16	,	,	PUNCT
bracis-28347	157	17	and	and	CCONJ
bracis-28347	157	18	edges	edge	NOUN
bracis-28347	157	19	.	.	PUNCT
bracis-28347	158	1	the	the	DET
bracis-28347	158	2	index	index	NOUN
bracis-28347	158	3	follows	follow	VERB
bracis-28347	158	4	the	the	DET
bracis-28347	158	5	format	format	NOUN
bracis-28347	158	6	\(a_{ikj}\	\(a_{ikj}\	NOUN
bracis-28347	158	7	)	)	PUNCT
bracis-28347	158	8	,	,	PUNCT
bracis-28347	158	9	where	where	SCONJ
bracis-28347	158	10	i	i	PRON
bracis-28347	158	11	represents	represent	VERB
bracis-28347	158	12	the	the	DET
bracis-28347	158	13	variation	variation	NOUN
bracis-28347	158	14	in	in	ADP
bracis-28347	158	15	the	the	DET
bracis-28347	158	16	number	number	NOUN
bracis-28347	158	17	of	of	ADP
bracis-28347	158	18	vertices	vertex	NOUN
bracis-28347	158	19	,	,	PUNCT
bracis-28347	158	20	k	k	PROPN
bracis-28347	158	21	represents	represent	VERB
bracis-28347	158	22	the	the	DET
bracis-28347	158	23	variation	variation	NOUN
bracis-28347	158	24	in	in	ADP
bracis-28347	158	25	the	the	DET
bracis-28347	158	26	number	number	NOUN
bracis-28347	158	27	of	of	ADP
bracis-28347	158	28	colors	color	NOUN
bracis-28347	158	29	,	,	PUNCT
bracis-28347	158	30	and	and	CCONJ
bracis-28347	158	31	j	j	PROPN
bracis-28347	158	32	represents	represent	VERB
bracis-28347	158	33	the	the	DET
bracis-28347	158	34	variation	variation	NOUN
bracis-28347	158	35	in	in	ADP
bracis-28347	158	36	the	the	DET
bracis-28347	158	37	number	number	NOUN
bracis-28347	158	38	of	of	ADP
bracis-28347	158	39	edges	edge	NOUN
bracis-28347	158	40	.	.	PUNCT
bracis-28347	159	1	the	the	DET
bracis-28347	159	2	instance	instance	NOUN
bracis-28347	159	3	identification	identification	NOUN
bracis-28347	159	4	table	table	NOUN
bracis-28347	159	5	is	be	AUX
bracis-28347	159	6	grouped	group	VERB
bracis-28347	159	7	by	by	ADP
bracis-28347	159	8	the	the	DET
bracis-28347	159	9	number	number	NOUN
bracis-28347	159	10	of	of	ADP
bracis-28347	159	11	vertices	vertex	NOUN
bracis-28347	159	12	|v|	|v|	PROPN
bracis-28347	159	13	,	,	PUNCT
bracis-28347	159	14	and	and	CCONJ
bracis-28347	159	15	each	each	DET
bracis-28347	159	16	set	set	NOUN
bracis-28347	159	17	contains	contain	VERB
bracis-28347	159	18	the	the	DET
bracis-28347	159	19	columns	column	NOUN
bracis-28347	159	20	:	:	PUNCT
bracis-28347	159	21	i	i	PROPN
bracis-28347	159	22	d	d	PROPN
bracis-28347	159	23	,	,	PUNCT
bracis-28347	159	24	number	number	NOUN
bracis-28347	159	25	of	of	ADP
bracis-28347	159	26	colors	color	NOUN
bracis-28347	159	27	\(|\mathcal	\(|\mathcal	X
bracis-28347	159	28	{	{	PUNCT
bracis-28347	159	29	c}|\	c}|\	NOUN
bracis-28347	159	30	)	)	PUNCT
bracis-28347	159	31	,	,	PUNCT
bracis-28347	159	32	and	and	CCONJ
bracis-28347	159	33	number	number	NOUN
bracis-28347	159	34	of	of	ADP
bracis-28347	159	35	edges	edge	NOUN
bracis-28347	159	36	|e|	|e|	PROPN
bracis-28347	159	37	.	.	PUNCT
bracis-28347	160	1	since	since	SCONJ
bracis-28347	160	2	the	the	DET
bracis-28347	160	3	cactus	cactus	NOUN
bracis-28347	160	4	graph	graph	NOUN
bracis-28347	160	5	has	have	VERB
bracis-28347	160	6	a	a	DET
bracis-28347	160	7	limited	limited	ADJ
bracis-28347	160	8	number	number	NOUN
bracis-28347	160	9	of	of	ADP
bracis-28347	160	10	edges	edge	NOUN
bracis-28347	160	11	compared	compare	VERB
bracis-28347	160	12	to	to	ADP
bracis-28347	160	13	a	a	DET
bracis-28347	160	14	traditional	traditional	ADJ
bracis-28347	160	15	graph	graph	NOUN
bracis-28347	160	16	,	,	PUNCT
bracis-28347	160	17	two	two	NUM
bracis-28347	160	18	variations	variation	NOUN
bracis-28347	160	19	on	on	ADP
bracis-28347	160	20	the	the	DET
bracis-28347	160	21	number	number	NOUN
bracis-28347	160	22	of	of	ADP
bracis-28347	160	23	edges	edge	NOUN
bracis-28347	160	24	were	be	AUX
bracis-28347	160	25	defined	define	VERB
bracis-28347	160	26	for	for	ADP
bracis-28347	160	27	each	each	DET
bracis-28347	160	28	cactus	cactus	NOUN
bracis-28347	160	29	graph	graph	NOUN
bracis-28347	160	30	of	of	ADP
bracis-28347	160	31	n	n	NOUN
bracis-28347	160	32	vertices	vertex	NOUN
bracis-28347	160	33	and	and	CCONJ
bracis-28347	160	34	k	k	PROPN
bracis-28347	160	35	colors	color	NOUN
bracis-28347	160	36	(	(	PUNCT
bracis-28347	160	37	table	table	NOUN
bracis-28347	160	38	 	 	SPACE
bracis-28347	160	39	1	1	NUM
bracis-28347	160	40	)	)	PUNCT
bracis-28347	160	41	.	.	PUNCT
bracis-28347	161	1	table	table	NOUN
bracis-28347	161	2	1	1	NUM
bracis-28347	161	3	.	.	PUNCT
bracis-28347	162	1	identification	identification	NOUN
bracis-28347	162	2	of	of	ADP
bracis-28347	162	3	real	real	ADJ
bracis-28347	162	4	-	-	PUNCT
bracis-28347	162	5	world	world	NOUN
bracis-28347	162	6	instances	instance	NOUN
bracis-28347	162	7	for	for	ADP
bracis-28347	162	8	graphs	graph	NOUN
bracis-28347	162	9	in	in	ADP
bracis-28347	162	10	generalfull	generalfull	ADJ
bracis-28347	162	11	size	size	NOUN
bracis-28347	162	12	table	table	NOUN
bracis-28347	162	13	table	table	NOUN
bracis-28347	162	14	2	2	NUM
bracis-28347	162	15	.	.	PUNCT
bracis-28347	162	16	identification	identification	NOUN
bracis-28347	162	17	of	of	ADP
bracis-28347	162	18	the	the	DET
bracis-28347	162	19	random	random	ADJ
bracis-28347	162	20	instances	instance	NOUN
bracis-28347	162	21	for	for	ADP
bracis-28347	162	22	graphs	graph	NOUN
bracis-28347	162	23	in	in	ADP
bracis-28347	162	24	generalfull	generalfull	ADJ
bracis-28347	162	25	size	size	NOUN
bracis-28347	162	26	table	table	NOUN
bracis-28347	162	27	table	table	NOUN
bracis-28347	162	28	3	3	NUM
bracis-28347	162	29	.	.	PUNCT
bracis-28347	162	30	identifying	identify	VERB
bracis-28347	162	31	random	random	ADJ
bracis-28347	162	32	instances	instance	NOUN
bracis-28347	162	33	of	of	ADP
bracis-28347	162	34	cactus	cactus	NOUN
bracis-28347	162	35	graphsfull	graphsfull	NOUN
bracis-28347	162	36	size	size	NOUN
bracis-28347	162	37	table	table	NOUN
bracis-28347	162	38	5.1	5.1	NUM
bracis-28347	162	39	computational	computational	ADJ
bracis-28347	162	40	results	result	NOUN
bracis-28347	162	41	the	the	DET
bracis-28347	162	42	results	result	NOUN
bracis-28347	162	43	of	of	ADP
bracis-28347	162	44	the	the	DET
bracis-28347	162	45	computational	computational	ADJ
bracis-28347	162	46	experiments	experiment	NOUN
bracis-28347	162	47	for	for	ADP
bracis-28347	162	48	the	the	DET
bracis-28347	162	49	ilp	ilp	ADJ
bracis-28347	162	50	model	model	NOUN
bracis-28347	162	51	and	and	CCONJ
bracis-28347	162	52	the	the	DET
bracis-28347	162	53	heuristic	heuristic	ADJ
bracis-28347	162	54	algorithm	algorithm	NOUN
bracis-28347	162	55	are	be	AUX
bracis-28347	162	56	presented	present	VERB
bracis-28347	162	57	in	in	ADP
bracis-28347	162	58	the	the	DET
bracis-28347	162	59	following	follow	VERB
bracis-28347	162	60	tables	table	NOUN
bracis-28347	162	61	:	:	PUNCT
bracis-28347	162	62	table	table	NOUN
bracis-28347	162	63	 	 	SPACE
bracis-28347	162	64	4	4	NUM
bracis-28347	162	65	,	,	PUNCT
bracis-28347	162	66	table	table	NOUN
bracis-28347	162	67	 	 	SPACE
bracis-28347	162	68	5	5	NUM
bracis-28347	162	69	and	and	CCONJ
bracis-28347	162	70	table	table	NOUN
bracis-28347	162	71	 	 	SPACE
bracis-28347	162	72	6	6	NUM
bracis-28347	162	73	and	and	CCONJ
bracis-28347	162	74	present	present	VERB
bracis-28347	162	75	the	the	DET
bracis-28347	162	76	following	follow	VERB
bracis-28347	162	77	nomenclatures	nomenclature	NOUN
bracis-28347	162	78	,	,	PUNCT
bracis-28347	162	79	from	from	ADP
bracis-28347	162	80	left	left	ADJ
bracis-28347	162	81	to	to	ADP
bracis-28347	162	82	right	right	NOUN
bracis-28347	162	83	:	:	PUNCT
bracis-28347	162	84	the	the	DET
bracis-28347	162	85	instance	instance	NOUN
bracis-28347	162	86	(	(	PUNCT
bracis-28347	162	87	i	i	PROPN
bracis-28347	162	88	d	d	PROPN
bracis-28347	162	89	)	)	PUNCT
bracis-28347	162	90	;	;	PUNCT
bracis-28347	162	91	the	the	DET
bracis-28347	162	92	cpu	cpu	NOUN
bracis-28347	162	93	time	time	NOUN
bracis-28347	162	94	spent	spend	VERB
bracis-28347	162	95	,	,	PUNCT
bracis-28347	162	96	in	in	ADP
bracis-28347	162	97	seconds	second	NOUN
bracis-28347	162	98	,	,	PUNCT
bracis-28347	162	99	to	to	PART
bracis-28347	162	100	obtain	obtain	VERB
bracis-28347	162	101	the	the	DET
bracis-28347	162	102	integer	integer	NOUN
bracis-28347	162	103	optimal	optimal	ADJ
bracis-28347	162	104	solution	solution	NOUN
bracis-28347	162	105	(	(	PUNCT
bracis-28347	162	106	\(t_{ilp}(s)\	\(t_{ilp}(s)\	NOUN
bracis-28347	162	107	)	)	PUNCT
bracis-28347	162	108	)	)	PUNCT
bracis-28347	162	109	;	;	PUNCT
bracis-28347	162	110	the	the	DET
bracis-28347	162	111	value	value	NOUN
bracis-28347	162	112	of	of	ADP
bracis-28347	162	113	the	the	DET
bracis-28347	162	114	integer	integer	NOUN
bracis-28347	162	115	optimal	optimal	ADJ
bracis-28347	162	116	solution	solution	NOUN
bracis-28347	162	117	(	(	PUNCT
bracis-28347	162	118	\(sol_{ilp}\	\(sol_{ilp}\	NOUN
bracis-28347	162	119	)	)	PUNCT
bracis-28347	162	120	)	)	PUNCT
bracis-28347	162	121	;	;	PUNCT
bracis-28347	162	122	the	the	DET
bracis-28347	162	123	cpu	cpu	NOUN
bracis-28347	162	124	time	time	NOUN
bracis-28347	162	125	spent	spend	VERB
bracis-28347	162	126	,	,	PUNCT
bracis-28347	162	127	in	in	ADP
bracis-28347	162	128	seconds	second	NOUN
bracis-28347	162	129	,	,	PUNCT
bracis-28347	162	130	of	of	ADP
bracis-28347	162	131	the	the	DET
bracis-28347	162	132	heuristic	heuristic	ADJ
bracis-28347	162	133	algorithm	algorithm	NOUN
bracis-28347	162	134	(	(	PUNCT
bracis-28347	162	135	\(t_{alg}(s)\	\(t_{alg}(s)\	NOUN
bracis-28347	162	136	)	)	PUNCT
bracis-28347	162	137	)	)	PUNCT
bracis-28347	162	138	;	;	PUNCT
bracis-28347	162	139	the	the	DET
bracis-28347	162	140	value	value	NOUN
bracis-28347	162	141	of	of	ADP
bracis-28347	162	142	the	the	DET
bracis-28347	162	143	solution	solution	NOUN
bracis-28347	162	144	returned	return	VERB
bracis-28347	162	145	by	by	ADP
bracis-28347	162	146	the	the	DET
bracis-28347	162	147	heuristic	heuristic	ADJ
bracis-28347	162	148	algorithm	algorithm	NOUN
bracis-28347	162	149	(	(	PUNCT
bracis-28347	162	150	\(sol_{alg}\	\(sol_{alg}\	NOUN
bracis-28347	162	151	)	)	PUNCT
bracis-28347	162	152	)	)	PUNCT
bracis-28347	162	153	;	;	PUNCT
bracis-28347	162	154	and	and	CCONJ
bracis-28347	162	155	finally	finally	ADV
bracis-28347	162	156	the	the	DET
bracis-28347	162	157	difference	difference	NOUN
bracis-28347	162	158	in	in	ADP
bracis-28347	162	159	percentage	percentage	NOUN
bracis-28347	162	160	between	between	ADP
bracis-28347	162	161	the	the	DET
bracis-28347	162	162	integer	integer	NOUN
bracis-28347	162	163	optimal	optimal	ADJ
bracis-28347	162	164	solution	solution	NOUN
bracis-28347	162	165	and	and	CCONJ
bracis-28347	162	166	the	the	DET
bracis-28347	162	167	approximate	approximate	ADJ
bracis-28347	162	168	solution	solution	NOUN
bracis-28347	162	169	of	of	ADP
bracis-28347	162	170	the	the	DET
bracis-28347	162	171	heuristic	heuristic	ADJ
bracis-28347	162	172	algorithm	algorithm	NOUN
bracis-28347	162	173	(	(	PUNCT
bracis-28347	162	174	\(gap_{sol}\	\(gap_{sol}\	PROPN
bracis-28347	162	175	)	)	PUNCT
bracis-28347	162	176	)	)	PUNCT
bracis-28347	162	177	.	.	PUNCT
bracis-28347	163	1	table	table	NOUN
bracis-28347	163	2	4	4	NUM
bracis-28347	163	3	.	.	PUNCT
bracis-28347	163	4	results	result	NOUN
bracis-28347	163	5	of	of	ADP
bracis-28347	163	6	the	the	DET
bracis-28347	163	7	computational	computational	ADJ
bracis-28347	163	8	experiments	experiment	NOUN
bracis-28347	163	9	on	on	ADP
bracis-28347	163	10	random	random	ADJ
bracis-28347	163	11	instances	instance	NOUN
bracis-28347	163	12	for	for	ADP
bracis-28347	163	13	graphs	graph	NOUN
bracis-28347	163	14	in	in	ADP
bracis-28347	163	15	generalfull	generalfull	ADJ
bracis-28347	163	16	size	size	NOUN
bracis-28347	163	17	table	table	NOUN
bracis-28347	163	18	from	from	ADP
bracis-28347	163	19	an	an	DET
bracis-28347	163	20	individual	individual	ADJ
bracis-28347	163	21	analysis	analysis	NOUN
bracis-28347	163	22	of	of	ADP
bracis-28347	163	23	the	the	DET
bracis-28347	163	24	ilp	ilp	ADJ
bracis-28347	163	25	model	model	NOUN
bracis-28347	163	26	,	,	PUNCT
bracis-28347	163	27	it	it	PRON
bracis-28347	163	28	was	be	AUX
bracis-28347	163	29	noted	note	VERB
bracis-28347	163	30	that	that	SCONJ
bracis-28347	163	31	even	even	ADV
bracis-28347	163	32	though	though	SCONJ
bracis-28347	163	33	some	some	DET
bracis-28347	163	34	instances	instance	NOUN
bracis-28347	163	35	exceeded	exceed	VERB
bracis-28347	163	36	the	the	DET
bracis-28347	163	37	proposed	propose	VERB
bracis-28347	163	38	execution	execution	NOUN
bracis-28347	163	39	time	time	NOUN
bracis-28347	163	40	limit	limit	NOUN
bracis-28347	163	41	of	of	ADP
bracis-28347	163	42	60	60	NUM
bracis-28347	163	43	 	 	SPACE
bracis-28347	163	44	min	min	NOUN
bracis-28347	163	45	,	,	PUNCT
bracis-28347	163	46	over	over	ADP
bracis-28347	163	47	\(77\%\	\(77\%\	NUM
bracis-28347	163	48	)	)	PUNCT
bracis-28347	163	49	of	of	ADP
bracis-28347	163	50	the	the	DET
bracis-28347	163	51	executed	execute	VERB
bracis-28347	163	52	instances	instance	NOUN
bracis-28347	163	53	obtained	obtain	VERB
bracis-28347	163	54	optimal	optimal	ADJ
bracis-28347	163	55	integer	integer	NOUN
bracis-28347	163	56	solutions	solution	NOUN
bracis-28347	163	57	in	in	ADP
bracis-28347	163	58	less	less	ADJ
bracis-28347	163	59	than	than	ADP
bracis-28347	163	60	seven	seven	NUM
bracis-28347	163	61	minutes	minute	NOUN
bracis-28347	163	62	.	.	PUNCT
bracis-28347	164	1	some	some	DET
bracis-28347	164	2	isolated	isolated	ADJ
bracis-28347	164	3	tests	test	NOUN
bracis-28347	164	4	obtained	obtain	VERB
bracis-28347	164	5	an	an	DET
bracis-28347	164	6	optimal	optimal	ADJ
bracis-28347	164	7	integer	integer	NOUN
bracis-28347	164	8	solution	solution	NOUN
bracis-28347	164	9	for	for	ADP
bracis-28347	164	10	instances	instance	NOUN
bracis-28347	164	11	of	of	ADP
bracis-28347	164	12	up	up	ADP
bracis-28347	164	13	to	to	PART
bracis-28347	164	14	1250	1250	NUM
bracis-28347	164	15	vertices	vertex	NOUN
bracis-28347	164	16	,	,	PUNCT
bracis-28347	164	17	1125	1125	NUM
bracis-28347	164	18	colors	color	NOUN
bracis-28347	164	19	,	,	PUNCT
bracis-28347	164	20	and	and	CCONJ
bracis-28347	164	21	1375	1375	NUM
bracis-28347	164	22	edges	edge	NOUN
bracis-28347	164	23	.	.	PUNCT
bracis-28347	165	1	table	table	NOUN
bracis-28347	165	2	5	5	NUM
bracis-28347	165	3	.	.	PUNCT
bracis-28347	166	1	results	result	NOUN
bracis-28347	166	2	of	of	ADP
bracis-28347	166	3	the	the	DET
bracis-28347	166	4	computational	computational	ADJ
bracis-28347	166	5	experiments	experiment	NOUN
bracis-28347	166	6	on	on	ADP
bracis-28347	166	7	real	real	ADJ
bracis-28347	166	8	-	-	PUNCT
bracis-28347	166	9	world	world	NOUN
bracis-28347	166	10	instances	instance	NOUN
bracis-28347	166	11	for	for	ADP
bracis-28347	166	12	graphs	graph	NOUN
bracis-28347	166	13	in	in	ADP
bracis-28347	166	14	generalfull	generalfull	ADJ
bracis-28347	166	15	size	size	NOUN
bracis-28347	166	16	table	table	NOUN
bracis-28347	166	17	from	from	ADP
bracis-28347	166	18	the	the	DET
bracis-28347	166	19	perspective	perspective	NOUN
bracis-28347	166	20	of	of	ADP
bracis-28347	166	21	random	random	ADJ
bracis-28347	166	22	graph	graph	NOUN
bracis-28347	166	23	instances	instance	NOUN
bracis-28347	166	24	in	in	ADP
bracis-28347	166	25	general	general	ADJ
bracis-28347	166	26	,	,	PUNCT
bracis-28347	166	27	the	the	DET
bracis-28347	166	28	heuristic	heuristic	ADJ
bracis-28347	166	29	algorithm	algorithm	NOUN
bracis-28347	166	30	found	find	VERB
bracis-28347	166	31	the	the	DET
bracis-28347	166	32	integer	integer	NOUN
bracis-28347	166	33	optimal	optimal	ADJ
bracis-28347	166	34	solution	solution	NOUN
bracis-28347	166	35	for	for	ADP
bracis-28347	166	36	\(28.26\%\	\(28.26\%\	PROPN
bracis-28347	166	37	)	)	PUNCT
bracis-28347	166	38	of	of	ADP
bracis-28347	166	39	the	the	DET
bracis-28347	166	40	instances	instance	NOUN
bracis-28347	166	41	;	;	PUNCT
bracis-28347	166	42	\(86.96\%\	\(86.96\%\	PROPN
bracis-28347	166	43	)	)	PUNCT
bracis-28347	166	44	of	of	ADP
bracis-28347	166	45	the	the	DET
bracis-28347	166	46	instances	instance	NOUN
bracis-28347	166	47	presented	present	VERB
bracis-28347	166	48	a	a	DET
bracis-28347	166	49	gap	gap	NOUN
bracis-28347	166	50	,	,	PUNCT
bracis-28347	166	51	that	that	ADV
bracis-28347	166	52	is	is	ADV
bracis-28347	166	53	,	,	PUNCT
bracis-28347	166	54	a	a	DET
bracis-28347	166	55	difference	difference	NOUN
bracis-28347	166	56	,	,	PUNCT
bracis-28347	166	57	in	in	ADP
bracis-28347	166	58	percent	percent	NOUN
bracis-28347	166	59	,	,	PUNCT
bracis-28347	166	60	between	between	ADP
bracis-28347	166	61	the	the	DET
bracis-28347	166	62	integer	integer	NOUN
bracis-28347	166	63	optimal	optimal	ADJ
bracis-28347	166	64	solution	solution	NOUN
bracis-28347	166	65	presented	present	VERB
bracis-28347	166	66	by	by	ADP
bracis-28347	166	67	the	the	DET
bracis-28347	166	68	ilp	ilp	ADJ
bracis-28347	166	69	model	model	NOUN
bracis-28347	166	70	and	and	CCONJ
bracis-28347	166	71	the	the	DET
bracis-28347	166	72	solution	solution	NOUN
bracis-28347	166	73	of	of	ADP
bracis-28347	166	74	the	the	DET
bracis-28347	166	75	heuristic	heuristic	ADJ
bracis-28347	166	76	algorithm	algorithm	NOUN
bracis-28347	166	77	,	,	PUNCT
bracis-28347	166	78	of	of	ADP
bracis-28347	166	79	less	less	ADJ
bracis-28347	166	80	than	than	ADP
bracis-28347	166	81	\(30\%\	\(30\%\	NUM
bracis-28347	166	82	)	)	PUNCT
bracis-28347	166	83	;	;	PUNCT
bracis-28347	166	84	and	and	CCONJ
bracis-28347	166	85	\(60.87\%\	\(60.87\%\	NOUN
bracis-28347	166	86	)	)	PUNCT
bracis-28347	166	87	of	of	ADP
bracis-28347	166	88	the	the	DET
bracis-28347	166	89	instances	instance	NOUN
bracis-28347	166	90	presented	present	VERB
bracis-28347	166	91	a	a	DET
bracis-28347	166	92	gap	gap	NOUN
bracis-28347	166	93	of	of	ADP
bracis-28347	166	94	less	less	ADJ
bracis-28347	166	95	than	than	ADP
bracis-28347	166	96	\(10\%\	\(10\%\	NUM
bracis-28347	166	97	)	)	PUNCT
bracis-28347	166	98	.	.	PUNCT
bracis-28347	167	1	the	the	DET
bracis-28347	167	2	worst	bad	ADJ
bracis-28347	167	3	case	case	NOUN
bracis-28347	167	4	had	have	VERB
bracis-28347	167	5	a	a	DET
bracis-28347	167	6	gap	gap	NOUN
bracis-28347	167	7	of	of	ADP
bracis-28347	167	8	\(38.16\%\	\(38.16\%\	NOUN
bracis-28347	167	9	)	)	PUNCT
bracis-28347	167	10	.	.	PUNCT
bracis-28347	168	1	it	it	PRON
bracis-28347	168	2	was	be	AUX
bracis-28347	168	3	also	also	ADV
bracis-28347	168	4	noted	note	VERB
bracis-28347	168	5	that	that	SCONJ
bracis-28347	168	6	,	,	PUNCT
bracis-28347	168	7	on	on	ADP
bracis-28347	168	8	average	average	ADJ
bracis-28347	168	9	,	,	PUNCT
bracis-28347	168	10	the	the	DET
bracis-28347	168	11	solution	solution	NOUN
bracis-28347	168	12	of	of	ADP
bracis-28347	168	13	the	the	DET
bracis-28347	168	14	heuristic	heuristic	ADJ
bracis-28347	168	15	algorithm	algorithm	NOUN
bracis-28347	168	16	diverges	diverge	VERB
bracis-28347	168	17	from	from	ADP
bracis-28347	168	18	the	the	DET
bracis-28347	168	19	optimal	optimal	ADJ
bracis-28347	168	20	solution	solution	NOUN
bracis-28347	168	21	presented	present	VERB
bracis-28347	168	22	by	by	ADP
bracis-28347	168	23	the	the	DET
bracis-28347	168	24	ilp	ilp	ADJ
bracis-28347	168	25	model	model	NOUN
bracis-28347	168	26	by	by	ADP
bracis-28347	168	27	\(11.37\%\	\(11.37\%\	NOUN
bracis-28347	168	28	)	)	PUNCT
bracis-28347	168	29	.	.	PUNCT
bracis-28347	169	1	table	table	NOUN
bracis-28347	169	2	6	6	NUM
bracis-28347	169	3	.	.	PUNCT
bracis-28347	170	1	results	result	NOUN
bracis-28347	170	2	of	of	ADP
bracis-28347	170	3	the	the	DET
bracis-28347	170	4	computational	computational	ADJ
bracis-28347	170	5	experiments	experiment	NOUN
bracis-28347	170	6	for	for	ADP
bracis-28347	170	7	cactus	cactus	NOUN
bracis-28347	170	8	graphsfull	graphsfull	NOUN
bracis-28347	170	9	size	size	NOUN
bracis-28347	170	10	table	table	NOUN
bracis-28347	170	11	for	for	ADP
bracis-28347	170	12	the	the	DET
bracis-28347	170	13	real	real	ADJ
bracis-28347	170	14	instances	instance	NOUN
bracis-28347	171	1	,	,	PUNCT
bracis-28347	171	2	the	the	DET
bracis-28347	171	3	heuristic	heuristic	ADJ
bracis-28347	171	4	algorithm	algorithm	NOUN
bracis-28347	171	5	found	find	VERB
bracis-28347	171	6	the	the	DET
bracis-28347	171	7	integer	integer	NOUN
bracis-28347	171	8	optimal	optimal	ADJ
bracis-28347	171	9	solution	solution	NOUN
bracis-28347	171	10	in	in	ADP
bracis-28347	171	11	\(42.86\%\	\(42.86\%\	NOUN
bracis-28347	171	12	)	)	PUNCT
bracis-28347	171	13	of	of	ADP
bracis-28347	171	14	the	the	DET
bracis-28347	171	15	instances	instance	NOUN
bracis-28347	171	16	;	;	PUNCT
bracis-28347	171	17	\(64.29\%\	\(64.29\%\	NOUN
bracis-28347	171	18	)	)	PUNCT
bracis-28347	171	19	of	of	ADP
bracis-28347	171	20	the	the	DET
bracis-28347	171	21	instances	instance	NOUN
bracis-28347	171	22	presented	present	VERB
bracis-28347	171	23	a	a	DET
bracis-28347	171	24	gap	gap	NOUN
bracis-28347	171	25	less	less	ADJ
bracis-28347	171	26	than	than	ADP
bracis-28347	171	27	\(30\%\	\(30\%\	NUM
bracis-28347	171	28	)	)	PUNCT
bracis-28347	171	29	;	;	PUNCT
bracis-28347	171	30	and	and	CCONJ
bracis-28347	171	31	\(50\%\	\(50\%\	X
bracis-28347	171	32	)	)	PUNCT
bracis-28347	171	33	of	of	ADP
bracis-28347	171	34	the	the	DET
bracis-28347	171	35	instances	instance	NOUN
bracis-28347	171	36	presented	present	VERB
bracis-28347	171	37	a	a	DET
bracis-28347	171	38	gap	gap	NOUN
bracis-28347	171	39	smaller	small	ADJ
bracis-28347	171	40	than	than	ADP
bracis-28347	171	41	\(10\%\	\(10\%\	NUM
bracis-28347	171	42	)	)	PUNCT
bracis-28347	171	43	.	.	PUNCT
bracis-28347	172	1	the	the	DET
bracis-28347	172	2	worst	bad	ADJ
bracis-28347	172	3	case	case	NOUN
bracis-28347	172	4	presented	present	VERB
bracis-28347	172	5	a	a	DET
bracis-28347	172	6	solution	solution	NOUN
bracis-28347	172	7	gap	gap	NOUN
bracis-28347	172	8	of	of	ADP
bracis-28347	172	9	\(56.64\%\	\(56.64\%\	NOUN
bracis-28347	172	10	)	)	PUNCT
bracis-28347	172	11	.	.	PUNCT
bracis-28347	173	1	for	for	ADP
bracis-28347	173	2	this	this	DET
bracis-28347	173	3	data	datum	NOUN
bracis-28347	173	4	set	set	VERB
bracis-28347	173	5	,	,	PUNCT
bracis-28347	173	6	the	the	DET
bracis-28347	173	7	solution	solution	NOUN
bracis-28347	173	8	of	of	ADP
bracis-28347	173	9	the	the	DET
bracis-28347	173	10	heuristic	heuristic	ADJ
bracis-28347	173	11	algorithm	algorithm	NOUN
bracis-28347	173	12	diverges	diverge	VERB
bracis-28347	173	13	,	,	PUNCT
bracis-28347	173	14	on	on	ADP
bracis-28347	173	15	average	average	ADJ
bracis-28347	173	16	,	,	PUNCT
bracis-28347	173	17	by	by	ADP
bracis-28347	173	18	\(19.04\%\	\(19.04\%\	NOUN
bracis-28347	173	19	)	)	PUNCT
bracis-28347	173	20	from	from	ADP
bracis-28347	173	21	the	the	DET
bracis-28347	173	22	optimal	optimal	ADJ
bracis-28347	173	23	solution	solution	NOUN
bracis-28347	173	24	presented	present	VERB
bracis-28347	173	25	by	by	ADP
bracis-28347	173	26	the	the	DET
bracis-28347	173	27	ilp	ilp	ADJ
bracis-28347	173	28	model	model	NOUN
bracis-28347	173	29	.	.	PUNCT
bracis-28347	174	1	for	for	ADP
bracis-28347	174	2	the	the	DET
bracis-28347	174	3	random	random	ADJ
bracis-28347	174	4	cactus	cactus	NOUN
bracis-28347	174	5	graph	graph	NOUN
bracis-28347	174	6	instances	instance	NOUN
bracis-28347	174	7	,	,	PUNCT
bracis-28347	174	8	the	the	DET
bracis-28347	174	9	heuristic	heuristic	ADJ
bracis-28347	174	10	algorithm	algorithm	NOUN
bracis-28347	174	11	found	find	VERB
bracis-28347	174	12	the	the	DET
bracis-28347	174	13	optimal	optimal	ADJ
bracis-28347	174	14	solution	solution	NOUN
bracis-28347	174	15	for	for	ADP
bracis-28347	174	16	\(83.33\%\	\(83.33\%\	NOUN
bracis-28347	174	17	)	)	PUNCT
bracis-28347	174	18	of	of	ADP
bracis-28347	174	19	the	the	DET
bracis-28347	174	20	instances	instance	NOUN
bracis-28347	174	21	;	;	PUNCT
bracis-28347	174	22	\(100\%\	\(100\%\	X
bracis-28347	174	23	)	)	PUNCT
bracis-28347	174	24	of	of	ADP
bracis-28347	174	25	the	the	DET
bracis-28347	174	26	instances	instance	NOUN
bracis-28347	174	27	presented	present	VERB
bracis-28347	174	28	a	a	DET
bracis-28347	174	29	gap	gap	NOUN
bracis-28347	174	30	less	less	ADJ
bracis-28347	174	31	than	than	ADP
bracis-28347	174	32	\(10\%\	\(10\%\	NUM
bracis-28347	174	33	)	)	PUNCT
bracis-28347	174	34	.	.	PUNCT
bracis-28347	175	1	the	the	DET
bracis-28347	175	2	worst	bad	ADJ
bracis-28347	175	3	-	-	PUNCT
bracis-28347	175	4	case	case	NOUN
bracis-28347	175	5	instance	instance	NOUN
bracis-28347	175	6	had	have	VERB
bracis-28347	175	7	a	a	DET
bracis-28347	175	8	gap	gap	NOUN
bracis-28347	175	9	of	of	ADP
bracis-28347	175	10	\(9.80\%\	\(9.80\%\	NOUN
bracis-28347	175	11	)	)	PUNCT
bracis-28347	175	12	,	,	PUNCT
bracis-28347	175	13	and	and	CCONJ
bracis-28347	175	14	on	on	ADP
bracis-28347	175	15	average	average	ADJ
bracis-28347	175	16	,	,	PUNCT
bracis-28347	175	17	this	this	DET
bracis-28347	175	18	gap	gap	NOUN
bracis-28347	175	19	was	be	AUX
bracis-28347	175	20	\(1.04\%\	\(1.04\%\	ADJ
bracis-28347	175	21	)	)	PUNCT
bracis-28347	175	22	.	.	PUNCT
bracis-28347	176	1	we	we	PRON
bracis-28347	176	2	noticed	notice	VERB
bracis-28347	176	3	an	an	DET
bracis-28347	176	4	improved	improved	ADJ
bracis-28347	176	5	behavior	behavior	NOUN
bracis-28347	176	6	of	of	ADP
bracis-28347	176	7	the	the	DET
bracis-28347	176	8	heuristic	heuristic	ADJ
bracis-28347	176	9	algorithm	algorithm	NOUN
bracis-28347	176	10	on	on	ADP
bracis-28347	176	11	graphs	graph	NOUN
bracis-28347	176	12	where	where	SCONJ
bracis-28347	176	13	the	the	DET
bracis-28347	176	14	number	number	NOUN
bracis-28347	176	15	of	of	ADP
bracis-28347	176	16	possible	possible	ADJ
bracis-28347	176	17	circuits	circuit	NOUN
bracis-28347	176	18	is	be	AUX
bracis-28347	176	19	limited	limit	VERB
bracis-28347	176	20	;	;	PUNCT
bracis-28347	176	21	moreover	moreover	ADV
bracis-28347	176	22	,	,	PUNCT
bracis-28347	176	23	in	in	ADP
bracis-28347	176	24	real	real	ADJ
bracis-28347	176	25	-	-	PUNCT
bracis-28347	176	26	world	world	NOUN
bracis-28347	176	27	instances	instance	NOUN
bracis-28347	176	28	,	,	PUNCT
bracis-28347	176	29	the	the	DET
bracis-28347	176	30	heuristic	heuristic	ADJ
bracis-28347	176	31	algorithm	algorithm	NOUN
bracis-28347	176	32	performed	perform	VERB
bracis-28347	176	33	better	well	ADV
bracis-28347	176	34	than	than	ADP
bracis-28347	176	35	in	in	ADP
bracis-28347	176	36	random	random	ADJ
bracis-28347	176	37	instances	instance	NOUN
bracis-28347	176	38	,	,	PUNCT
bracis-28347	176	39	which	which	PRON
bracis-28347	176	40	concludes	conclude	VERB
bracis-28347	176	41	that	that	SCONJ
bracis-28347	176	42	in	in	ADP
bracis-28347	176	43	general	general	ADJ
bracis-28347	176	44	,	,	PUNCT
bracis-28347	176	45	the	the	DET
bracis-28347	176	46	algorithm	algorithm	NOUN
bracis-28347	176	47	is	be	AUX
bracis-28347	176	48	a	a	DET
bracis-28347	176	49	good	good	ADJ
bracis-28347	176	50	tool	tool	NOUN
bracis-28347	176	51	to	to	PART
bracis-28347	176	52	obtain	obtain	VERB
bracis-28347	176	53	lower	low	ADJ
bracis-28347	176	54	bounds	bound	NOUN
bracis-28347	176	55	for	for	ADP
bracis-28347	176	56	the	the	DET
bracis-28347	176	57	mtpp	mtpp	NOUN
bracis-28347	176	58	.	.	PUNCT
bracis-28347	177	1	6	6	NUM
bracis-28347	177	2	concluding	conclude	VERB
bracis-28347	177	3	remarks	remark	NOUN
bracis-28347	177	4	in	in	ADP
bracis-28347	177	5	this	this	DET
bracis-28347	177	6	article	article	NOUN
bracis-28347	177	7	,	,	PUNCT
bracis-28347	177	8	a	a	DET
bracis-28347	177	9	contribution	contribution	NOUN
bracis-28347	177	10	to	to	ADP
bracis-28347	177	11	the	the	DET
bracis-28347	177	12	state	state	NOUN
bracis-28347	177	13	of	of	ADP
bracis-28347	177	14	the	the	DET
bracis-28347	177	15	art	art	NOUN
bracis-28347	177	16	of	of	ADP
bracis-28347	177	17	the	the	DET
bracis-28347	177	18	problem	problem	NOUN
bracis-28347	177	19	of	of	ADP
bracis-28347	177	20	tropical	tropical	ADJ
bracis-28347	177	21	paths	path	NOUN
bracis-28347	177	22	in	in	ADP
bracis-28347	177	23	graphs	graph	NOUN
bracis-28347	177	24	is	be	AUX
bracis-28347	177	25	proposed	propose	VERB
bracis-28347	177	26	from	from	ADP
bracis-28347	177	27	the	the	DET
bracis-28347	177	28	perspective	perspective	NOUN
bracis-28347	177	29	of	of	ADP
bracis-28347	177	30	combinatory	combinatory	ADJ
bracis-28347	177	31	optimization	optimization	NOUN
bracis-28347	177	32	.	.	PUNCT
bracis-28347	178	1	specifically	specifically	ADV
bracis-28347	178	2	,	,	PUNCT
bracis-28347	178	3	an	an	DET
bracis-28347	178	4	integer	integer	NOUN
bracis-28347	178	5	linear	linear	NOUN
bracis-28347	178	6	optimization	optimization	NOUN
bracis-28347	178	7	model	model	NOUN
bracis-28347	178	8	for	for	ADP
bracis-28347	178	9	mtpp	mtpp	PROPN
bracis-28347	178	10	has	have	AUX
bracis-28347	178	11	been	be	AUX
bracis-28347	178	12	developed	develop	VERB
bracis-28347	178	13	.	.	PUNCT
bracis-28347	179	1	this	this	DET
bracis-28347	179	2	model	model	NOUN
bracis-28347	179	3	contains	contain	VERB
bracis-28347	179	4	,	,	PUNCT
bracis-28347	179	5	in	in	ADP
bracis-28347	179	6	order	order	NOUN
bracis-28347	179	7	,	,	PUNCT
bracis-28347	179	8	o(nk	o(nk	ADJ
bracis-28347	179	9	)	)	PUNCT
bracis-28347	179	10	variables	variable	NOUN
bracis-28347	179	11	,	,	PUNCT
bracis-28347	179	12	being	be	AUX
bracis-28347	179	13	n	n	CCONJ
bracis-28347	179	14	the	the	DET
bracis-28347	179	15	number	number	NOUN
bracis-28347	179	16	of	of	ADP
bracis-28347	179	17	vertices	vertex	NOUN
bracis-28347	179	18	,	,	PUNCT
bracis-28347	179	19	and	and	CCONJ
bracis-28347	179	20	k	k	X
bracis-28347	179	21	the	the	DET
bracis-28347	179	22	number	number	NOUN
bracis-28347	179	23	of	of	ADP
bracis-28347	179	24	colors	color	NOUN
bracis-28347	179	25	,	,	PUNCT
bracis-28347	179	26	and	and	CCONJ
bracis-28347	179	27	o(n	o(n	NUM
bracis-28347	179	28	)	)	PUNCT
bracis-28347	179	29	linear	linear	PROPN
bracis-28347	179	30	inequalities	inequality	NOUN
bracis-28347	179	31	.	.	PUNCT
bracis-28347	180	1	due	due	ADP
bracis-28347	180	2	to	to	ADP
bracis-28347	180	3	being	be	AUX
bracis-28347	180	4	an	an	DET
bracis-28347	180	5	np	np	ADJ
bracis-28347	180	6	-	-	PUNCT
bracis-28347	180	7	hard	hard	ADJ
bracis-28347	180	8	problem	problem	NOUN
bracis-28347	180	9	,	,	PUNCT
bracis-28347	180	10	its	its	PRON
bracis-28347	180	11	execution	execution	NOUN
bracis-28347	180	12	is	be	AUX
bracis-28347	180	13	impractical	impractical	ADJ
bracis-28347	180	14	for	for	ADP
bracis-28347	180	15	large	large	ADJ
bracis-28347	180	16	instances	instance	NOUN
bracis-28347	180	17	.	.	PUNCT
bracis-28347	181	1	additionally	additionally	ADV
bracis-28347	181	2	,	,	PUNCT
bracis-28347	181	3	a	a	DET
bracis-28347	181	4	polynomial	polynomial	ADJ
bracis-28347	181	5	-	-	PUNCT
bracis-28347	181	6	time	time	NOUN
bracis-28347	181	7	heuristic	heuristic	ADJ
bracis-28347	181	8	algorithm	algorithm	NOUN
bracis-28347	181	9	was	be	AUX
bracis-28347	181	10	also	also	ADV
bracis-28347	181	11	presented	present	VERB
bracis-28347	181	12	,	,	PUNCT
bracis-28347	181	13	which	which	PRON
bracis-28347	181	14	,	,	PUNCT
bracis-28347	181	15	as	as	ADV
bracis-28347	181	16	far	far	ADV
bracis-28347	181	17	as	as	SCONJ
bracis-28347	181	18	it	it	PRON
bracis-28347	181	19	is	be	AUX
bracis-28347	181	20	known	know	VERB
bracis-28347	181	21	,	,	PUNCT
bracis-28347	181	22	is	be	AUX
bracis-28347	181	23	the	the	DET
bracis-28347	181	24	first	first	ADJ
bracis-28347	181	25	result	result	NOUN
bracis-28347	181	26	of	of	ADP
bracis-28347	181	27	this	this	DET
bracis-28347	181	28	line	line	NOUN
bracis-28347	181	29	of	of	ADP
bracis-28347	181	30	research	research	NOUN
bracis-28347	181	31	.	.	PUNCT
bracis-28347	182	1	the	the	DET
bracis-28347	182	2	differential	differential	NOUN
bracis-28347	182	3	of	of	ADP
bracis-28347	182	4	the	the	DET
bracis-28347	182	5	optimization	optimization	NOUN
bracis-28347	182	6	model	model	NOUN
bracis-28347	182	7	was	be	AUX
bracis-28347	182	8	the	the	DET
bracis-28347	182	9	association	association	NOUN
bracis-28347	182	10	of	of	ADP
bracis-28347	182	11	two	two	NUM
bracis-28347	182	12	important	important	ADJ
bracis-28347	182	13	inequalities	inequality	NOUN
bracis-28347	182	14	that	that	PRON
bracis-28347	182	15	together	together	ADV
bracis-28347	182	16	guaranteed	guarantee	VERB
bracis-28347	182	17	both	both	DET
bracis-28347	182	18	the	the	DET
bracis-28347	182	19	connectivity	connectivity	NOUN
bracis-28347	182	20	and	and	CCONJ
bracis-28347	182	21	the	the	DET
bracis-28347	182	22	absence	absence	NOUN
bracis-28347	182	23	of	of	ADP
bracis-28347	182	24	circuits	circuit	NOUN
bracis-28347	182	25	in	in	ADP
bracis-28347	182	26	the	the	DET
bracis-28347	182	27	solution	solution	NOUN
bracis-28347	182	28	,	,	PUNCT
bracis-28347	182	29	unlike	unlike	ADP
bracis-28347	182	30	the	the	DET
bracis-28347	182	31	commonly	commonly	ADV
bracis-28347	182	32	used	use	VERB
bracis-28347	182	33	models	model	NOUN
bracis-28347	182	34	in	in	ADP
bracis-28347	182	35	which	which	PRON
bracis-28347	182	36	an	an	DET
bracis-28347	182	37	exponential	exponential	ADJ
bracis-28347	182	38	number	number	NOUN
bracis-28347	182	39	of	of	ADP
bracis-28347	182	40	subsets	subset	NOUN
bracis-28347	182	41	of	of	ADP
bracis-28347	182	42	graphs	graph	NOUN
bracis-28347	182	43	are	be	AUX
bracis-28347	182	44	exploited	exploit	VERB
bracis-28347	182	45	for	for	ADP
bracis-28347	182	46	this	this	DET
bracis-28347	182	47	purpose	purpose	NOUN
bracis-28347	182	48	.	.	PUNCT
bracis-28347	183	1	the	the	DET
bracis-28347	183	2	proposed	propose	VERB
bracis-28347	183	3	heuristic	heuristic	ADJ
bracis-28347	183	4	algorithm	algorithm	NOUN
bracis-28347	183	5	is	be	AUX
bracis-28347	183	6	a	a	DET
bracis-28347	183	7	recursive	recursive	ADJ
bracis-28347	183	8	algorithm	algorithm	NOUN
bracis-28347	183	9	that	that	SCONJ
bracis-28347	183	10	,	,	PUNCT
bracis-28347	183	11	for	for	ADP
bracis-28347	183	12	a	a	DET
bracis-28347	183	13	given	give	VERB
bracis-28347	183	14	random	random	ADJ
bracis-28347	183	15	root	root	NOUN
bracis-28347	183	16	,	,	PUNCT
bracis-28347	183	17	finds	find	VERB
bracis-28347	183	18	the	the	DET
bracis-28347	183	19	path	path	NOUN
bracis-28347	183	20	with	with	ADP
bracis-28347	183	21	the	the	DET
bracis-28347	183	22	largest	large	ADJ
bracis-28347	183	23	number	number	NOUN
bracis-28347	183	24	of	of	ADP
bracis-28347	183	25	colors	color	NOUN
bracis-28347	183	26	containing	contain	VERB
bracis-28347	183	27	that	that	DET
bracis-28347	183	28	root	root	NOUN
bracis-28347	183	29	.	.	PUNCT
bracis-28347	184	1	all	all	DET
bracis-28347	184	2	vertices	vertex	NOUN
bracis-28347	184	3	are	be	AUX
bracis-28347	184	4	visited	visit	VERB
bracis-28347	184	5	as	as	ADP
bracis-28347	184	6	roots	root	NOUN
bracis-28347	184	7	,	,	PUNCT
bracis-28347	184	8	and	and	CCONJ
bracis-28347	184	9	the	the	DET
bracis-28347	184	10	best	good	ADJ
bracis-28347	184	11	path	path	NOUN
bracis-28347	184	12	in	in	ADP
bracis-28347	184	13	these	these	DET
bracis-28347	184	14	terms	term	NOUN
bracis-28347	184	15	is	be	AUX
bracis-28347	184	16	returned	return	VERB
bracis-28347	184	17	.	.	PUNCT
bracis-28347	185	1	the	the	DET
bracis-28347	185	2	proposed	propose	VERB
bracis-28347	185	3	heuristics	heuristic	NOUN
bracis-28347	185	4	were	be	AUX
bracis-28347	185	5	tested	test	VERB
bracis-28347	185	6	on	on	ADP
bracis-28347	185	7	a	a	DET
bracis-28347	185	8	benchmark	benchmark	NOUN
bracis-28347	185	9	consisting	consist	VERB
bracis-28347	185	10	of	of	ADP
bracis-28347	185	11	93	93	NUM
bracis-28347	185	12	instances	instance	NOUN
bracis-28347	185	13	,	,	PUNCT
bracis-28347	185	14	among	among	ADP
bracis-28347	185	15	them	they	PRON
bracis-28347	185	16	random	random	ADJ
bracis-28347	185	17	and	and	CCONJ
bracis-28347	185	18	real	real	ADJ
bracis-28347	185	19	-	-	PUNCT
bracis-28347	185	20	world	world	NOUN
bracis-28347	185	21	,	,	PUNCT
bracis-28347	185	22	of	of	ADP
bracis-28347	185	23	various	various	ADJ
bracis-28347	185	24	dimensions	dimension	NOUN
bracis-28347	185	25	.	.	PUNCT
bracis-28347	186	1	the	the	DET
bracis-28347	186	2	results	result	NOUN
bracis-28347	186	3	were	be	AUX
bracis-28347	186	4	compared	compare	VERB
bracis-28347	186	5	with	with	ADP
bracis-28347	186	6	the	the	DET
bracis-28347	186	7	respective	respective	ADJ
bracis-28347	186	8	entire	entire	ADJ
bracis-28347	186	9	optimal	optimal	ADJ
bracis-28347	186	10	solutions	solution	NOUN
bracis-28347	186	11	of	of	ADP
bracis-28347	186	12	the	the	DET
bracis-28347	186	13	model	model	NOUN
bracis-28347	186	14	,	,	PUNCT
bracis-28347	186	15	and	and	CCONJ
bracis-28347	186	16	the	the	DET
bracis-28347	186	17	experimental	experimental	ADJ
bracis-28347	186	18	results	result	NOUN
bracis-28347	186	19	pointed	point	VERB
bracis-28347	186	20	out	out	ADP
bracis-28347	186	21	that	that	SCONJ
bracis-28347	186	22	the	the	DET
bracis-28347	186	23	average	average	ADJ
bracis-28347	186	24	percentage	percentage	NOUN
bracis-28347	186	25	of	of	ADP
bracis-28347	186	26	the	the	DET
bracis-28347	186	27	difference	difference	NOUN
bracis-28347	186	28	between	between	ADP
bracis-28347	186	29	the	the	DET
bracis-28347	186	30	optimal	optimal	ADJ
bracis-28347	186	31	solution	solution	NOUN
bracis-28347	186	32	and	and	CCONJ
bracis-28347	186	33	the	the	DET
bracis-28347	186	34	heuristic	heuristic	ADJ
bracis-28347	186	35	algorithm	algorithm	NOUN
bracis-28347	186	36	solution	solution	NOUN
bracis-28347	186	37	is	be	AUX
bracis-28347	186	38	less	less	ADJ
bracis-28347	186	39	than	than	ADP
bracis-28347	186	40	\(11\%\	\(11\%\	PRON
bracis-28347	186	41	)	)	PUNCT
bracis-28347	186	42	,	,	PUNCT
bracis-28347	186	43	which	which	PRON
bracis-28347	186	44	proves	prove	VERB
bracis-28347	186	45	experimentally	experimentally	ADV
bracis-28347	186	46	the	the	DET
bracis-28347	186	47	strength	strength	NOUN
bracis-28347	186	48	of	of	ADP
bracis-28347	186	49	the	the	DET
bracis-28347	186	50	proposed	propose	VERB
bracis-28347	186	51	heuristic	heuristic	ADJ
bracis-28347	186	52	algorithm	algorithm	NOUN
bracis-28347	186	53	.	.	PUNCT
bracis-28347	187	1	in	in	ADP
bracis-28347	187	2	practice	practice	NOUN
bracis-28347	187	3	,	,	PUNCT
bracis-28347	187	4	when	when	SCONJ
bracis-28347	187	5	faced	face	VERB
bracis-28347	187	6	with	with	ADP
bracis-28347	187	7	computationally	computationally	ADV
bracis-28347	187	8	intractable	intractable	ADJ
bracis-28347	187	9	problems	problem	NOUN
bracis-28347	187	10	,	,	PUNCT
bracis-28347	187	11	it	it	PRON
bracis-28347	187	12	is	be	AUX
bracis-28347	187	13	natural	natural	ADJ
bracis-28347	187	14	to	to	PART
bracis-28347	187	15	sacrifice	sacrifice	VERB
bracis-28347	187	16	optimality	optimality	NOUN
bracis-28347	187	17	in	in	ADP
bracis-28347	187	18	favor	favor	NOUN
bracis-28347	187	19	of	of	ADP
bracis-28347	187	20	computational	computational	ADJ
bracis-28347	187	21	time	time	NOUN
bracis-28347	187	22	to	to	PART
bracis-28347	187	23	obtain	obtain	VERB
bracis-28347	187	24	a	a	DET
bracis-28347	187	25	competitive	competitive	ADJ
bracis-28347	187	26	solution	solution	NOUN
bracis-28347	187	27	.	.	PUNCT
bracis-28347	188	1	in	in	ADP
bracis-28347	188	2	this	this	DET
bracis-28347	188	3	regard	regard	NOUN
bracis-28347	188	4	,	,	PUNCT
bracis-28347	188	5	the	the	DET
bracis-28347	188	6	recursive	recursive	ADJ
bracis-28347	188	7	algorithm	algorithm	NOUN
bracis-28347	188	8	proved	prove	VERB
bracis-28347	188	9	to	to	PART
bracis-28347	188	10	be	be	AUX
bracis-28347	188	11	an	an	DET
bracis-28347	188	12	advantageous	advantageous	ADJ
bracis-28347	188	13	tool	tool	NOUN
bracis-28347	188	14	for	for	ADP
bracis-28347	188	15	obtaining	obtain	VERB
bracis-28347	188	16	good	good	ADJ
bracis-28347	188	17	solutions	solution	NOUN
bracis-28347	188	18	for	for	ADP
bracis-28347	188	19	the	the	DET
bracis-28347	188	20	mtpp	mtpp	PROPN
bracis-28347	188	21	.	.	PUNCT
bracis-28347	189	1	references	reference	NOUN
bracis-28347	189	2	anglès	anglès	VERB
bracis-28347	189	3	d’auriac	d’auriac	NOUN
bracis-28347	189	4	,	,	PUNCT
bracis-28347	189	5	j.a	j.a	PROPN
bracis-28347	189	6	.	.	PROPN
bracis-28347	189	7	,	,	PUNCT
bracis-28347	189	8	et	et	PROPN
bracis-28347	189	9	al	al	PROPN
bracis-28347	189	10	.	.	PUNCT
bracis-28347	189	11	:	:	PUNCT
bracis-28347	190	1	tropical	tropical	ADJ
bracis-28347	190	2	dominating	dominating	NOUN
bracis-28347	190	3	sets	set	NOUN
bracis-28347	190	4	in	in	ADP
bracis-28347	190	5	vertex	vertex	NOUN
bracis-28347	190	6	-	-	PUNCT
bracis-28347	190	7	coloured	colour	VERB
bracis-28347	190	8	graphs	graph	NOUN
bracis-28347	190	9	.	.	PUNCT
bracis-28347	191	1	j.	j.	PROPN
bracis-28347	191	2	disc	disc	PROPN
bracis-28347	191	3	.	.	PUNCT
bracis-28347	192	1	algor	algor	PROPN
bracis-28347	192	2	.	.	PUNCT
bracis-28347	193	1	48	48	NUM
bracis-28347	193	2	,	,	PUNCT
bracis-28347	193	3	27–41	27–41	NUM
bracis-28347	193	4	(	(	PUNCT
bracis-28347	193	5	2018	2018	NUM
bracis-28347	193	6	)	)	PUNCT
bracis-28347	193	7	.	.	PUNCT
bracis-28347	194	1	https://doi.org/10.1016/j.jda.2018.03.001	https://doi.org/10.1016/j.jda.2018.03.001	NOUN
bracis-28347	194	2	.	.	PUNCT
bracis-28347	195	1	https://www.sciencedirect.com/science/article/pii/s1570866718300595	https://www.sciencedirect.com/science/article/pii/s1570866718300595	PROPN
bracis-28347	195	2	chapelle	chapelle	PROPN
bracis-28347	195	3	,	,	PUNCT
bracis-28347	195	4	m.	m.	NOUN
bracis-28347	195	5	,	,	PUNCT
bracis-28347	195	6	cochefert	cochefert	PROPN
bracis-28347	195	7	,	,	PUNCT
bracis-28347	195	8	m.	m.	NOUN
bracis-28347	195	9	,	,	PUNCT
bracis-28347	195	10	kratsch	kratsch	PROPN
bracis-28347	195	11	,	,	PUNCT
bracis-28347	195	12	d.	d.	PROPN
bracis-28347	195	13	,	,	PUNCT
bracis-28347	195	14	letourneur	letourneur	PROPN
bracis-28347	195	15	,	,	PUNCT
bracis-28347	195	16	r.	r.	PROPN
bracis-28347	195	17	,	,	PUNCT
bracis-28347	195	18	liedloff	liedloff	NOUN
bracis-28347	195	19	,	,	PUNCT
bracis-28347	195	20	m.	m.	NOUN
bracis-28347	195	21	:	:	PUNCT
bracis-28347	195	22	exact	exact	ADJ
bracis-28347	195	23	exponential	exponential	ADJ
bracis-28347	195	24	algorithms	algorithm	NOUN
bracis-28347	195	25	to	to	PART
bracis-28347	195	26	find	find	VERB
bracis-28347	195	27	tropical	tropical	ADJ
bracis-28347	195	28	connected	connect	VERB
bracis-28347	195	29	sets	set	NOUN
bracis-28347	195	30	of	of	ADP
bracis-28347	195	31	minimum	minimum	ADJ
bracis-28347	195	32	size	size	NOUN
bracis-28347	195	33	.	.	PUNCT
bracis-28347	196	1	theor	theor	PROPN
bracis-28347	196	2	.	.	PUNCT
bracis-28347	197	1	comput	comput	PROPN
bracis-28347	197	2	.	.	PUNCT
bracis-28347	198	1	sci	sci	PROPN
bracis-28347	198	2	.	.	PROPN
bracis-28347	198	3	676	676	NUM
bracis-28347	198	4	,	,	PUNCT
bracis-28347	198	5	33–41	33–41	NUM
bracis-28347	198	6	(	(	PUNCT
bracis-28347	198	7	2017	2017	NUM
bracis-28347	198	8	)	)	PUNCT
bracis-28347	198	9	.	.	PUNCT
bracis-28347	199	1	https://doi.org/10.1016/j.tcs.2017.03.003	https://doi.org/10.1016/j.tcs.2017.03.003	PROPN
bracis-28347	199	2	.	.	PUNCT
bracis-28347	200	1	https://www.sciencedirect.com/science/article/pii/s0304397517301883	https://www.sciencedirect.com/science/article/pii/s0304397517301883	PROPN
bracis-28347	200	2	cohen	cohen	PROPN
bracis-28347	200	3	,	,	PUNCT
bracis-28347	200	4	j.	j.	PROPN
bracis-28347	200	5	,	,	PUNCT
bracis-28347	200	6	manoussakis	manoussakis	PROPN
bracis-28347	200	7	,	,	PUNCT
bracis-28347	200	8	y.	y.	PROPN
bracis-28347	200	9	,	,	PUNCT
bracis-28347	200	10	phong	phong	PROPN
bracis-28347	200	11	,	,	PUNCT
bracis-28347	200	12	h.	h.	PROPN
bracis-28347	200	13	,	,	PUNCT
bracis-28347	200	14	tuza	tuza	PROPN
bracis-28347	200	15	,	,	PUNCT
bracis-28347	200	16	z.	z.	PROPN
bracis-28347	200	17	:	:	PUNCT
bracis-28347	200	18	tropical	tropical	ADJ
bracis-28347	200	19	matchings	matching	NOUN
bracis-28347	200	20	in	in	ADP
bracis-28347	200	21	vertex	vertex	NOUN
bracis-28347	200	22	-	-	PUNCT
bracis-28347	200	23	colored	color	VERB
bracis-28347	200	24	graphs	graph	NOUN
bracis-28347	200	25	.	.	PUNCT
bracis-28347	201	1	electron	electron	PROPN
bracis-28347	201	2	.	.	PUNCT
bracis-28347	202	1	notes	note	NOUN
bracis-28347	202	2	disc	disc	PROPN
bracis-28347	202	3	.	.	PUNCT
bracis-28347	203	1	math	math	NOUN
bracis-28347	203	2	.	.	PUNCT
bracis-28347	204	1	62	62	NUM
bracis-28347	204	2	,	,	PUNCT
bracis-28347	204	3	219–224	219–224	NUM
bracis-28347	204	4	(	(	PUNCT
bracis-28347	204	5	2017	2017	NUM
bracis-28347	204	6	)	)	PUNCT
bracis-28347	204	7	.	.	PUNCT
bracis-28347	205	1	https://doi.org/10.1016/j.endm.2017.10.038	https://doi.org/10.1016/j.endm.2017.10.038	PROPN
bracis-28347	205	2	,	,	PUNCT
bracis-28347	205	3	https://www.sciencedirect.com/science/article/pii/s1571065317302779	https://www.sciencedirect.com/science/article/pii/s1571065317302779	PROPN
bracis-28347	205	4	cohen	cohen	PROPN
bracis-28347	205	5	,	,	PUNCT
bracis-28347	205	6	j.	j.	PROPN
bracis-28347	205	7	,	,	PUNCT
bracis-28347	205	8	italiano	italiano	PROPN
bracis-28347	205	9	,	,	PUNCT
bracis-28347	205	10	g.f	g.f	PROPN
bracis-28347	205	11	.	.	PROPN
bracis-28347	205	12	,	,	PUNCT
bracis-28347	205	13	manoussakis	manoussakis	PROPN
bracis-28347	205	14	,	,	PUNCT
bracis-28347	205	15	y.	y.	PROPN
bracis-28347	205	16	,	,	PUNCT
bracis-28347	205	17	nguyen	nguyen	PROPN
bracis-28347	205	18	,	,	PUNCT
bracis-28347	205	19	k.t	k.t	PROPN
bracis-28347	205	20	.	.	PROPN
bracis-28347	205	21	,	,	PUNCT
bracis-28347	205	22	pham	pham	PROPN
bracis-28347	205	23	,	,	PUNCT
bracis-28347	205	24	h.p	h.p	PROPN
bracis-28347	205	25	.	.	PROPN
bracis-28347	205	26	:	:	PUNCT
bracis-28347	206	1	tropical	tropical	ADJ
bracis-28347	206	2	paths	path	NOUN
bracis-28347	206	3	in	in	ADP
bracis-28347	206	4	vertex	vertex	NOUN
bracis-28347	206	5	-	-	PUNCT
bracis-28347	206	6	colored	color	VERB
bracis-28347	206	7	graphs	graph	NOUN
bracis-28347	206	8	.	.	PUNCT
bracis-28347	207	1	in	in	ADP
bracis-28347	207	2	:	:	PUNCT
bracis-28347	207	3	gao	gao	PROPN
bracis-28347	207	4	,	,	PUNCT
bracis-28347	207	5	x.	x.	PROPN
bracis-28347	207	6	,	,	PUNCT
bracis-28347	207	7	du	du	PROPN
bracis-28347	207	8	,	,	PUNCT
bracis-28347	207	9	h.	h.	PROPN
bracis-28347	207	10	,	,	PUNCT
bracis-28347	207	11	han	han	PROPN
bracis-28347	207	12	,	,	PUNCT
bracis-28347	207	13	m.	m.	NOUN
bracis-28347	207	14	(	(	PUNCT
bracis-28347	207	15	eds	ed	NOUN
bracis-28347	207	16	.	.	PUNCT
bracis-28347	207	17	)	)	PUNCT
bracis-28347	207	18	cocoa	cocoa	NOUN
bracis-28347	207	19	2017	2017	NUM
bracis-28347	207	20	.	.	PUNCT
bracis-28347	208	1	lncs	lncs	PROPN
bracis-28347	208	2	,	,	PUNCT
bracis-28347	208	3	vol	vol	NOUN
bracis-28347	208	4	.	.	PROPN
bracis-28347	208	5	10628	10628	NUM
bracis-28347	208	6	,	,	PUNCT
bracis-28347	208	7	pp	pp	ADJ
bracis-28347	208	8	.	.	PUNCT
bracis-28347	209	1	291–305	291–305	NUM
bracis-28347	209	2	.	.	PUNCT
bracis-28347	209	3	springer	springer	NOUN
bracis-28347	209	4	,	,	PUNCT
bracis-28347	209	5	cham	cham	PROPN
bracis-28347	209	6	(	(	PUNCT
bracis-28347	209	7	2017	2017	NUM
bracis-28347	209	8	)	)	PUNCT
bracis-28347	209	9	.	.	PUNCT
bracis-28347	210	1	https://doi.org/10.1007/978-3-319-71147-8_20	https://doi.org/10.1007/978-3-319-71147-8_20	PROPN
bracis-28347	210	2	chapter	chapter	NOUN
bracis-28347	210	3	  	  	SPACE
bracis-28347	210	4	google	google	PROPN
bracis-28347	210	5	scholar	scholar	NOUN
bracis-28347	210	6	  	  	SPACE
bracis-28347	210	7	deville	deville	NOUN
bracis-28347	210	8	,	,	PUNCT
bracis-28347	210	9	y.	y.	PROPN
bracis-28347	210	10	,	,	PUNCT
bracis-28347	210	11	gilbert	gilbert	PROPN
bracis-28347	210	12	,	,	PUNCT
bracis-28347	210	13	d.r	d.r	PROPN
bracis-28347	210	14	.	.	PROPN
bracis-28347	210	15	,	,	PUNCT
bracis-28347	210	16	van	van	PROPN
bracis-28347	210	17	helden	helden	PROPN
bracis-28347	210	18	,	,	PUNCT
bracis-28347	210	19	j.	j.	PROPN
bracis-28347	210	20	,	,	PUNCT
bracis-28347	210	21	wodak	wodak	PROPN
bracis-28347	210	22	,	,	PUNCT
bracis-28347	210	23	s.j	s.j	PROPN
bracis-28347	210	24	.	.	PROPN
bracis-28347	210	25	:	:	PUNCT
bracis-28347	211	1	an	an	DET
bracis-28347	211	2	overview	overview	NOUN
bracis-28347	211	3	of	of	ADP
bracis-28347	211	4	data	datum	NOUN
bracis-28347	211	5	models	model	NOUN
bracis-28347	211	6	for	for	ADP
bracis-28347	211	7	the	the	DET
bracis-28347	211	8	analysis	analysis	NOUN
bracis-28347	211	9	of	of	ADP
bracis-28347	211	10	biochemical	biochemical	ADJ
bracis-28347	211	11	pathways	pathway	NOUN
bracis-28347	211	12	.	.	PUNCT
bracis-28347	212	1	brief	brief	ADJ
bracis-28347	212	2	.	.	PUNCT
bracis-28347	213	1	bioinf	bioinf	VERB
bracis-28347	213	2	.	.	PUNCT
bracis-28347	214	1	4(3	4(3	NUM
bracis-28347	214	2	)	)	PUNCT
bracis-28347	214	3	,	,	PUNCT
bracis-28347	215	1	246–259	246–259	NUM
bracis-28347	215	2	(	(	PUNCT
bracis-28347	215	3	2003	2003	NUM
bracis-28347	215	4	)	)	PUNCT
bracis-28347	215	5	.	.	PUNCT
bracis-28347	216	1	https://doi.org/10.1093/bib/4.3.246	https://doi.org/10.1093/bib/4.3.246	PROPN
bracis-28347	216	2	article	article	NOUN
bracis-28347	216	3	  	  	SPACE
bracis-28347	216	4	math	math	NOUN
bracis-28347	216	5	  	  	SPACE
bracis-28347	216	6	google	google	PROPN
bracis-28347	216	7	scholar	scholar	NOUN
bracis-28347	216	8	  	  	SPACE
bracis-28347	216	9	foucaud	foucaud	PROPN
bracis-28347	216	10	,	,	PUNCT
bracis-28347	216	11	f.	f.	PROPN
bracis-28347	216	12	,	,	PUNCT
bracis-28347	216	13	harutyunyan	harutyunyan	PROPN
bracis-28347	216	14	,	,	PUNCT
bracis-28347	216	15	a.	a.	NOUN
bracis-28347	216	16	,	,	PUNCT
bracis-28347	216	17	hell	hell	INTJ
bracis-28347	216	18	,	,	PUNCT
bracis-28347	216	19	p.	p.	NOUN
bracis-28347	216	20	,	,	PUNCT
bracis-28347	216	21	legay	legay	NOUN
bracis-28347	216	22	,	,	PUNCT
bracis-28347	216	23	s.	s.	PROPN
bracis-28347	216	24	,	,	PUNCT
bracis-28347	216	25	manoussakis	manoussakis	PROPN
bracis-28347	216	26	,	,	PUNCT
bracis-28347	216	27	y.	y.	PROPN
bracis-28347	216	28	,	,	PUNCT
bracis-28347	216	29	naserasr	naserasr	NOUN
bracis-28347	216	30	,	,	PUNCT
bracis-28347	216	31	r.	r.	PROPN
bracis-28347	216	32	:	:	PUNCT
bracis-28347	216	33	the	the	DET
bracis-28347	216	34	complexity	complexity	NOUN
bracis-28347	216	35	of	of	ADP
bracis-28347	216	36	tropical	tropical	ADJ
bracis-28347	216	37	graph	graph	NOUN
bracis-28347	216	38	homomorphisms	homomorphism	NOUN
bracis-28347	216	39	.	.	PUNCT
bracis-28347	217	1	disc	disc	PROPN
bracis-28347	217	2	.	.	PUNCT
bracis-28347	217	3	appl	appl	PROPN
bracis-28347	217	4	.	.	PROPN
bracis-28347	217	5	math	math	NOUN
bracis-28347	217	6	.	.	PUNCT
bracis-28347	218	1	229(c	229(c	X
bracis-28347	218	2	)	)	PUNCT
bracis-28347	218	3	,	,	PUNCT
bracis-28347	218	4	64–81	64–81	NUM
bracis-28347	218	5	(	(	PUNCT
bracis-28347	218	6	2017	2017	NUM
bracis-28347	218	7	)	)	PUNCT
bracis-28347	218	8	.	.	PUNCT
bracis-28347	219	1	https://doi.org/10.1016/j.dam.2017.04.027	https://doi.org/10.1016/j.dam.2017.04.027	PROPN
bracis-28347	219	2	article	article	PROPN
bracis-28347	219	3	  	  	SPACE
bracis-28347	219	4	mathscinet	mathscinet	NOUN
bracis-28347	219	5	  	  	SPACE
bracis-28347	219	6	math	math	NOUN
bracis-28347	219	7	  	  	SPACE
bracis-28347	219	8	google	google	PROPN
bracis-28347	219	9	scholar	scholar	NOUN
bracis-28347	219	10	  	  	SPACE
bracis-28347	219	11	gabow	gabow	NOUN
bracis-28347	219	12	,	,	PUNCT
bracis-28347	219	13	h.n	h.n	PROPN
bracis-28347	219	14	.	.	PROPN
bracis-28347	219	15	,	,	PUNCT
bracis-28347	219	16	nie	nie	PROPN
bracis-28347	219	17	,	,	PUNCT
bracis-28347	219	18	s.	s.	PROPN
bracis-28347	219	19	:	:	PUNCT
bracis-28347	219	20	finding	find	VERB
bracis-28347	219	21	a	a	DET
bracis-28347	219	22	long	long	ADJ
bracis-28347	219	23	directed	direct	VERB
bracis-28347	219	24	cycle	cycle	NOUN
bracis-28347	219	25	.	.	PUNCT
bracis-28347	220	1	acm	acm	PROPN
bracis-28347	220	2	trans	trans	PROPN
bracis-28347	220	3	.	.	PROPN
bracis-28347	220	4	algor	algor	PROPN
bracis-28347	220	5	.	.	PUNCT
bracis-28347	221	1	(	(	PUNCT
bracis-28347	221	2	talg	talg	NOUN
bracis-28347	221	3	)	)	PUNCT
bracis-28347	221	4	4(1	4(1	NOUN
bracis-28347	221	5	)	)	PUNCT
bracis-28347	221	6	,	,	PUNCT
bracis-28347	221	7	1–21	1–21	PROPN
bracis-28347	221	8	(	(	PUNCT
bracis-28347	221	9	2008	2008	NUM
bracis-28347	221	10	)	)	PUNCT
bracis-28347	221	11	article	article	NOUN
bracis-28347	221	12	  	  	SPACE
bracis-28347	221	13	mathscinet	mathscinet	NOUN
bracis-28347	221	14	  	  	SPACE
bracis-28347	221	15	math	math	NOUN
bracis-28347	221	16	  	  	SPACE
bracis-28347	221	17	google	google	PROPN
bracis-28347	221	18	scholar	scholar	NOUN
bracis-28347	221	19	  	  	SPACE
bracis-28347	221	20	gephi	gephi	ADJ
bracis-28347	221	21	:	:	PUNCT
bracis-28347	221	22	conjuntos	conjuntos	PROPN
bracis-28347	221	23	de	de	PROPN
bracis-28347	221	24	dados	dados	PROPN
bracis-28347	221	25	gephi	gephi	ADJ
bracis-28347	221	26	(	(	PUNCT
bracis-28347	221	27	2009	2009	NUM
bracis-28347	221	28	)	)	PUNCT
bracis-28347	221	29	.	.	PUNCT
bracis-28347	222	1	https://github.com/gephi/gephi/wiki/datasets	https://github.com/gephi/gephi/wiki/dataset	NOUN
bracis-28347	222	2	.	.	PUNCT
bracis-28347	223	1	accessed	access	VERB
bracis-28347	223	2	27	27	NUM
bracis-28347	223	3	sept	sept	PROPN
bracis-28347	223	4	2021	2021	NUM
bracis-28347	223	5	kelley	kelley	PROPN
bracis-28347	223	6	,	,	PUNCT
bracis-28347	223	7	b.p	b.p	PROPN
bracis-28347	223	8	.	.	PROPN
bracis-28347	223	9	,	,	PUNCT
bracis-28347	223	10	et	et	PROPN
bracis-28347	223	11	al	al	PROPN
bracis-28347	223	12	.	.	PROPN
bracis-28347	223	13	:	:	PUNCT
bracis-28347	224	1	conserved	conserve	VERB
bracis-28347	224	2	pathways	pathway	NOUN
bracis-28347	224	3	within	within	ADP
bracis-28347	224	4	bacteria	bacteria	NOUN
bracis-28347	224	5	and	and	CCONJ
bracis-28347	224	6	yeast	yeast	NOUN
bracis-28347	224	7	as	as	SCONJ
bracis-28347	224	8	revealed	reveal	VERB
bracis-28347	224	9	by	by	ADP
bracis-28347	224	10	global	global	ADJ
bracis-28347	224	11	protein	protein	NOUN
bracis-28347	224	12	network	network	NOUN
bracis-28347	224	13	alignment	alignment	NOUN
bracis-28347	224	14	.	.	PUNCT
bracis-28347	225	1	proc	proc	PROPN
bracis-28347	225	2	.	.	PUNCT
bracis-28347	226	1	natl	natl	PROPN
bracis-28347	226	2	.	.	PUNCT
bracis-28347	227	1	acad	acad	PROPN
bracis-28347	227	2	.	.	PUNCT
bracis-28347	228	1	sci	sci	PROPN
bracis-28347	228	2	.	.	PROPN
bracis-28347	229	1	100(20	100(20	NUM
bracis-28347	229	2	)	)	PUNCT
bracis-28347	229	3	,	,	PUNCT
bracis-28347	229	4	11394–11399	11394–11399	NUM
bracis-28347	229	5	(	(	PUNCT
bracis-28347	229	6	2003	2003	NUM
bracis-28347	229	7	)	)	PUNCT
bracis-28347	229	8	.	.	PUNCT
bracis-28347	230	1	https://doi.org/10.1073/pnas.1534710100	https://doi.org/10.1073/pnas.1534710100	PROPN
bracis-28347	230	2	.	.	PUNCT
bracis-28347	231	1	https://www.pnas.org/content/100/20/11394	https://www.pnas.org/content/100/20/11394	X
bracis-28347	231	2	lacroix	lacroix	PROPN
bracis-28347	231	3	,	,	PUNCT
bracis-28347	231	4	v.	v.	PROPN
bracis-28347	231	5	,	,	PUNCT
bracis-28347	231	6	fernandes	fernande	NOUN
bracis-28347	231	7	,	,	PUNCT
bracis-28347	231	8	c.g	c.g	PROPN
bracis-28347	231	9	.	.	PROPN
bracis-28347	231	10	,	,	PUNCT
bracis-28347	231	11	sagot	sagot	PROPN
bracis-28347	231	12	,	,	PUNCT
bracis-28347	231	13	m.f	m.f	PROPN
bracis-28347	231	14	.	.	PUNCT
bracis-28347	231	15	:	:	PUNCT
bracis-28347	232	1	motif	motif	NOUN
bracis-28347	232	2	search	search	NOUN
bracis-28347	232	3	in	in	ADP
bracis-28347	232	4	graphs	graph	NOUN
bracis-28347	232	5	:	:	PUNCT
bracis-28347	232	6	application	application	NOUN
bracis-28347	232	7	to	to	ADP
bracis-28347	232	8	metabolic	metabolic	NOUN
bracis-28347	232	9	networks	network	NOUN
bracis-28347	232	10	.	.	PUNCT
bracis-28347	233	1	ieee	ieee	PROPN
bracis-28347	233	2	/	/	SYM
bracis-28347	233	3	acm	acm	PROPN
bracis-28347	233	4	trans	trans	PROPN
bracis-28347	233	5	.	.	PUNCT
bracis-28347	234	1	comput	comput	NOUN
bracis-28347	234	2	.	.	PUNCT
bracis-28347	235	1	biol	biol	PROPN
bracis-28347	235	2	.	.	PUNCT
bracis-28347	236	1	bioinf	bioinf	PROPN
bracis-28347	236	2	.	.	PUNCT
bracis-28347	237	1	3(4	3(4	NUM
bracis-28347	237	2	)	)	PUNCT
bracis-28347	237	3	,	,	PUNCT
bracis-28347	237	4	360–368	360–368	NUM
bracis-28347	237	5	(	(	PUNCT
bracis-28347	237	6	2006	2006	NUM
bracis-28347	237	7	)	)	PUNCT
bracis-28347	237	8	.	.	PUNCT
bracis-28347	238	1	http://doi.ieeecomputersociety.org/10.1109/tcbb.2006.55	http://doi.ieeecomputersociety.org/10.1109/tcbb.2006.55	NOUN
bracis-28347	238	2	markov	markov	PROPN
bracis-28347	238	3	,	,	PUNCT
bracis-28347	238	4	m.	m.	NOUN
bracis-28347	238	5	,	,	PUNCT
bracis-28347	238	6	ionut	ionut	PROPN
bracis-28347	238	7	andreica	andreica	PROPN
bracis-28347	238	8	,	,	PUNCT
bracis-28347	238	9	m.	m.	NOUN
bracis-28347	238	10	,	,	PUNCT
bracis-28347	238	11	manev	manev	PROPN
bracis-28347	238	12	,	,	PUNCT
bracis-28347	238	13	k.	k.	PROPN
bracis-28347	238	14	,	,	PUNCT
bracis-28347	238	15	tapus	tapus	PROPN
bracis-28347	238	16	,	,	PUNCT
bracis-28347	238	17	n.	n.	NOUN
bracis-28347	238	18	:	:	PUNCT
bracis-28347	238	19	a	a	DET
bracis-28347	238	20	linear	linear	ADJ
bracis-28347	238	21	time	time	NOUN
bracis-28347	238	22	algorithm	algorithm	NOUN
bracis-28347	238	23	for	for	ADP
bracis-28347	238	24	computing	compute	VERB
bracis-28347	238	25	longest	long	ADJ
bracis-28347	238	26	paths	path	NOUN
bracis-28347	238	27	in	in	ADP
bracis-28347	238	28	cactus	cactus	NOUN
bracis-28347	238	29	graphs	graph	NOUN
bracis-28347	238	30	.	.	PUNCT
bracis-28347	239	1	serdica	serdica	PROPN
bracis-28347	239	2	j.	j.	PROPN
bracis-28347	239	3	comput	comput	PROPN
bracis-28347	239	4	.	.	PUNCT
bracis-28347	240	1	6(3	6(3	NUM
bracis-28347	240	2	)	)	PUNCT
bracis-28347	240	3	,	,	PUNCT
bracis-28347	240	4	287p–298p	287p–298p	NUM
bracis-28347	240	5	(	(	PUNCT
bracis-28347	240	6	2012	2012	NUM
bracis-28347	240	7	)	)	PUNCT
bracis-28347	240	8	article	article	NOUN
bracis-28347	240	9	  	  	SPACE
bracis-28347	240	10	mathscinet	mathscinet	NOUN
bracis-28347	240	11	  	  	SPACE
bracis-28347	240	12	math	math	NOUN
bracis-28347	240	13	  	  	SPACE
bracis-28347	240	14	google	google	PROPN
bracis-28347	240	15	scholar	scholar	NOUN
bracis-28347	240	16	  	  	SPACE
bracis-28347	240	17	miller	miller	PROPN
bracis-28347	240	18	,	,	PUNCT
bracis-28347	240	19	c.e	c.e	PROPN
bracis-28347	240	20	.	.	PROPN
bracis-28347	240	21	,	,	PUNCT
bracis-28347	240	22	tucker	tucker	PROPN
bracis-28347	240	23	,	,	PUNCT
bracis-28347	240	24	a.w	a.w	PROPN
bracis-28347	240	25	.	.	PROPN
bracis-28347	240	26	,	,	PUNCT
bracis-28347	240	27	zemlin	zemlin	PROPN
bracis-28347	240	28	,	,	PUNCT
bracis-28347	240	29	r.a	r.a	PROPN
bracis-28347	240	30	.	.	PROPN
bracis-28347	240	31	:	:	PUNCT
bracis-28347	240	32	integer	integer	NOUN
bracis-28347	240	33	programming	programming	NOUN
bracis-28347	240	34	formulation	formulation	NOUN
bracis-28347	240	35	of	of	ADP
bracis-28347	240	36	traveling	travel	VERB
bracis-28347	240	37	salesman	salesman	NOUN
bracis-28347	240	38	problems	problem	NOUN
bracis-28347	240	39	.	.	PUNCT
bracis-28347	241	1	j.	j.	PROPN
bracis-28347	241	2	acm	acm	PROPN
bracis-28347	241	3	(	(	PUNCT
bracis-28347	241	4	jacm	jacm	NOUN
bracis-28347	241	5	)	)	PUNCT
bracis-28347	241	6	7(4	7(4	NUM
bracis-28347	241	7	)	)	PUNCT
bracis-28347	241	8	,	,	PUNCT
bracis-28347	241	9	326–329	326–329	NUM
bracis-28347	241	10	(	(	PUNCT
bracis-28347	241	11	1960	1960	NUM
bracis-28347	241	12	)	)	PUNCT
bracis-28347	241	13	article	article	NOUN
bracis-28347	241	14	  	  	SPACE
bracis-28347	241	15	mathscinet	mathscinet	NOUN
bracis-28347	241	16	  	  	SPACE
bracis-28347	241	17	math	math	NOUN
bracis-28347	241	18	  	  	SPACE
bracis-28347	241	19	google	google	PROPN
bracis-28347	241	20	scholar	scholar	NOUN
bracis-28347	241	21	  	  	SPACE
bracis-28347	241	22	download	download	NOUN
bracis-28347	241	23	references	reference	NOUN
bracis-28347	241	24	author	author	NOUN
bracis-28347	241	25	information	information	NOUN
bracis-28347	241	26	authors	author	NOUN
bracis-28347	241	27	and	and	CCONJ
bracis-28347	241	28	affiliations	affiliation	NOUN
bracis-28347	241	29	university	university	PROPN
bracis-28347	241	30	of	of	ADP
bracis-28347	241	31	sao	sao	PROPN
bracis-28347	241	32	paulo	paulo	PROPN
bracis-28347	241	33	usp	usp	PROPN
bracis-28347	241	34	,	,	PUNCT
bracis-28347	241	35	sao	sao	PROPN
bracis-28347	241	36	paulo	paulo	PROPN
bracis-28347	241	37	,	,	PUNCT
bracis-28347	241	38	brazil	brazil	PROPN
bracis-28347	241	39	igor	igor	PROPN
bracis-28347	241	40	m.	m.	PROPN
bracis-28347	241	41	sampaio	sampaio	PROPN
bracis-28347	241	42	 	 	SPACE
bracis-28347	241	43	&	&	CCONJ
bracis-28347	241	44	 	 	SPACE
bracis-28347	241	45	karla	karla	PROPN
bracis-28347	241	46	roberta	roberta	PROPN
bracis-28347	241	47	p.	p.	PROPN
bracis-28347	241	48	s.	s.	PROPN
bracis-28347	242	1	lima	lima	PROPN
bracis-28347	242	2	authors	authors	PROPN
bracis-28347	242	3	igor	igor	PROPN
bracis-28347	242	4	m.	m.	PROPN
bracis-28347	242	5	sampaioview	sampaioview	PROPN
bracis-28347	242	6	author	author	NOUN
bracis-28347	242	7	publications	publication	NOUN
bracis-28347	242	8	search	search	NOUN
bracis-28347	242	9	author	author	NOUN
bracis-28347	242	10	on	on	ADP
bracis-28347	242	11	:	:	PUNCT
bracis-28347	242	12	pubmed	pubmed	PROPN
bracis-28347	242	13	 	 	SPACE
bracis-28347	242	14	google	google	PROPN
bracis-28347	242	15	scholar	scholar	NOUN
bracis-28347	242	16	karla	karla	PROPN
bracis-28347	242	17	roberta	roberta	PROPN
bracis-28347	242	18	p.	p.	PROPN
bracis-28347	242	19	s.	s.	PROPN
bracis-28347	243	1	limaview	limaview	PROPN
bracis-28347	243	2	author	author	NOUN
bracis-28347	243	3	publications	publication	NOUN
bracis-28347	243	4	search	search	NOUN
bracis-28347	243	5	author	author	NOUN
bracis-28347	243	6	on	on	ADP
bracis-28347	243	7	:	:	PUNCT
bracis-28347	243	8	pubmed	pubmed	PROPN
bracis-28347	243	9	 	 	SPACE
bracis-28347	243	10	google	google	PROPN
bracis-28347	243	11	scholar	scholar	NOUN
bracis-28347	243	12	corresponding	correspond	VERB
bracis-28347	243	13	author	author	NOUN
bracis-28347	243	14	correspondence	correspondence	NOUN
bracis-28347	243	15	to	to	ADP
bracis-28347	243	16	igor	igor	PROPN
bracis-28347	243	17	m.	m.	PROPN
bracis-28347	243	18	sampaio	sampaio	PROPN
bracis-28347	243	19	.	.	PUNCT
bracis-28347	244	1	editor	editor	NOUN
bracis-28347	244	2	information	information	NOUN
bracis-28347	244	3	editors	editor	NOUN
bracis-28347	244	4	and	and	CCONJ
bracis-28347	244	5	affiliations	affiliation	NOUN
bracis-28347	244	6	federal	federal	PROPN
bracis-28347	244	7	university	university	PROPN
bracis-28347	244	8	of	of	ADP
bracis-28347	244	9	são	são	PROPN
bracis-28347	244	10	carlos	carlos	PROPN
bracis-28347	244	11	,	,	PUNCT
bracis-28347	244	12	são	são	PROPN
bracis-28347	244	13	carlos	carlos	PROPN
bracis-28347	244	14	,	,	PUNCT
bracis-28347	244	15	brazil	brazil	PROPN
bracis-28347	244	16	murilo	murilo	PROPN
bracis-28347	244	17	c.	c.	PROPN
bracis-28347	244	18	naldi	naldi	PROPN
bracis-28347	244	19	centro	centro	PROPN
bracis-28347	244	20	universitario	universitario	PROPN
bracis-28347	244	21	da	da	PROPN
bracis-28347	244	22	fei	fei	PROPN
bracis-28347	244	23	,	,	PUNCT
bracis-28347	244	24	são	são	PROPN
bracis-28347	244	25	bernardo	bernardo	PROPN
bracis-28347	244	26	do	do	AUX
bracis-28347	244	27	campo	campo	PROPN
bracis-28347	244	28	,	,	PUNCT
bracis-28347	244	29	brazil	brazil	PROPN
bracis-28347	244	30	reinaldo	reinaldo	PROPN
bracis-28347	244	31	a.	a.	PROPN
bracis-28347	244	32	c.	c.	PROPN
bracis-28347	244	33	bianchi	bianchi	PROPN
bracis-28347	244	34	rights	right	NOUN
bracis-28347	244	35	and	and	CCONJ
bracis-28347	244	36	permissions	permission	NOUN
bracis-28347	244	37	reprints	reprint	NOUN
bracis-28347	244	38	and	and	CCONJ
bracis-28347	244	39	permissions	permission	VERB
bracis-28347	244	40	copyright	copyright	NOUN
bracis-28347	244	41	information	information	NOUN
bracis-28347	244	42	©	©	ADP
bracis-28347	244	43	2023	2023	NUM
bracis-28347	244	44	the	the	DET
bracis-28347	244	45	author(s	author(s	NOUN
bracis-28347	244	46	)	)	PUNCT
bracis-28347	244	47	,	,	PUNCT
bracis-28347	244	48	under	under	ADP
bracis-28347	244	49	exclusive	exclusive	ADJ
bracis-28347	244	50	license	license	NOUN
bracis-28347	244	51	to	to	ADP
bracis-28347	244	52	springer	springer	NOUN
bracis-28347	244	53	nature	nature	PROPN
bracis-28347	244	54	switzerland	switzerland	PROPN
bracis-28347	244	55	ag	ag	PROPN
bracis-28347	244	56	about	about	ADP
bracis-28347	244	57	this	this	DET
bracis-28347	244	58	paper	paper	NOUN
bracis-28347	244	59	cite	cite	VERB
bracis-28347	244	60	this	this	DET
bracis-28347	244	61	paper	paper	NOUN
bracis-28347	244	62	sampaio	sampaio	PROPN
bracis-28347	244	63	,	,	PUNCT
bracis-28347	244	64	i.m	i.m	PROPN
bracis-28347	244	65	.	.	PROPN
bracis-28347	244	66	,	,	PUNCT
bracis-28347	244	67	lima	lima	PROPN
bracis-28347	244	68	,	,	PUNCT
bracis-28347	244	69	k.r.p.s	k.r.p.s	PROPN
bracis-28347	244	70	.	.	PUNCT
bracis-28347	245	1	(	(	PUNCT
bracis-28347	245	2	2023	2023	NUM
bracis-28347	245	3	)	)	PUNCT
bracis-28347	245	4	.	.	PUNCT
bracis-28347	246	1	a	a	DET
bracis-28347	246	2	combinatorial	combinatorial	ADJ
bracis-28347	246	3	optimization	optimization	NOUN
bracis-28347	246	4	model	model	NOUN
bracis-28347	246	5	and	and	CCONJ
bracis-28347	246	6	 	 	SPACE
bracis-28347	246	7	polynomial	polynomial	ADJ
bracis-28347	246	8	time	time	NOUN
bracis-28347	246	9	heuristic	heuristic	ADJ
bracis-28347	246	10	for	for	ADP
bracis-28347	246	11	 	 	SPACE
bracis-28347	246	12	a	a	DET
bracis-28347	246	13	 	 	SPACE
bracis-28347	246	14	problem	problem	NOUN
bracis-28347	246	15	of	of	ADP
bracis-28347	246	16	 	 	SPACE
bracis-28347	246	17	finding	find	VERB
bracis-28347	246	18	specific	specific	ADJ
bracis-28347	246	19	structural	structural	ADJ
bracis-28347	246	20	patterns	pattern	NOUN
bracis-28347	246	21	in	in	ADP
bracis-28347	246	22	 	 	SPACE
bracis-28347	246	23	networks	network	NOUN
bracis-28347	246	24	.	.	PUNCT
bracis-28347	247	1	in	in	ADP
bracis-28347	247	2	:	:	PUNCT
bracis-28347	247	3	naldi	naldi	PROPN
bracis-28347	247	4	,	,	PUNCT
bracis-28347	247	5	m.c	m.c	PROPN
bracis-28347	247	6	.	.	PROPN
bracis-28347	247	7	,	,	PUNCT
bracis-28347	247	8	bianchi	bianchi	PROPN
bracis-28347	247	9	,	,	PUNCT
bracis-28347	247	10	r.a.c	r.a.c	ADP
bracis-28347	247	11	.	.	PUNCT
bracis-28347	247	12	(	(	PUNCT
bracis-28347	247	13	eds	ed	NOUN
bracis-28347	247	14	)	)	PUNCT
bracis-28347	247	15	intelligent	intelligent	ADJ
bracis-28347	247	16	systems	system	NOUN
bracis-28347	247	17	.	.	PUNCT
bracis-28347	248	1	bracis	bracis	PROPN
bracis-28347	248	2	2023	2023	NUM
bracis-28347	248	3	.	.	PUNCT
bracis-28347	249	1	lecture	lecture	NOUN
bracis-28347	249	2	notes	note	NOUN
bracis-28347	249	3	in	in	ADP
bracis-28347	249	4	computer	computer	NOUN
bracis-28347	249	5	science	science	NOUN
bracis-28347	249	6	(	(	PUNCT
bracis-28347	249	7	)	)	PUNCT
bracis-28347	249	8	,	,	PUNCT
bracis-28347	249	9	vol	vol	NOUN
bracis-28347	249	10	14195	14195	NUM
bracis-28347	249	11	.	.	PUNCT
bracis-28347	250	1	springer	springer	NOUN
bracis-28347	250	2	,	,	PUNCT
bracis-28347	250	3	cham	cham	PROPN
bracis-28347	250	4	.	.	PUNCT
bracis-28347	251	1	https://doi.org/10.1007/978-3-031-45368-7_3	https://doi.org/10.1007/978-3-031-45368-7_3	NOUN
bracis-28347	251	2	download	download	NOUN
bracis-28347	251	3	citation	citation	NOUN
bracis-28347	251	4	.ris	.ris	PUNCT
bracis-28347	252	1	.enw	.enw	PROPN
bracis-28347	252	2	.bib	.bib	PUNCT
bracis-28347	253	1	doi	doi	PROPN
bracis-28347	253	2	:	:	PUNCT
bracis-28347	253	3	https://doi.org/10.1007/978-3-031-45368-7_3	https://doi.org/10.1007/978-3-031-45368-7_3	NUM
bracis-28347	253	4	published	publish	VERB
bracis-28347	253	5	:	:	PUNCT
bracis-28347	253	6	12	12	NUM
bracis-28347	253	7	october	october	PROPN
bracis-28347	253	8	2023	2023	NUM
bracis-28347	253	9	publisher	publisher	NOUN
bracis-28347	253	10	name	name	NOUN
bracis-28347	253	11	:	:	PUNCT
bracis-28347	253	12	springer	springer	NOUN
bracis-28347	253	13	,	,	PUNCT
bracis-28347	253	14	cham	cham	PROPN
bracis-28347	253	15	print	print	PROPN
bracis-28347	253	16	isbn	isbn	PROPN
bracis-28347	253	17	:	:	PUNCT
bracis-28347	253	18	978	978	NUM
bracis-28347	253	19	-	-	SYM
bracis-28347	253	20	3	3	NUM
bracis-28347	253	21	-	-	PUNCT
bracis-28347	253	22	031	031	NUM
bracis-28347	253	23	-	-	PUNCT
bracis-28347	253	24	45367	45367	NUM
bracis-28347	253	25	-	-	PUNCT
bracis-28347	253	26	0	0	NUM
bracis-28347	253	27	online	online	ADJ
bracis-28347	253	28	isbn	isbn	NOUN
bracis-28347	253	29	:	:	PUNCT
bracis-28347	253	30	978	978	NUM
bracis-28347	253	31	-	-	SYM
bracis-28347	253	32	3	3	NUM
bracis-28347	253	33	-	-	PUNCT
bracis-28347	253	34	031	031	NUM
bracis-28347	253	35	-	-	PUNCT
bracis-28347	253	36	45368	45368	NUM
bracis-28347	253	37	-	-	PUNCT
bracis-28347	253	38	7	7	NUM
bracis-28347	253	39	ebook	ebook	NOUN
bracis-28347	253	40	packages	package	NOUN
bracis-28347	253	41	:	:	PUNCT
bracis-28347	253	42	computer	computer	NOUN
bracis-28347	253	43	sciencecomputer	sciencecomputer	NOUN
bracis-28347	253	44	science	science	NOUN
bracis-28347	253	45	(	(	PUNCT
bracis-28347	253	46	r0	r0	NOUN
bracis-28347	253	47	)	)	PUNCT
bracis-28347	253	48	share	share	VERB
bracis-28347	253	49	this	this	DET
bracis-28347	253	50	paper	paper	NOUN
bracis-28347	253	51	anyone	anyone	PRON
bracis-28347	253	52	you	you	PRON
bracis-28347	253	53	share	share	VERB
bracis-28347	253	54	the	the	DET
bracis-28347	253	55	following	follow	VERB
bracis-28347	253	56	link	link	NOUN
bracis-28347	253	57	with	with	ADP
bracis-28347	253	58	will	will	AUX
bracis-28347	253	59	be	be	AUX
bracis-28347	253	60	able	able	ADJ
bracis-28347	253	61	to	to	PART
bracis-28347	253	62	read	read	VERB
bracis-28347	253	63	this	this	DET
bracis-28347	253	64	content	content	NOUN
bracis-28347	253	65	:	:	PUNCT
bracis-28347	253	66	get	get	VERB
bracis-28347	253	67	shareable	shareable	ADJ
bracis-28347	253	68	linksorry	linksorry	NOUN
bracis-28347	253	69	,	,	PUNCT
bracis-28347	253	70	a	a	DET
bracis-28347	253	71	shareable	shareable	ADJ
bracis-28347	253	72	link	link	NOUN
bracis-28347	253	73	is	be	AUX
bracis-28347	253	74	not	not	PART
bracis-28347	253	75	currently	currently	ADV
bracis-28347	253	76	available	available	ADJ
bracis-28347	253	77	for	for	ADP
bracis-28347	253	78	this	this	DET
bracis-28347	253	79	article	article	NOUN
bracis-28347	253	80	.	.	PUNCT
bracis-28347	254	1	copy	copy	VERB
bracis-28347	254	2	shareable	shareable	ADJ
bracis-28347	254	3	link	link	NOUN
bracis-28347	254	4	to	to	PART
bracis-28347	254	5	clipboard	clipboard	NOUN
bracis-28347	254	6	provided	provide	VERB
bracis-28347	254	7	by	by	ADP
bracis-28347	254	8	the	the	DET
bracis-28347	254	9	springer	springer	NOUN
bracis-28347	254	10	nature	nature	PROPN
bracis-28347	254	11	sharedit	sharedit	PROPN
bracis-28347	254	12	content	content	NOUN
bracis-28347	254	13	-	-	PUNCT
bracis-28347	254	14	sharing	share	VERB
bracis-28347	254	15	initiative	initiative	NOUN
bracis-28347	254	16	keywords	keyword	NOUN
bracis-28347	254	17	optimization	optimization	NOUN
bracis-28347	254	18	combinatorial	combinatorial	ADJ
bracis-28347	254	19	integer	integer	NOUN
bracis-28347	254	20	linear	linear	NOUN
bracis-28347	254	21	programming	programming	NOUN
bracis-28347	254	22	graphs	graph	NOUN
bracis-28347	254	23	publish	publish	VERB
bracis-28347	254	24	with	with	ADP
bracis-28347	254	25	us	us	PROPN
bracis-28347	254	26	policies	policy	NOUN
bracis-28347	254	27	and	and	CCONJ
bracis-28347	254	28	ethics	ethic	NOUN
bracis-28347	254	29	search	search	NOUN
bracis-28347	254	30	search	search	NOUN
bracis-28347	254	31	by	by	ADP
bracis-28347	254	32	keyword	keyword	NOUN
bracis-28347	254	33	or	or	CCONJ
bracis-28347	254	34	author	author	NOUN
bracis-28347	254	35	search	search	NOUN
bracis-28347	254	36	navigation	navigation	NOUN
bracis-28347	254	37	find	find	VERB
bracis-28347	254	38	a	a	DET
bracis-28347	254	39	journal	journal	NOUN
bracis-28347	254	40	publish	publish	VERB
bracis-28347	254	41	with	with	ADP
bracis-28347	254	42	us	we	PRON
bracis-28347	254	43	track	track	VERB
bracis-28347	254	44	your	your	PRON
bracis-28347	254	45	research	research	NOUN
bracis-28347	254	46	discover	discover	VERB
bracis-28347	254	47	content	content	NOUN
bracis-28347	254	48	journals	journal	NOUN
bracis-28347	254	49	a	a	DET
bracis-28347	254	50	-	-	PUNCT
bracis-28347	254	51	z	z	NOUN
bracis-28347	254	52	books	book	NOUN
bracis-28347	254	53	a	a	DET
bracis-28347	254	54	-	-	PUNCT
bracis-28347	254	55	z	z	NOUN
bracis-28347	254	56	publish	publish	NOUN
bracis-28347	254	57	with	with	ADP
bracis-28347	254	58	us	us	PROPN
bracis-28347	254	59	journal	journal	PROPN
bracis-28347	254	60	finder	finder	PROPN
bracis-28347	254	61	publish	publish	VERB
bracis-28347	254	62	your	your	PRON
bracis-28347	254	63	research	research	NOUN
bracis-28347	254	64	language	language	NOUN
bracis-28347	254	65	editing	edit	VERB
bracis-28347	254	66	open	open	ADJ
bracis-28347	254	67	access	access	NOUN
bracis-28347	254	68	publishing	publishing	NOUN
bracis-28347	254	69	products	product	NOUN
bracis-28347	254	70	and	and	CCONJ
bracis-28347	254	71	services	service	NOUN
bracis-28347	254	72	our	our	PRON
bracis-28347	254	73	products	product	NOUN
bracis-28347	254	74	librarians	librarian	VERB
bracis-28347	254	75	societies	society	NOUN
bracis-28347	254	76	partners	partner	NOUN
bracis-28347	254	77	and	and	CCONJ
bracis-28347	254	78	advertisers	advertiser	NOUN
bracis-28347	254	79	our	our	PRON
bracis-28347	254	80	brands	brand	NOUN
bracis-28347	254	81	springer	springer	NOUN
bracis-28347	254	82	nature	nature	PROPN
bracis-28347	254	83	portfolio	portfolio	PROPN
bracis-28347	254	84	bmc	bmc	PROPN
bracis-28347	254	85	palgrave	palgrave	PROPN
bracis-28347	254	86	macmillan	macmillan	PROPN
bracis-28347	254	87	apress	apress	PROPN
bracis-28347	254	88	discover	discover	VERB
bracis-28347	254	89	your	your	PRON
bracis-28347	254	90	privacy	privacy	NOUN
bracis-28347	254	91	choices	choice	NOUN
bracis-28347	254	92	/	/	SYM
bracis-28347	254	93	manage	manage	NOUN
bracis-28347	254	94	cookies	cookie	NOUN
bracis-28347	254	95	your	your	PRON
bracis-28347	254	96	us	us	PROPN
bracis-28347	255	1	state	state	NOUN
bracis-28347	255	2	privacy	privacy	NOUN
bracis-28347	255	3	rights	right	NOUN
bracis-28347	255	4	accessibility	accessibility	NOUN
bracis-28347	255	5	statement	statement	NOUN
bracis-28347	255	6	terms	term	NOUN
bracis-28347	255	7	and	and	CCONJ
bracis-28347	255	8	conditions	condition	NOUN
bracis-28347	255	9	privacy	privacy	NOUN
bracis-28347	255	10	policy	policy	NOUN
bracis-28347	255	11	help	help	NOUN
bracis-28347	255	12	and	and	CCONJ
bracis-28347	255	13	support	support	VERB
bracis-28347	255	14	legal	legal	ADJ
bracis-28347	255	15	notice	notice	NOUN
bracis-28347	255	16	cancel	cancel	VERB
bracis-28347	255	17	contracts	contract	NOUN
bracis-28347	255	18	here	here	ADV
bracis-28347	255	19	129.74.145.123	129.74.145.123	NUM
bracis-28347	255	20	hesburgh	hesburgh	PROPN
bracis-28347	255	21	library	library	PROPN
bracis-28347	255	22	er	er	INTJ
bracis-28347	255	23	unit	unit	NOUN
bracis-28347	255	24	(	(	PUNCT
bracis-28347	255	25	3005732405	3005732405	NUM
bracis-28347	255	26	)	)	PUNCT
bracis-28347	255	27	northeast	northeast	ADJ
bracis-28347	255	28	research	research	NOUN
bracis-28347	255	29	libraries	library	NOUN
bracis-28347	255	30	(	(	PUNCT
bracis-28347	255	31	nerl	nerl	PROPN
bracis-28347	255	32	)	)	PUNCT
bracis-28347	255	33	(	(	PUNCT
bracis-28347	255	34	8200828607	8200828607	NUM
bracis-28347	255	35	)	)	PUNCT
bracis-28347	255	36	nerl	nerl	VERB
bracis-28347	255	37	ta	ta	X
bracis-28347	255	38	account	account	NOUN
bracis-28347	255	39	(	(	PUNCT
bracis-28347	255	40	3006206169	3006206169	NUM
bracis-28347	255	41	)	)	PUNCT
bracis-28347	255	42	university	university	NOUN
bracis-28347	255	43	of	of	ADP
bracis-28347	255	44	notre	notre	PROPN
bracis-28347	255	45	dame	dame	PROPN
bracis-28347	255	46	hesburgh	hesburgh	PROPN
bracis-28347	255	47	library	library	NOUN
bracis-28347	255	48	(	(	PUNCT
bracis-28347	255	49	3000184373	3000184373	NUM
bracis-28347	255	50	)	)	PUNCT
bracis-28347	256	1	©	©	ADP
bracis-28347	256	2	2025	2025	NUM
bracis-28347	256	3	springer	springer	NOUN
bracis-28347	256	4	nature	nature	NOUN