id	sid	tid	token	lemma	pos
ijassa-1597	1	1	adv	adv	PROPN
ijassa-1597	1	2	syst	syst	PROPN
ijassa-1597	1	3	sci	sci	PROPN
ijassa-1597	1	4	appl	appl	PROPN
ijassa-1597	1	5	2024	2024	NUM
ijassa-1597	1	6	;	;	PUNCT
ijassa-1597	1	7	02:94–102	02:94–102	NUM
ijassa-1597	1	8	published	publish	VERB
ijassa-1597	1	9	online	online	ADV
ijassa-1597	1	10	at	at	ADP
ijassa-1597	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADJ
ijassa-1597	1	12	.	.	PUNCT
ijassa-1597	2	1	practical	practical	ADJ
ijassa-1597	2	2	applicability	applicability	NOUN
ijassa-1597	2	3	of	of	ADP
ijassa-1597	2	4	the	the	DET
ijassa-1597	2	5	metric	metric	ADJ
ijassa-1597	2	6	approach	approach	NOUN
ijassa-1597	2	7	for	for	ADP
ijassa-1597	2	8	a	a	DET
ijassa-1597	2	9	scheduling	scheduling	NOUN
ijassa-1597	2	10	problem	problem	NOUN
ijassa-1597	2	11	alexander	alexander	PROPN
ijassa-1597	2	12	lazarev1	lazarev1	PROPN
ijassa-1597	2	13	*	*	PROPN
ijassa-1597	2	14	,	,	PUNCT
ijassa-1597	2	15	darya	darya	PROPN
ijassa-1597	2	16	lemtyuzhnikova1,2	lemtyuzhnikova1,2	PROPN
ijassa-1597	2	17	,	,	PUNCT
ijassa-1597	2	18	ilja	ilja	ADJ
ijassa-1597	2	19	kudinov1	kudinov1	NOUN
ijassa-1597	2	20	1v.a	1v.a	NUM
ijassa-1597	2	21	.	.	PUNCT
ijassa-1597	2	22	trapeznikov	trapeznikov	PROPN
ijassa-1597	2	23	institute	institute	PROPN
ijassa-1597	2	24	of	of	ADP
ijassa-1597	2	25	control	control	PROPN
ijassa-1597	2	26	sciences	sciences	PROPN
ijassa-1597	2	27	of	of	ADP
ijassa-1597	2	28	russian	russian	ADJ
ijassa-1597	2	29	academy	academy	PROPN
ijassa-1597	2	30	of	of	ADP
ijassa-1597	2	31	sciences	sciences	PROPN
ijassa-1597	2	32	,	,	PUNCT
ijassa-1597	2	33	moscow	moscow	PROPN
ijassa-1597	2	34	,	,	PUNCT
ijassa-1597	2	35	russia	russia	PROPN
ijassa-1597	2	36	,	,	PUNCT
ijassa-1597	2	37	2moscow	2moscow	NUM
ijassa-1597	2	38	aviation	aviation	NOUN
ijassa-1597	2	39	institute	institute	NOUN
ijassa-1597	2	40	,	,	PUNCT
ijassa-1597	2	41	moscow	moscow	PROPN
ijassa-1597	2	42	,	,	PUNCT
ijassa-1597	2	43	russia	russia	PROPN
ijassa-1597	2	44	abstract	abstract	NOUN
ijassa-1597	2	45	:	:	PUNCT
ijassa-1597	2	46	a	a	DET
ijassa-1597	2	47	given	give	VERB
ijassa-1597	2	48	special	special	ADJ
ijassa-1597	2	49	case	case	NOUN
ijassa-1597	2	50	of	of	ADP
ijassa-1597	2	51	np	np	NOUN
ijassa-1597	2	52	-	-	PUNCT
ijassa-1597	2	53	complete	complete	ADJ
ijassa-1597	2	54	scheduling	scheduling	NOUN
ijassa-1597	2	55	problem	problem	NOUN
ijassa-1597	2	56	can	can	AUX
ijassa-1597	2	57	be	be	AUX
ijassa-1597	2	58	approximated	approximate	VERB
ijassa-1597	2	59	by	by	ADP
ijassa-1597	2	60	solving	solve	VERB
ijassa-1597	2	61	a	a	DET
ijassa-1597	2	62	special	special	ADJ
ijassa-1597	2	63	case	case	NOUN
ijassa-1597	2	64	of	of	ADP
ijassa-1597	2	65	similar	similar	ADJ
ijassa-1597	2	66	problem	problem	NOUN
ijassa-1597	2	67	with	with	ADP
ijassa-1597	2	68	the	the	DET
ijassa-1597	2	69	same	same	ADJ
ijassa-1597	2	70	precedence	precedence	NOUN
ijassa-1597	2	71	graph	graph	NOUN
ijassa-1597	2	72	.	.	PUNCT
ijassa-1597	3	1	we	we	PRON
ijassa-1597	3	2	construct	construct	VERB
ijassa-1597	3	3	a	a	DET
ijassa-1597	3	4	metric	metric	ADJ
ijassa-1597	3	5	space	space	NOUN
ijassa-1597	3	6	over	over	ADP
ijassa-1597	3	7	a	a	DET
ijassa-1597	3	8	set	set	NOUN
ijassa-1597	3	9	of	of	ADP
ijassa-1597	3	10	special	special	ADJ
ijassa-1597	3	11	cases	case	NOUN
ijassa-1597	3	12	of	of	ADP
ijassa-1597	3	13	this	this	DET
ijassa-1597	3	14	problem	problem	NOUN
ijassa-1597	3	15	and	and	CCONJ
ijassa-1597	3	16	consider	consider	VERB
ijassa-1597	3	17	the	the	DET
ijassa-1597	3	18	statistical	statistical	ADJ
ijassa-1597	3	19	relationship	relationship	NOUN
ijassa-1597	3	20	between	between	ADP
ijassa-1597	3	21	distance	distance	NOUN
ijassa-1597	3	22	between	between	ADP
ijassa-1597	3	23	a	a	DET
ijassa-1597	3	24	pair	pair	NOUN
ijassa-1597	3	25	of	of	ADP
ijassa-1597	3	26	special	special	ADJ
ijassa-1597	3	27	cases	case	NOUN
ijassa-1597	3	28	of	of	ADP
ijassa-1597	3	29	the	the	DET
ijassa-1597	3	30	under	under	ADP
ijassa-1597	3	31	consideration	consideration	NOUN
ijassa-1597	3	32	and	and	CCONJ
ijassa-1597	3	33	the	the	DET
ijassa-1597	3	34	average	average	ADJ
ijassa-1597	3	35	error	error	NOUN
ijassa-1597	3	36	of	of	ADP
ijassa-1597	3	37	the	the	DET
ijassa-1597	3	38	approximated	approximate	VERB
ijassa-1597	3	39	solution	solution	NOUN
ijassa-1597	3	40	.	.	PUNCT
ijassa-1597	4	1	sethi	sethi	PROPN
ijassa-1597	4	2	,	,	PUNCT
ijassa-1597	4	3	gabow	gabow	PROPN
ijassa-1597	4	4	,	,	PUNCT
ijassa-1597	4	5	coffman	coffman	PROPN
ijassa-1597	4	6	’s	’s	PART
ijassa-1597	4	7	and	and	CCONJ
ijassa-1597	4	8	fujii	fujii	PROPN
ijassa-1597	4	9	’s	’s	PART
ijassa-1597	4	10	algorithms	algorithm	NOUN
ijassa-1597	4	11	for	for	ADP
ijassa-1597	4	12	this	this	DET
ijassa-1597	4	13	problem	problem	NOUN
ijassa-1597	4	14	are	be	AUX
ijassa-1597	4	15	used	use	VERB
ijassa-1597	4	16	.	.	PUNCT
ijassa-1597	5	1	it	it	PRON
ijassa-1597	5	2	is	be	AUX
ijassa-1597	5	3	shown	show	VERB
ijassa-1597	5	4	that	that	SCONJ
ijassa-1597	5	5	the	the	DET
ijassa-1597	5	6	absolute	absolute	ADJ
ijassa-1597	5	7	and	and	CCONJ
ijassa-1597	5	8	the	the	DET
ijassa-1597	5	9	relative	relative	ADJ
ijassa-1597	5	10	error	error	NOUN
ijassa-1597	5	11	of	of	ADP
ijassa-1597	5	12	the	the	DET
ijassa-1597	5	13	objective	objective	ADJ
ijassa-1597	5	14	function	function	NOUN
ijassa-1597	5	15	decreases	decrease	VERB
ijassa-1597	5	16	over	over	ADP
ijassa-1597	5	17	the	the	DET
ijassa-1597	5	18	density	density	NOUN
ijassa-1597	5	19	of	of	ADP
ijassa-1597	5	20	a	a	DET
ijassa-1597	5	21	graph	graph	NOUN
ijassa-1597	5	22	with	with	ADP
ijassa-1597	5	23	a	a	DET
ijassa-1597	5	24	fixed	fix	VERB
ijassa-1597	5	25	number	number	NOUN
ijassa-1597	5	26	of	of	ADP
ijassa-1597	5	27	jobs	job	NOUN
ijassa-1597	5	28	.	.	PUNCT
ijassa-1597	6	1	in	in	ADP
ijassa-1597	6	2	general	general	ADJ
ijassa-1597	6	3	case	case	NOUN
ijassa-1597	6	4	,	,	PUNCT
ijassa-1597	6	5	relative	relative	ADJ
ijassa-1597	6	6	non	non	ADJ
ijassa-1597	6	7	-	-	ADJ
ijassa-1597	6	8	zero	zero	NUM
ijassa-1597	6	9	error	error	NOUN
ijassa-1597	6	10	value	value	NOUN
ijassa-1597	6	11	increases	increase	VERB
ijassa-1597	6	12	with	with	ADP
ijassa-1597	6	13	the	the	DET
ijassa-1597	6	14	number	number	NOUN
ijassa-1597	6	15	of	of	ADP
ijassa-1597	6	16	jobs	job	NOUN
ijassa-1597	6	17	.	.	PUNCT
ijassa-1597	7	1	keywords	keyword	NOUN
ijassa-1597	7	2	:	:	PUNCT
ijassa-1597	7	3	scheduling	scheduling	NOUN
ijassa-1597	7	4	,	,	PUNCT
ijassa-1597	7	5	optimization	optimization	NOUN
ijassa-1597	7	6	and	and	CCONJ
ijassa-1597	7	7	control	control	NOUN
ijassa-1597	7	8	,	,	PUNCT
ijassa-1597	7	9	operations	operation	NOUN
ijassa-1597	7	10	research	research	NOUN
ijassa-1597	7	11	,	,	PUNCT
ijassa-1597	7	12	makespan	makespan	ADV
ijassa-1597	7	13	1	1	NUM
ijassa-1597	7	14	.	.	PUNCT
ijassa-1597	8	1	introduction	introduction	NOUN
ijassa-1597	8	2	nowadays	nowadays	ADV
ijassa-1597	8	3	various	various	ADJ
ijassa-1597	8	4	polynomial	polynomial	ADJ
ijassa-1597	8	5	algorithms	algorithm	NOUN
ijassa-1597	8	6	for	for	ADP
ijassa-1597	8	7	many	many	ADJ
ijassa-1597	8	8	combinatoric	combinatoric	ADJ
ijassa-1597	8	9	optimization	optimization	NOUN
ijassa-1597	8	10	problems	problem	NOUN
ijassa-1597	8	11	have	have	AUX
ijassa-1597	8	12	been	be	AUX
ijassa-1597	8	13	developed	develop	VERB
ijassa-1597	8	14	,	,	PUNCT
ijassa-1597	8	15	but	but	CCONJ
ijassa-1597	8	16	there	there	PRON
ijassa-1597	8	17	remain	remain	VERB
ijassa-1597	8	18	many	many	ADJ
ijassa-1597	8	19	of	of	ADP
ijassa-1597	8	20	them	they	PRON
ijassa-1597	8	21	for	for	ADP
ijassa-1597	8	22	which	which	PRON
ijassa-1597	8	23	the	the	DET
ijassa-1597	8	24	question	question	NOUN
ijassa-1597	8	25	of	of	ADP
ijassa-1597	8	26	existence	existence	NOUN
ijassa-1597	8	27	of	of	ADP
ijassa-1597	8	28	polynomial	polynomial	ADJ
ijassa-1597	8	29	algorithm	algorithm	NOUN
ijassa-1597	8	30	is	be	AUX
ijassa-1597	8	31	still	still	ADV
ijassa-1597	8	32	open	open	ADJ
ijassa-1597	8	33	.	.	PUNCT
ijassa-1597	9	1	at	at	ADP
ijassa-1597	9	2	the	the	DET
ijassa-1597	9	3	same	same	ADJ
ijassa-1597	9	4	time	time	NOUN
ijassa-1597	9	5	absolute	absolute	ADJ
ijassa-1597	9	6	approximate	approximate	ADJ
ijassa-1597	9	7	algorithms	algorithm	NOUN
ijassa-1597	9	8	are	be	AUX
ijassa-1597	9	9	known	know	VERB
ijassa-1597	9	10	for	for	ADP
ijassa-1597	9	11	very	very	ADV
ijassa-1597	9	12	few	few	ADJ
ijassa-1597	9	13	np	np	ADJ
ijassa-1597	9	14	-	-	PUNCT
ijassa-1597	9	15	hard	hard	ADJ
ijassa-1597	9	16	optimization	optimization	NOUN
ijassa-1597	9	17	problems	problem	NOUN
ijassa-1597	9	18	and	and	CCONJ
ijassa-1597	9	19	in	in	ADP
ijassa-1597	9	20	most	most	ADJ
ijassa-1597	9	21	cases	case	NOUN
ijassa-1597	9	22	only	only	ADV
ijassa-1597	9	23	relative	relative	ADJ
ijassa-1597	9	24	error	error	NOUN
ijassa-1597	9	25	of	of	ADP
ijassa-1597	9	26	objective	objective	ADJ
ijassa-1597	9	27	function	function	NOUN
ijassa-1597	9	28	value	value	NOUN
ijassa-1597	9	29	estimates	estimate	NOUN
ijassa-1597	9	30	are	be	AUX
ijassa-1597	9	31	available	available	ADJ
ijassa-1597	9	32	.	.	PUNCT
ijassa-1597	10	1	therefore	therefore	ADV
ijassa-1597	10	2	,	,	PUNCT
ijassa-1597	10	3	it	it	PRON
ijassa-1597	10	4	is	be	AUX
ijassa-1597	10	5	important	important	ADJ
ijassa-1597	10	6	to	to	PART
ijassa-1597	10	7	develop	develop	VERB
ijassa-1597	10	8	approximate	approximate	ADJ
ijassa-1597	10	9	algorithms	algorithm	NOUN
ijassa-1597	10	10	that	that	PRON
ijassa-1597	10	11	allow	allow	VERB
ijassa-1597	10	12	to	to	PART
ijassa-1597	10	13	obtain	obtain	VERB
ijassa-1597	10	14	solutions	solution	NOUN
ijassa-1597	10	15	of	of	ADP
ijassa-1597	10	16	the	the	DET
ijassa-1597	10	17	problem	problem	NOUN
ijassa-1597	10	18	with	with	ADP
ijassa-1597	10	19	an	an	DET
ijassa-1597	10	20	acceptable	acceptable	ADJ
ijassa-1597	10	21	error	error	NOUN
ijassa-1597	10	22	estimation	estimation	NOUN
ijassa-1597	10	23	.	.	PUNCT
ijassa-1597	11	1	the	the	DET
ijassa-1597	11	2	metric	metric	ADJ
ijassa-1597	11	3	approach	approach	NOUN
ijassa-1597	11	4	as	as	ADP
ijassa-1597	11	5	one	one	NUM
ijassa-1597	11	6	of	of	ADP
ijassa-1597	11	7	the	the	DET
ijassa-1597	11	8	effective	effective	ADJ
ijassa-1597	11	9	modern	modern	ADJ
ijassa-1597	11	10	approach	approach	NOUN
ijassa-1597	11	11	is	be	AUX
ijassa-1597	11	12	considered	consider	VERB
ijassa-1597	11	13	in	in	ADP
ijassa-1597	11	14	this	this	DET
ijassa-1597	11	15	paper	paper	NOUN
ijassa-1597	11	16	.	.	PUNCT
ijassa-1597	12	1	the	the	DET
ijassa-1597	12	2	main	main	ADJ
ijassa-1597	12	3	idea	idea	NOUN
ijassa-1597	12	4	of	of	ADP
ijassa-1597	12	5	this	this	PRON
ijassa-1597	12	6	is	be	AUX
ijassa-1597	12	7	following	follow	VERB
ijassa-1597	12	8	.	.	PUNCT
ijassa-1597	13	1	assume	assume	VERB
ijassa-1597	13	2	a	a	DET
ijassa-1597	13	3	metric	metric	ADJ
ijassa-1597	13	4	ρ	ρ	NOUN
ijassa-1597	13	5	between	between	ADP
ijassa-1597	13	6	a	a	DET
ijassa-1597	13	7	pair	pair	NOUN
ijassa-1597	13	8	of	of	ADP
ijassa-1597	13	9	instances	instance	NOUN
ijassa-1597	13	10	a	a	DET
ijassa-1597	13	11	,	,	PUNCT
ijassa-1597	13	12	b	b	NOUN
ijassa-1597	13	13	of	of	ADP
ijassa-1597	13	14	some	some	DET
ijassa-1597	13	15	problem	problem	NOUN
ijassa-1597	13	16	:	:	PUNCT
ijassa-1597	13	17	ρ(a	ρ(a	PROPN
ijassa-1597	13	18	,	,	PUNCT
ijassa-1597	13	19	b	b	NOUN
ijassa-1597	13	20	)	)	PUNCT
ijassa-1597	13	21	≥	≥	NOUN
ijassa-1597	13	22	fa(x∗	fa(x∗	NUM
ijassa-1597	13	23	b)−	b)−	PROPN
ijassa-1597	13	24	fa(x∗	fa(x∗	PROPN
ijassa-1597	13	25	a	a	PRON
ijassa-1597	13	26	)	)	PUNCT
ijassa-1597	13	27	,	,	PUNCT
ijassa-1597	13	28	(	(	PUNCT
ijassa-1597	13	29	1.1	1.1	NUM
ijassa-1597	13	30	)	)	PUNCT
ijassa-1597	13	31	where	where	SCONJ
ijassa-1597	13	32	fa(x	fa(x	NOUN
ijassa-1597	13	33	)	)	PUNCT
ijassa-1597	13	34	is	be	AUX
ijassa-1597	13	35	objective	objective	ADJ
ijassa-1597	13	36	function	function	NOUN
ijassa-1597	13	37	values	value	NOUN
ijassa-1597	13	38	of	of	ADP
ijassa-1597	13	39	instance	instance	NOUN
ijassa-1597	13	40	a	a	PRON
ijassa-1597	13	41	,	,	PUNCT
ijassa-1597	13	42	and	and	CCONJ
ijassa-1597	13	43	the	the	DET
ijassa-1597	13	44	arguments	argument	NOUN
ijassa-1597	13	45	x∗	x∗	VERB
ijassa-1597	13	46	a	a	PRON
ijassa-1597	13	47	and	and	CCONJ
ijassa-1597	13	48	x∗	x∗	PROPN
ijassa-1597	13	49	b	b	X
ijassa-1597	13	50	are	be	AUX
ijassa-1597	13	51	an	an	DET
ijassa-1597	13	52	optimal	optimal	ADJ
ijassa-1597	13	53	solution	solution	NOUN
ijassa-1597	13	54	of	of	ADP
ijassa-1597	13	55	instances	instance	NOUN
ijassa-1597	13	56	a	a	DET
ijassa-1597	13	57	and	and	CCONJ
ijassa-1597	13	58	b	b	NOUN
ijassa-1597	13	59	corresponding	corresponding	NOUN
ijassa-1597	13	60	.	.	PUNCT
ijassa-1597	14	1	then	then	ADV
ijassa-1597	14	2	,	,	PUNCT
ijassa-1597	14	3	the	the	DET
ijassa-1597	14	4	metric	metric	NOUN
ijassa-1597	14	5	become	become	VERB
ijassa-1597	14	6	an	an	DET
ijassa-1597	14	7	upper	upper	ADJ
ijassa-1597	14	8	bound	bind	VERB
ijassa-1597	14	9	of	of	ADP
ijassa-1597	14	10	the	the	DET
ijassa-1597	14	11	absolute	absolute	ADJ
ijassa-1597	14	12	error	error	NOUN
ijassa-1597	14	13	of	of	ADP
ijassa-1597	14	14	using	use	VERB
ijassa-1597	14	15	the	the	DET
ijassa-1597	14	16	optimal	optimal	ADJ
ijassa-1597	14	17	solution	solution	NOUN
ijassa-1597	14	18	x∗	x∗	PROPN
ijassa-1597	14	19	b	b	PROPN
ijassa-1597	14	20	of	of	ADP
ijassa-1597	14	21	instance	instance	PROPN
ijassa-1597	14	22	b	b	PROPN
ijassa-1597	14	23	as	as	ADP
ijassa-1597	14	24	an	an	DET
ijassa-1597	14	25	approximate	approximate	ADJ
ijassa-1597	14	26	solution	solution	NOUN
ijassa-1597	14	27	of	of	ADP
ijassa-1597	14	28	instance	instance	NOUN
ijassa-1597	14	29	a.	a.	NOUN
ijassa-1597	14	30	if	if	SCONJ
ijassa-1597	14	31	the	the	DET
ijassa-1597	14	32	searching	search	VERB
ijassa-1597	14	33	for	for	ADP
ijassa-1597	14	34	an	an	DET
ijassa-1597	14	35	optimal	optimal	ADJ
ijassa-1597	14	36	solution	solution	NOUN
ijassa-1597	14	37	of	of	ADP
ijassa-1597	14	38	instance	instance	NOUN
ijassa-1597	14	39	a	a	PRON
ijassa-1597	14	40	is	be	AUX
ijassa-1597	14	41	significantly	significantly	ADV
ijassa-1597	14	42	more	more	ADJ
ijassa-1597	14	43	time	time	NOUN
ijassa-1597	14	44	-	-	PUNCT
ijassa-1597	14	45	consuming	consume	VERB
ijassa-1597	14	46	compared	compare	VERB
ijassa-1597	14	47	to	to	ADP
ijassa-1597	14	48	finding	find	VERB
ijassa-1597	14	49	that	that	PRON
ijassa-1597	14	50	of	of	ADP
ijassa-1597	14	51	b	b	NOUN
ijassa-1597	14	52	,	,	PUNCT
ijassa-1597	14	53	and	and	CCONJ
ijassa-1597	14	54	we	we	PRON
ijassa-1597	14	55	know	know	VERB
ijassa-1597	14	56	a	a	DET
ijassa-1597	14	57	rather	rather	ADV
ijassa-1597	14	58	small	small	ADJ
ijassa-1597	14	59	upper	upper	ADJ
ijassa-1597	14	60	bound	bind	VERB
ijassa-1597	14	61	of	of	ADP
ijassa-1597	14	62	ρ(a	ρ(a	PROPN
ijassa-1597	14	63	,	,	PUNCT
ijassa-1597	14	64	b	b	NOUN
ijassa-1597	14	65	)	)	PUNCT
ijassa-1597	14	66	,	,	PUNCT
ijassa-1597	14	67	we	we	PRON
ijassa-1597	14	68	can	can	AUX
ijassa-1597	14	69	use	use	VERB
ijassa-1597	14	70	x∗	x∗	PROPN
ijassa-1597	14	71	b	b	PROPN
ijassa-1597	14	72	as	as	ADP
ijassa-1597	14	73	a	a	DET
ijassa-1597	14	74	approximate	approximate	ADJ
ijassa-1597	14	75	solution	solution	NOUN
ijassa-1597	14	76	of	of	ADP
ijassa-1597	14	77	instance	instance	NOUN
ijassa-1597	14	78	a.	a.	NOUN
ijassa-1597	14	79	in	in	ADP
ijassa-1597	14	80	this	this	DET
ijassa-1597	14	81	paper	paper	NOUN
ijassa-1597	14	82	we	we	PRON
ijassa-1597	14	83	investigate	investigate	VERB
ijassa-1597	14	84	the	the	DET
ijassa-1597	14	85	feasibility	feasibility	NOUN
ijassa-1597	14	86	and	and	CCONJ
ijassa-1597	14	87	practicability	practicability	NOUN
ijassa-1597	14	88	of	of	ADP
ijassa-1597	14	89	applying	apply	VERB
ijassa-1597	14	90	the	the	DET
ijassa-1597	14	91	metric	metric	ADJ
ijassa-1597	14	92	approach	approach	NOUN
ijassa-1597	14	93	to	to	PART
ijassa-1597	14	94	solve	solve	VERB
ijassa-1597	14	95	the	the	DET
ijassa-1597	14	96	np	np	NOUN
ijassa-1597	14	97	-	-	PUNCT
ijassa-1597	14	98	complete	complete	ADJ
ijassa-1597	14	99	scheduling	scheduling	NOUN
ijassa-1597	14	100	problem	problem	NOUN
ijassa-1597	14	101	of	of	ADP
ijassa-1597	14	102	processing	processing	NOUN
ijassa-1597	14	103	jobs	job	NOUN
ijassa-1597	14	104	on	on	ADP
ijassa-1597	14	105	two	two	NUM
ijassa-1597	14	106	parallel	parallel	ADJ
ijassa-1597	14	107	machines	machine	NOUN
ijassa-1597	14	108	with	with	ADP
ijassa-1597	14	109	a	a	DET
ijassa-1597	14	110	partial	partial	ADJ
ijassa-1597	14	111	ordered	order	VERB
ijassa-1597	14	112	set	set	NOUN
ijassa-1597	14	113	of	of	ADP
ijassa-1597	14	114	jobs	job	NOUN
ijassa-1597	14	115	:	:	PUNCT
ijassa-1597	14	116	p2	p2	PROPN
ijassa-1597	14	117	|	|	ADV
ijassa-1597	14	118	prec	prec	X
ijassa-1597	14	119	,	,	PUNCT
ijassa-1597	14	120	pj	pj	PROPN
ijassa-1597	14	121	∈	∈	PROPN
ijassa-1597	14	122	{	{	PUNCT
ijassa-1597	14	123	1	1	NUM
ijassa-1597	14	124	,	,	PUNCT
ijassa-1597	14	125	2	2	NUM
ijassa-1597	14	126	}	}	PUNCT
ijassa-1597	14	127	|	|	ADV
ijassa-1597	14	128	cmax	cmax	NOUN
ijassa-1597	14	129	,	,	PUNCT
ijassa-1597	14	130	where	where	SCONJ
ijassa-1597	14	131	processing	processing	NOUN
ijassa-1597	14	132	times	time	NOUN
ijassa-1597	14	133	of	of	ADP
ijassa-1597	14	134	jobs	job	NOUN
ijassa-1597	14	135	equal	equal	VERB
ijassa-1597	14	136	1	1	NUM
ijassa-1597	14	137	or	or	CCONJ
ijassa-1597	14	138	2	2	NUM
ijassa-1597	14	139	.	.	X
ijassa-1597	14	140	∗corresponding	∗corresponde	VERB
ijassa-1597	14	141	author	author	NOUN
ijassa-1597	14	142	:	:	PUNCT
ijassa-1597	14	143	alexander	alexander	PROPN
ijassa-1597	14	144	lazarev	lazarev	PROPN
ijassa-1597	14	145	,	,	PUNCT
ijassa-1597	14	146	jobmath@mail.ru	jobmath@mail.ru	ADV
ijassa-1597	14	147	practical	practical	ADJ
ijassa-1597	14	148	applicability	applicability	NOUN
ijassa-1597	14	149	of	of	ADP
ijassa-1597	14	150	the	the	DET
ijassa-1597	14	151	metric	metric	ADJ
ijassa-1597	14	152	approach	approach	NOUN
ijassa-1597	14	153	...	...	PUNCT
ijassa-1597	14	154	95	95	NUM
ijassa-1597	14	155	there	there	PRON
ijassa-1597	14	156	exist	exist	VERB
ijassa-1597	14	157	a	a	DET
ijassa-1597	14	158	little	little	ADJ
ijassa-1597	14	159	of	of	ADP
ijassa-1597	14	160	experiments	experiment	NOUN
ijassa-1597	14	161	conducted	conduct	VERB
ijassa-1597	14	162	as	as	ADP
ijassa-1597	14	163	a	a	DET
ijassa-1597	14	164	proof	proof	NOUN
ijassa-1597	14	165	of	of	ADP
ijassa-1597	14	166	method	method	NOUN
ijassa-1597	14	167	applicability	applicability	NOUN
ijassa-1597	14	168	to	to	ADP
ijassa-1597	14	169	problems	problem	NOUN
ijassa-1597	14	170	of	of	ADP
ijassa-1597	14	171	different	different	ADJ
ijassa-1597	14	172	types	type	NOUN
ijassa-1597	14	173	.	.	PUNCT
ijassa-1597	15	1	our	our	PRON
ijassa-1597	15	2	research	research	NOUN
ijassa-1597	15	3	is	be	AUX
ijassa-1597	15	4	based	base	VERB
ijassa-1597	15	5	on	on	ADP
ijassa-1597	15	6	lazarev	lazarev	PROPN
ijassa-1597	15	7	’s	’s	PART
ijassa-1597	15	8	papers	paper	NOUN
ijassa-1597	15	9	[	[	X
ijassa-1597	15	10	1	1	X
ijassa-1597	15	11	]	]	PUNCT
ijassa-1597	15	12	and	and	CCONJ
ijassa-1597	15	13	[	[	X
ijassa-1597	15	14	2	2	NUM
ijassa-1597	15	15	]	]	PUNCT
ijassa-1597	15	16	,	,	PUNCT
ijassa-1597	15	17	in	in	ADP
ijassa-1597	15	18	which	which	PRON
ijassa-1597	15	19	the	the	DET
ijassa-1597	15	20	way	way	NOUN
ijassa-1597	15	21	of	of	ADP
ijassa-1597	15	22	metric	metric	NOUN
ijassa-1597	15	23	’s	’s	PART
ijassa-1597	15	24	construction	construction	NOUN
ijassa-1597	15	25	for	for	ADP
ijassa-1597	15	26	multiple	multiple	ADJ
ijassa-1597	15	27	problems	problem	NOUN
ijassa-1597	15	28	is	be	AUX
ijassa-1597	15	29	discussed	discuss	VERB
ijassa-1597	15	30	.	.	PUNCT
ijassa-1597	16	1	moreover	moreover	ADV
ijassa-1597	16	2	,	,	PUNCT
ijassa-1597	16	3	we	we	PRON
ijassa-1597	16	4	conducted	conduct	VERB
ijassa-1597	16	5	an	an	DET
ijassa-1597	16	6	experiment	experiment	NOUN
ijassa-1597	16	7	for	for	ADP
ijassa-1597	16	8	a	a	DET
ijassa-1597	16	9	single	single	ADJ
ijassa-1597	16	10	machine	machine	NOUN
ijassa-1597	16	11	scheduling	scheduling	NOUN
ijassa-1597	16	12	problem	problem	NOUN
ijassa-1597	16	13	.	.	PUNCT
ijassa-1597	17	1	to	to	PART
ijassa-1597	17	2	fulfill	fulfill	VERB
ijassa-1597	17	3	the	the	DET
ijassa-1597	17	4	existing	exist	VERB
ijassa-1597	17	5	knowledge	knowledge	NOUN
ijassa-1597	17	6	of	of	ADP
ijassa-1597	17	7	feasibility	feasibility	NOUN
ijassa-1597	17	8	to	to	PART
ijassa-1597	17	9	apply	apply	VERB
ijassa-1597	17	10	metric	metric	ADJ
ijassa-1597	17	11	approach	approach	NOUN
ijassa-1597	17	12	for	for	ADP
ijassa-1597	17	13	various	various	ADJ
ijassa-1597	17	14	types	type	NOUN
ijassa-1597	17	15	of	of	ADP
ijassa-1597	17	16	problems	problem	NOUN
ijassa-1597	17	17	,	,	PUNCT
ijassa-1597	17	18	we	we	PRON
ijassa-1597	17	19	conduct	conduct	VERB
ijassa-1597	17	20	experiments	experiment	NOUN
ijassa-1597	17	21	for	for	ADP
ijassa-1597	17	22	problem	problem	NOUN
ijassa-1597	17	23	p2	p2	NOUN
ijassa-1597	17	24	|	|	ADV
ijassa-1597	17	25	prec	prec	X
ijassa-1597	17	26	,	,	PUNCT
ijassa-1597	17	27	pj	pj	PROPN
ijassa-1597	17	28	∈	∈	PROPN
ijassa-1597	17	29	{	{	PUNCT
ijassa-1597	17	30	1	1	NUM
ijassa-1597	17	31	,	,	PUNCT
ijassa-1597	17	32	2	2	NUM
ijassa-1597	17	33	}	}	PUNCT
ijassa-1597	17	34	|	|	ADV
ijassa-1597	17	35	cmax	cmax	VERB
ijassa-1597	17	36	.	.	PUNCT
ijassa-1597	18	1	we	we	PRON
ijassa-1597	18	2	chose	choose	VERB
ijassa-1597	18	3	this	this	DET
ijassa-1597	18	4	simplification	simplification	NOUN
ijassa-1597	18	5	of	of	ADP
ijassa-1597	18	6	the	the	DET
ijassa-1597	18	7	problem	problem	NOUN
ijassa-1597	18	8	p2	p2	PROPN
ijassa-1597	18	9	|	|	ADV
ijassa-1597	18	10	prec	prec	X
ijassa-1597	18	11	,	,	PUNCT
ijassa-1597	18	12	pj	pj	PROPN
ijassa-1597	18	13	=	=	SYM
ijassa-1597	18	14	k	k	PROPN
ijassa-1597	19	1	|	|	ADV
ijassa-1597	19	2	cmax	cmax	VERB
ijassa-1597	19	3	for	for	ADP
ijassa-1597	19	4	conduction	conduction	NOUN
ijassa-1597	19	5	the	the	DET
ijassa-1597	19	6	experiments	experiment	NOUN
ijassa-1597	19	7	due	due	ADP
ijassa-1597	19	8	to	to	ADP
ijassa-1597	19	9	the	the	DET
ijassa-1597	19	10	existence	existence	NOUN
ijassa-1597	19	11	of	of	ADP
ijassa-1597	19	12	the	the	DET
ijassa-1597	19	13	variety	variety	NOUN
ijassa-1597	19	14	of	of	ADP
ijassa-1597	19	15	polynomial	polynomial	ADJ
ijassa-1597	19	16	algorithms	algorithm	NOUN
ijassa-1597	19	17	for	for	ADP
ijassa-1597	19	18	the	the	DET
ijassa-1597	19	19	problem	problem	NOUN
ijassa-1597	19	20	p2	p2	PROPN
ijassa-1597	19	21	|	|	ADV
ijassa-1597	19	22	prec	prec	X
ijassa-1597	19	23	,	,	PUNCT
ijassa-1597	19	24	pj	pj	PROPN
ijassa-1597	19	25	=	=	SYM
ijassa-1597	19	26	1	1	NUM
ijassa-1597	19	27	|	|	ADV
ijassa-1597	19	28	cmax	cmax	VERB
ijassa-1597	19	29	,	,	PUNCT
ijassa-1597	19	30	to	to	PART
ijassa-1597	19	31	which	which	PRON
ijassa-1597	19	32	we	we	PRON
ijassa-1597	19	33	can	can	AUX
ijassa-1597	19	34	easily	easily	ADV
ijassa-1597	19	35	apply	apply	VERB
ijassa-1597	19	36	metric	metric	ADJ
ijassa-1597	19	37	approach	approach	NOUN
ijassa-1597	19	38	.	.	PUNCT
ijassa-1597	20	1	nevertheless	nevertheless	ADV
ijassa-1597	20	2	,	,	PUNCT
ijassa-1597	20	3	we	we	PRON
ijassa-1597	20	4	apply	apply	VERB
ijassa-1597	20	5	the	the	DET
ijassa-1597	20	6	proof	proof	NOUN
ijassa-1597	20	7	of	of	ADP
ijassa-1597	20	8	metric	metric	ADJ
ijassa-1597	20	9	construction	construction	NOUN
ijassa-1597	20	10	for	for	ADP
ijassa-1597	20	11	the	the	DET
ijassa-1597	20	12	problem	problem	NOUN
ijassa-1597	20	13	p2	p2	PROPN
ijassa-1597	20	14	|	|	ADV
ijassa-1597	20	15	prec	prec	X
ijassa-1597	20	16	,	,	PUNCT
ijassa-1597	20	17	pj	pj	PROPN
ijassa-1597	20	18	=	=	SYM
ijassa-1597	20	19	k	k	PROPN
ijassa-1597	20	20	|	|	ADV
ijassa-1597	20	21	cmax	cmax	NOUN
ijassa-1597	20	22	,	,	PUNCT
ijassa-1597	20	23	where	where	SCONJ
ijassa-1597	20	24	k	k	PROPN
ijassa-1597	20	25	∈	∈	PROPN
ijassa-1597	20	26	z+	z+	PUNCT
ijassa-1597	20	27	.	.	PUNCT
ijassa-1597	21	1	one	one	NUM
ijassa-1597	21	2	of	of	ADP
ijassa-1597	21	3	the	the	DET
ijassa-1597	21	4	first	first	ADJ
ijassa-1597	21	5	papers	paper	NOUN
ijassa-1597	21	6	concerning	concern	VERB
ijassa-1597	21	7	an	an	DET
ijassa-1597	21	8	algorithm	algorithm	NOUN
ijassa-1597	21	9	for	for	ADP
ijassa-1597	21	10	optimal	optimal	ADJ
ijassa-1597	21	11	solution	solution	NOUN
ijassa-1597	21	12	obtaining	obtain	VERB
ijassa-1597	21	13	for	for	ADP
ijassa-1597	21	14	problem	problem	NOUN
ijassa-1597	21	15	p2	p2	PROPN
ijassa-1597	21	16	|	|	ADV
ijassa-1597	21	17	prec	prec	X
ijassa-1597	21	18	,	,	PUNCT
ijassa-1597	21	19	pj	pj	PROPN
ijassa-1597	21	20	=	=	SYM
ijassa-1597	21	21	1	1	NUM
ijassa-1597	21	22	|	|	ADV
ijassa-1597	21	23	cmax	cmax	NOUN
ijassa-1597	21	24	is	be	AUX
ijassa-1597	21	25	the	the	DET
ijassa-1597	21	26	work	work	NOUN
ijassa-1597	21	27	of	of	ADP
ijassa-1597	21	28	fujii	fujii	PROPN
ijassa-1597	21	29	[	[	X
ijassa-1597	21	30	4	4	NUM
ijassa-1597	21	31	]	]	PUNCT
ijassa-1597	21	32	,	,	PUNCT
ijassa-1597	21	33	in	in	ADP
ijassa-1597	21	34	which	which	PRON
ijassa-1597	21	35	the	the	DET
ijassa-1597	21	36	algorithm	algorithm	NOUN
ijassa-1597	21	37	based	base	VERB
ijassa-1597	21	38	on	on	ADP
ijassa-1597	21	39	finding	find	VERB
ijassa-1597	21	40	the	the	DET
ijassa-1597	21	41	maximum	maximum	ADJ
ijassa-1597	21	42	matching	matching	NOUN
ijassa-1597	21	43	in	in	ADP
ijassa-1597	21	44	precedence	precedence	NOUN
ijassa-1597	21	45	graph	graph	NOUN
ijassa-1597	21	46	was	be	AUX
ijassa-1597	21	47	proposed	propose	VERB
ijassa-1597	21	48	.	.	PUNCT
ijassa-1597	22	1	the	the	DET
ijassa-1597	22	2	upper	upper	ADJ
ijassa-1597	22	3	bound	bound	NOUN
ijassa-1597	22	4	of	of	ADP
ijassa-1597	22	5	the	the	DET
ijassa-1597	22	6	number	number	NOUN
ijassa-1597	22	7	of	of	ADP
ijassa-1597	22	8	operations	operation	NOUN
ijassa-1597	22	9	required	require	VERB
ijassa-1597	22	10	to	to	PART
ijassa-1597	22	11	find	find	VERB
ijassa-1597	22	12	the	the	DET
ijassa-1597	22	13	optimal	optimal	ADJ
ijassa-1597	22	14	sequence	sequence	NOUN
ijassa-1597	22	15	is	be	AUX
ijassa-1597	22	16	o(n3	o(n3	NOUN
ijassa-1597	22	17	)	)	PUNCT
ijassa-1597	22	18	operations	operation	NOUN
ijassa-1597	22	19	where	where	SCONJ
ijassa-1597	22	20	n	n	PRON
ijassa-1597	22	21	is	be	AUX
ijassa-1597	22	22	number	number	NOUN
ijassa-1597	22	23	of	of	ADP
ijassa-1597	22	24	jobs	job	NOUN
ijassa-1597	22	25	.	.	PUNCT
ijassa-1597	23	1	the	the	DET
ijassa-1597	23	2	coffman	coffman	PROPN
ijassa-1597	23	3	[	[	X
ijassa-1597	23	4	5	5	NUM
ijassa-1597	23	5	]	]	PUNCT
ijassa-1597	23	6	and	and	CCONJ
ijassa-1597	23	7	sethi	sethi	PROPN
ijassa-1597	24	1	[	[	X
ijassa-1597	24	2	6	6	NUM
ijassa-1597	24	3	]	]	PUNCT
ijassa-1597	24	4	proposed	propose	VERB
ijassa-1597	24	5	algorithms	algorithm	NOUN
ijassa-1597	24	6	which	which	PRON
ijassa-1597	24	7	,	,	PUNCT
ijassa-1597	24	8	as	as	ADP
ijassa-1597	24	9	the	the	DET
ijassa-1597	24	10	fujii	fujii	PROPN
ijassa-1597	24	11	’s	’s	PART
ijassa-1597	24	12	algorithm	algorithm	NOUN
ijassa-1597	24	13	,	,	PUNCT
ijassa-1597	24	14	are	be	AUX
ijassa-1597	24	15	based	base	VERB
ijassa-1597	24	16	on	on	ADP
ijassa-1597	24	17	a	a	DET
ijassa-1597	24	18	list	list	NOUN
ijassa-1597	24	19	of	of	ADP
ijassa-1597	24	20	jobs	job	NOUN
ijassa-1597	24	21	,	,	PUNCT
ijassa-1597	24	22	the	the	DET
ijassa-1597	24	23	list	list	NOUN
ijassa-1597	24	24	is	be	AUX
ijassa-1597	24	25	used	use	VERB
ijassa-1597	24	26	to	to	PART
ijassa-1597	24	27	sequentially	sequentially	ADV
ijassa-1597	24	28	take	take	VERB
ijassa-1597	24	29	elements	element	NOUN
ijassa-1597	24	30	for	for	ADP
ijassa-1597	24	31	distribution	distribution	NOUN
ijassa-1597	24	32	on	on	ADP
ijassa-1597	24	33	two	two	NUM
ijassa-1597	24	34	machines	machine	NOUN
ijassa-1597	24	35	.	.	PUNCT
ijassa-1597	25	1	coffman	coffman	PROPN
ijassa-1597	25	2	’s	’s	PART
ijassa-1597	25	3	algorithm	algorithm	PROPN
ijassa-1597	25	4	has	have	AUX
ijassa-1597	25	5	found	find	VERB
ijassa-1597	25	6	the	the	DET
ijassa-1597	25	7	upper	upper	ADJ
ijassa-1597	25	8	bound	bind	VERB
ijassa-1597	25	9	is	be	AUX
ijassa-1597	25	10	o(n2	o(n2	ADJ
ijassa-1597	25	11	)	)	PUNCT
ijassa-1597	25	12	operations	operation	NOUN
ijassa-1597	25	13	,	,	PUNCT
ijassa-1597	25	14	and	and	CCONJ
ijassa-1597	25	15	sethi	sethi	PROPN
ijassa-1597	25	16	’s	’s	PART
ijassa-1597	25	17	work	work	NOUN
ijassa-1597	25	18	presents	present	VERB
ijassa-1597	25	19	two	two	NUM
ijassa-1597	25	20	algorithms	algorithm	NOUN
ijassa-1597	25	21	,	,	PUNCT
ijassa-1597	25	22	one	one	NUM
ijassa-1597	25	23	of	of	ADP
ijassa-1597	25	24	which	which	PRON
ijassa-1597	25	25	makes	make	VERB
ijassa-1597	25	26	the	the	DET
ijassa-1597	25	27	labeling	labeling	NOUN
ijassa-1597	25	28	for	for	ADP
ijassa-1597	25	29	o(e+	o(e+	NOUN
ijassa-1597	25	30	n	n	CCONJ
ijassa-1597	25	31	)	)	PUNCT
ijassa-1597	25	32	operations	operation	NOUN
ijassa-1597	25	33	,	,	PUNCT
ijassa-1597	25	34	and	and	CCONJ
ijassa-1597	25	35	the	the	DET
ijassa-1597	25	36	other	other	ADJ
ijassa-1597	25	37	makes	make	VERB
ijassa-1597	25	38	the	the	DET
ijassa-1597	25	39	schedule	schedule	NOUN
ijassa-1597	25	40	for	for	ADP
ijassa-1597	25	41	o(e+	o(e+	NOUN
ijassa-1597	25	42	nα(n	nα(n	NOUN
ijassa-1597	25	43	)	)	PUNCT
ijassa-1597	25	44	)	)	PUNCT
ijassa-1597	26	1	operations	operation	NOUN
ijassa-1597	26	2	,	,	PUNCT
ijassa-1597	26	3	where	where	SCONJ
ijassa-1597	26	4	e	e	X
ijassa-1597	26	5	–	–	PUNCT
ijassa-1597	26	6	the	the	DET
ijassa-1597	26	7	number	number	NOUN
ijassa-1597	26	8	of	of	ADP
ijassa-1597	26	9	edges	edge	NOUN
ijassa-1597	26	10	in	in	ADP
ijassa-1597	26	11	the	the	DET
ijassa-1597	26	12	precedence	precedence	NOUN
ijassa-1597	26	13	graph	graph	NOUN
ijassa-1597	26	14	,	,	PUNCT
ijassa-1597	26	15	and	and	CCONJ
ijassa-1597	26	16	α(n	α(n	NOUN
ijassa-1597	26	17	)	)	PUNCT
ijassa-1597	26	18	–	–	PUNCT
ijassa-1597	26	19	ackerman	ackerman	PROPN
ijassa-1597	26	20	’s	’s	PART
ijassa-1597	26	21	function	function	NOUN
ijassa-1597	26	22	,	,	PUNCT
ijassa-1597	26	23	which	which	PRON
ijassa-1597	26	24	slowly	slowly	ADV
ijassa-1597	26	25	grows	grow	VERB
ijassa-1597	26	26	.	.	PUNCT
ijassa-1597	27	1	the	the	DET
ijassa-1597	27	2	labeling	labeling	NOUN
ijassa-1597	27	3	algorithm	algorithm	NOUN
ijassa-1597	27	4	proposed	propose	VERB
ijassa-1597	27	5	by	by	ADP
ijassa-1597	27	6	sethi	sethi	PROPN
ijassa-1597	27	7	is	be	AUX
ijassa-1597	27	8	largely	largely	ADV
ijassa-1597	27	9	based	base	VERB
ijassa-1597	27	10	on	on	ADP
ijassa-1597	27	11	coffman	coffman	PROPN
ijassa-1597	27	12	’s	’s	PART
ijassa-1597	27	13	algorithm	algorithm	NOUN
ijassa-1597	27	14	,	,	PUNCT
ijassa-1597	27	15	but	but	CCONJ
ijassa-1597	27	16	it	it	PRON
ijassa-1597	27	17	adds	add	VERB
ijassa-1597	27	18	an	an	DET
ijassa-1597	27	19	additional	additional	ADJ
ijassa-1597	27	20	examination	examination	NOUN
ijassa-1597	27	21	of	of	ADP
ijassa-1597	27	22	the	the	DET
ijassa-1597	27	23	structure	structure	NOUN
ijassa-1597	27	24	at	at	ADP
ijassa-1597	27	25	each	each	DET
ijassa-1597	27	26	level	level	NOUN
ijassa-1597	27	27	of	of	ADP
ijassa-1597	27	28	the	the	DET
ijassa-1597	27	29	graph	graph	NOUN
ijassa-1597	27	30	.	.	PUNCT
ijassa-1597	28	1	gabow	gabow	NOUN
ijassa-1597	28	2	’s	’s	PART
ijassa-1597	28	3	algorithm	algorithm	NOUN
ijassa-1597	28	4	[	[	X
ijassa-1597	28	5	7	7	X
ijassa-1597	28	6	]	]	X
ijassa-1597	28	7	works	work	NOUN
ijassa-1597	28	8	according	accord	VERB
ijassa-1597	28	9	to	to	ADP
ijassa-1597	28	10	the	the	DET
ijassa-1597	28	11	”	"	PUNCT
ijassa-1597	28	12	high	high	ADJ
ijassa-1597	28	13	level	level	NOUN
ijassa-1597	28	14	first	first	ADV
ijassa-1597	28	15	”	"	PUNCT
ijassa-1597	28	16	(	(	PUNCT
ijassa-1597	28	17	hlf	hlf	PROPN
ijassa-1597	28	18	)	)	PUNCT
ijassa-1597	28	19	principle	principle	NOUN
ijassa-1597	28	20	and	and	CCONJ
ijassa-1597	28	21	requires	require	VERB
ijassa-1597	28	22	o(e+	o(e+	NOUN
ijassa-1597	28	23	nα(n	nα(n	NOUN
ijassa-1597	28	24	)	)	PUNCT
ijassa-1597	28	25	)	)	PUNCT
ijassa-1597	28	26	operations	operation	NOUN
ijassa-1597	28	27	.	.	PUNCT
ijassa-1597	29	1	the	the	DET
ijassa-1597	29	2	np	np	NOUN
ijassa-1597	29	3	-	-	PUNCT
ijassa-1597	29	4	completeness	completeness	NOUN
ijassa-1597	29	5	of	of	ADP
ijassa-1597	29	6	the	the	DET
ijassa-1597	29	7	problems	problem	NOUN
ijassa-1597	29	8	p2	p2	VERB
ijassa-1597	29	9	|	|	ADV
ijassa-1597	29	10	prec	prec	X
ijassa-1597	29	11	,	,	PUNCT
ijassa-1597	29	12	pj	pj	PROPN
ijassa-1597	29	13	=	=	SYM
ijassa-1597	29	14	1	1	NUM
ijassa-1597	29	15	|	|	ADV
ijassa-1597	29	16	cmax	cmax	VERB
ijassa-1597	29	17	and	and	CCONJ
ijassa-1597	29	18	p2	p2	PROPN
ijassa-1597	29	19	|	|	CCONJ
ijassa-1597	29	20	prec	prec	X
ijassa-1597	29	21	,	,	PUNCT
ijassa-1597	29	22	pj	pj	PROPN
ijassa-1597	29	23	∈	∈	PROPN
ijassa-1597	29	24	{	{	PUNCT
ijassa-1597	29	25	1	1	NUM
ijassa-1597	29	26	,	,	PUNCT
ijassa-1597	29	27	2	2	NUM
ijassa-1597	29	28	}	}	PUNCT
ijassa-1597	30	1	|	|	ADV
ijassa-1597	30	2	cmax	cmax	NOUN
ijassa-1597	30	3	was	be	AUX
ijassa-1597	30	4	first	first	ADV
ijassa-1597	30	5	proved	prove	VERB
ijassa-1597	30	6	ullman	ullman	NOUN
ijassa-1597	31	1	[	[	X
ijassa-1597	31	2	8	8	NUM
ijassa-1597	31	3	]	]	PUNCT
ijassa-1597	31	4	.	.	PUNCT
ijassa-1597	32	1	furthermore	furthermore	ADV
ijassa-1597	32	2	,	,	PUNCT
ijassa-1597	32	3	the	the	DET
ijassa-1597	32	4	bevern	bevern	NOUN
ijassa-1597	32	5	in	in	ADP
ijassa-1597	32	6	paper	paper	NOUN
ijassa-1597	32	7	[	[	X
ijassa-1597	32	8	9	9	NUM
ijassa-1597	32	9	]	]	PUNCT
ijassa-1597	32	10	proves	prove	VERB
ijassa-1597	32	11	that	that	SCONJ
ijassa-1597	32	12	the	the	DET
ijassa-1597	32	13	problem	problem	NOUN
ijassa-1597	32	14	p2	p2	VERB
ijassa-1597	32	15	|	|	ADV
ijassa-1597	32	16	prec	prec	X
ijassa-1597	32	17	,	,	PUNCT
ijassa-1597	32	18	pj	pj	PROPN
ijassa-1597	32	19	∈	∈	PROPN
ijassa-1597	32	20	{	{	PUNCT
ijassa-1597	32	21	1	1	NUM
ijassa-1597	32	22	,	,	PUNCT
ijassa-1597	32	23	2	2	NUM
ijassa-1597	32	24	}	}	PUNCT
ijassa-1597	32	25	|	|	ADV
ijassa-1597	32	26	cmax	cmax	NOUN
ijassa-1597	32	27	is	be	AUX
ijassa-1597	32	28	w	w	ADP
ijassa-1597	32	29	[	[	X
ijassa-1597	32	30	2]-hard	2]-hard	NUM
ijassa-1597	32	31	parameterized	parameterized	ADJ
ijassa-1597	32	32	by	by	ADP
ijassa-1597	32	33	the	the	DET
ijassa-1597	32	34	width	width	NOUN
ijassa-1597	32	35	of	of	ADP
ijassa-1597	32	36	the	the	DET
ijassa-1597	32	37	partial	partial	ADJ
ijassa-1597	32	38	order	order	NOUN
ijassa-1597	32	39	.	.	PUNCT
ijassa-1597	33	1	however	however	ADV
ijassa-1597	33	2	it	it	PRON
ijassa-1597	33	3	is	be	AUX
ijassa-1597	33	4	an	an	DET
ijassa-1597	33	5	open	open	ADJ
ijassa-1597	33	6	question	question	NOUN
ijassa-1597	33	7	if	if	SCONJ
ijassa-1597	33	8	pm	pm	NOUN
ijassa-1597	33	9	|	|	ADV
ijassa-1597	33	10	prec	prec	X
ijassa-1597	33	11	,	,	PUNCT
ijassa-1597	33	12	pj	pj	PROPN
ijassa-1597	33	13	=	=	SYM
ijassa-1597	33	14	1	1	NUM
ijassa-1597	33	15	|	|	ADV
ijassa-1597	33	16	cmax	cmax	NOUN
ijassa-1597	33	17	is	be	AUX
ijassa-1597	33	18	np	np	INTJ
ijassa-1597	33	19	-	-	PUNCT
ijassa-1597	33	20	hard	hard	ADJ
ijassa-1597	33	21	for	for	ADP
ijassa-1597	33	22	m	m	VERB
ijassa-1597	33	23	⩾	⩾	NOUN
ijassa-1597	33	24	3	3	NUM
ijassa-1597	33	25	.	.	X
ijassa-1597	34	1	in	in	ADP
ijassa-1597	34	2	literature	literature	NOUN
ijassa-1597	34	3	there	there	PRON
ijassa-1597	34	4	are	be	VERB
ijassa-1597	34	5	references	reference	NOUN
ijassa-1597	34	6	to	to	ADP
ijassa-1597	34	7	the	the	DET
ijassa-1597	34	8	work	work	NOUN
ijassa-1597	34	9	of	of	ADP
ijassa-1597	34	10	[	[	X
ijassa-1597	34	11	10	10	NUM
ijassa-1597	34	12	]	]	PUNCT
ijassa-1597	34	13	,	,	PUNCT
ijassa-1597	34	14	which	which	PRON
ijassa-1597	34	15	gives	give	VERB
ijassa-1597	34	16	an	an	DET
ijassa-1597	34	17	algorithm	algorithm	NOUN
ijassa-1597	34	18	whose	whose	DET
ijassa-1597	34	19	complexity	complexity	NOUN
ijassa-1597	34	20	is	be	AUX
ijassa-1597	34	21	o(n	o(n	PROPN
ijassa-1597	34	22	log	log	NOUN
ijassa-1597	34	23	n	n	CCONJ
ijassa-1597	34	24	)	)	PUNCT
ijassa-1597	34	25	operations	operation	NOUN
ijassa-1597	34	26	for	for	ADP
ijassa-1597	34	27	the	the	DET
ijassa-1597	34	28	problem	problem	NOUN
ijassa-1597	34	29	p2	p2	PROPN
ijassa-1597	34	30	|	|	ADV
ijassa-1597	34	31	prec	prec	X
ijassa-1597	34	32	,	,	PUNCT
ijassa-1597	34	33	pj	pj	PROPN
ijassa-1597	34	34	∈	∈	PROPN
ijassa-1597	34	35	{	{	PUNCT
ijassa-1597	34	36	1	1	NUM
ijassa-1597	34	37	,	,	PUNCT
ijassa-1597	34	38	2	2	NUM
ijassa-1597	34	39	}	}	PUNCT
ijassa-1597	34	40	|	|	ADV
ijassa-1597	34	41	cmax	cmax	VERB
ijassa-1597	34	42	,	,	PUNCT
ijassa-1597	34	43	and	and	CCONJ
ijassa-1597	34	44	a	a	DET
ijassa-1597	34	45	heuristic	heuristic	ADJ
ijassa-1597	34	46	algorithm	algorithm	NOUN
ijassa-1597	35	1	[	[	X
ijassa-1597	35	2	11	11	NUM
ijassa-1597	35	3	]	]	PUNCT
ijassa-1597	35	4	,	,	PUNCT
ijassa-1597	35	5	in	in	ADP
ijassa-1597	35	6	the	the	DET
ijassa-1597	35	7	worst	bad	ADJ
ijassa-1597	35	8	case	case	NOUN
ijassa-1597	35	9	giving	give	VERB
ijassa-1597	35	10	error	error	NOUN
ijassa-1597	35	11	equal	equal	ADJ
ijassa-1597	35	12	to	to	ADP
ijassa-1597	35	13	one	one	NUM
ijassa-1597	35	14	for	for	ADP
ijassa-1597	35	15	the	the	DET
ijassa-1597	35	16	problem	problem	NOUN
ijassa-1597	35	17	p2	p2	PROPN
ijassa-1597	35	18	|	|	ADV
ijassa-1597	35	19	prec	prec	X
ijassa-1597	35	20	,	,	PUNCT
ijassa-1597	35	21	pj	pj	PROPN
ijassa-1597	35	22	∈	∈	PROPN
ijassa-1597	35	23	{	{	PUNCT
ijassa-1597	35	24	1	1	NUM
ijassa-1597	35	25	,	,	PUNCT
ijassa-1597	35	26	2	2	NUM
ijassa-1597	35	27	}	}	PUNCT
ijassa-1597	35	28	|	|	ADV
ijassa-1597	35	29	cmax	cmax	VERB
ijassa-1597	35	30	.	.	PUNCT
ijassa-1597	36	1	in	in	ADP
ijassa-1597	36	2	addition	addition	NOUN
ijassa-1597	36	3	,	,	PUNCT
ijassa-1597	36	4	in	in	ADP
ijassa-1597	36	5	[	[	X
ijassa-1597	36	6	12	12	NUM
ijassa-1597	36	7	]	]	X
ijassa-1597	36	8	an	an	DET
ijassa-1597	36	9	algorithm	algorithm	NOUN
ijassa-1597	36	10	is	be	AUX
ijassa-1597	36	11	given	give	VERB
ijassa-1597	36	12	that	that	SCONJ
ijassa-1597	36	13	yields	yield	VERB
ijassa-1597	36	14	the	the	DET
ijassa-1597	36	15	optimal	optimal	ADJ
ijassa-1597	36	16	solution	solution	NOUN
ijassa-1597	36	17	for	for	ADP
ijassa-1597	36	18	the	the	DET
ijassa-1597	36	19	problem	problem	NOUN
ijassa-1597	36	20	p2	p2	PROPN
ijassa-1597	36	21	|	|	ADV
ijassa-1597	36	22	prec	prec	X
ijassa-1597	36	23	,	,	PUNCT
ijassa-1597	36	24	pj	pj	PROPN
ijassa-1597	36	25	∈	∈	PROPN
ijassa-1597	36	26	{	{	PUNCT
ijassa-1597	36	27	1	1	NUM
ijassa-1597	36	28	,	,	PUNCT
ijassa-1597	36	29	2	2	NUM
ijassa-1597	36	30	}	}	PUNCT
ijassa-1597	36	31	|	|	ADV
ijassa-1597	36	32	cmax	cmax	NOUN
ijassa-1597	36	33	using	use	VERB
ijassa-1597	36	34	o(n2	o(n2	ADJ
ijassa-1597	36	35	log	log	NOUN
ijassa-1597	36	36	n	n	CCONJ
ijassa-1597	36	37	)	)	PUNCT
ijassa-1597	36	38	operations	operation	NOUN
ijassa-1597	36	39	.	.	PUNCT
ijassa-1597	36	40	hu	hu	PROPN
ijassa-1597	37	1	[	[	X
ijassa-1597	37	2	13	13	NUM
ijassa-1597	37	3	]	]	PUNCT
ijassa-1597	37	4	demonstrates	demonstrate	VERB
ijassa-1597	37	5	polynomial	polynomial	ADJ
ijassa-1597	37	6	algorithm	algorithm	NOUN
ijassa-1597	37	7	for	for	ADP
ijassa-1597	37	8	the	the	DET
ijassa-1597	37	9	problem	problem	NOUN
ijassa-1597	37	10	p2	p2	PROPN
ijassa-1597	37	11	|	|	ADV
ijassa-1597	37	12	prec	prec	X
ijassa-1597	37	13	,	,	PUNCT
ijassa-1597	37	14	pj	pj	PROPN
ijassa-1597	37	15	=	=	SYM
ijassa-1597	37	16	1	1	NUM
ijassa-1597	37	17	|	|	ADV
ijassa-1597	37	18	cmax	cmax	VERB
ijassa-1597	37	19	,	,	PUNCT
ijassa-1597	37	20	if	if	SCONJ
ijassa-1597	37	21	graph	graph	NOUN
ijassa-1597	37	22	of	of	ADP
ijassa-1597	37	23	ordering	order	VERB
ijassa-1597	37	24	restrictions	restriction	NOUN
ijassa-1597	37	25	is	be	AUX
ijassa-1597	37	26	a	a	DET
ijassa-1597	37	27	tree	tree	NOUN
ijassa-1597	37	28	and	and	CCONJ
ijassa-1597	37	29	number	number	NOUN
ijassa-1597	37	30	of	of	ADP
ijassa-1597	37	31	jobs	job	NOUN
ijassa-1597	37	32	satisfies	satisfy	VERB
ijassa-1597	37	33	some	some	DET
ijassa-1597	37	34	conditions	condition	NOUN
ijassa-1597	37	35	.	.	PUNCT
ijassa-1597	38	1	by	by	ADP
ijassa-1597	38	2	the	the	DET
ijassa-1597	38	3	way	way	NOUN
ijassa-1597	38	4	,	,	PUNCT
ijassa-1597	38	5	dolev	dolev	NOUN
ijassa-1597	38	6	’s	’s	PART
ijassa-1597	38	7	methods	method	NOUN
ijassa-1597	38	8	[	[	X
ijassa-1597	38	9	14	14	NUM
ijassa-1597	38	10	]	]	PUNCT
ijassa-1597	38	11	lead	lead	NOUN
ijassa-1597	38	12	to	to	ADP
ijassa-1597	38	13	polynomial	polynomial	ADJ
ijassa-1597	38	14	algorithms	algorithm	NOUN
ijassa-1597	38	15	for	for	ADP
ijassa-1597	38	16	the	the	DET
ijassa-1597	38	17	problem	problem	NOUN
ijassa-1597	38	18	p2	p2	PROPN
ijassa-1597	38	19	|	|	ADV
ijassa-1597	38	20	prec	prec	X
ijassa-1597	38	21	,	,	PUNCT
ijassa-1597	38	22	pj	pj	PROPN
ijassa-1597	38	23	=	=	SYM
ijassa-1597	38	24	1	1	NUM
ijassa-1597	38	25	|	|	ADV
ijassa-1597	38	26	cmax	cmax	VERB
ijassa-1597	38	27	if	if	SCONJ
ijassa-1597	38	28	the	the	DET
ijassa-1597	38	29	number	number	NOUN
ijassa-1597	38	30	of	of	ADP
ijassa-1597	38	31	machines	machine	NOUN
ijassa-1597	38	32	is	be	AUX
ijassa-1597	38	33	fixed	fix	VERB
ijassa-1597	38	34	and	and	CCONJ
ijassa-1597	38	35	the	the	DET
ijassa-1597	38	36	precedence	precedence	NOUN
ijassa-1597	38	37	graph	graph	NOUN
ijassa-1597	38	38	has	have	VERB
ijassa-1597	38	39	a	a	DET
ijassa-1597	38	40	certain	certain	ADJ
ijassa-1597	38	41	form	form	NOUN
ijassa-1597	38	42	.	.	PUNCT
ijassa-1597	39	1	in	in	ADP
ijassa-1597	39	2	particular	particular	ADJ
ijassa-1597	39	3	,	,	PUNCT
ijassa-1597	39	4	if	if	SCONJ
ijassa-1597	39	5	the	the	DET
ijassa-1597	39	6	precedence	precedence	NOUN
ijassa-1597	39	7	graph	graph	NOUN
ijassa-1597	39	8	contains	contain	VERB
ijassa-1597	39	9	only	only	ADV
ijassa-1597	39	10	in	in	ADP
ijassa-1597	39	11	-	-	PUNCT
ijassa-1597	39	12	trees	tree	NOUN
ijassa-1597	39	13	or	or	CCONJ
ijassa-1597	39	14	out	out	ADV
ijassa-1597	39	15	-	-	PUNCT
ijassa-1597	39	16	trees	tree	NOUN
ijassa-1597	39	17	,	,	PUNCT
ijassa-1597	39	18	the	the	DET
ijassa-1597	39	19	result	result	NOUN
ijassa-1597	39	20	leads	lead	VERB
ijassa-1597	39	21	to	to	ADP
ijassa-1597	39	22	linear	linear	ADJ
ijassa-1597	39	23	algorithms	algorithm	NOUN
ijassa-1597	39	24	for	for	ADP
ijassa-1597	39	25	finding	find	VERB
ijassa-1597	39	26	an	an	DET
ijassa-1597	39	27	optimal	optimal	ADJ
ijassa-1597	39	28	schedule	schedule	NOUN
ijassa-1597	39	29	on	on	ADP
ijassa-1597	39	30	two	two	NUM
ijassa-1597	39	31	and	and	CCONJ
ijassa-1597	39	32	three	three	NUM
ijassa-1597	39	33	machines	machine	NOUN
ijassa-1597	39	34	.	.	PUNCT
ijassa-1597	40	1	the	the	DET
ijassa-1597	40	2	structure	structure	NOUN
ijassa-1597	40	3	of	of	ADP
ijassa-1597	40	4	the	the	DET
ijassa-1597	40	5	paper	paper	NOUN
ijassa-1597	40	6	is	be	AUX
ijassa-1597	40	7	organized	organize	VERB
ijassa-1597	40	8	as	as	SCONJ
ijassa-1597	40	9	follows	follow	VERB
ijassa-1597	40	10	.	.	PUNCT
ijassa-1597	41	1	in	in	ADP
ijassa-1597	41	2	section	section	NOUN
ijassa-1597	41	3	2	2	NUM
ijassa-1597	41	4	the	the	DET
ijassa-1597	41	5	mathematical	mathematical	ADJ
ijassa-1597	41	6	formulation	formulation	NOUN
ijassa-1597	41	7	of	of	ADP
ijassa-1597	41	8	the	the	DET
ijassa-1597	41	9	problem	problem	NOUN
ijassa-1597	41	10	p2	p2	PROPN
ijassa-1597	41	11	|	|	ADV
ijassa-1597	41	12	prec	prec	X
ijassa-1597	41	13	,	,	PUNCT
ijassa-1597	41	14	pj	pj	PROPN
ijassa-1597	41	15	∈	∈	PROPN
ijassa-1597	41	16	{	{	PUNCT
ijassa-1597	41	17	1	1	NUM
ijassa-1597	41	18	,	,	PUNCT
ijassa-1597	41	19	2	2	NUM
ijassa-1597	41	20	}	}	PUNCT
ijassa-1597	41	21	|	|	ADV
ijassa-1597	41	22	cmax	cmax	NOUN
ijassa-1597	41	23	is	be	AUX
ijassa-1597	41	24	given	give	VERB
ijassa-1597	41	25	.	.	PUNCT
ijassa-1597	42	1	in	in	ADP
ijassa-1597	42	2	section	section	NOUN
ijassa-1597	42	3	3	3	NUM
ijassa-1597	42	4	we	we	PRON
ijassa-1597	42	5	define	define	VERB
ijassa-1597	42	6	the	the	DET
ijassa-1597	42	7	metric	metric	NOUN
ijassa-1597	42	8	we	we	PRON
ijassa-1597	42	9	use	use	VERB
ijassa-1597	42	10	.	.	PUNCT
ijassa-1597	43	1	in	in	ADP
ijassa-1597	43	2	section	section	NOUN
ijassa-1597	43	3	4	4	NUM
ijassa-1597	43	4	we	we	PRON
ijassa-1597	43	5	describe	describe	VERB
ijassa-1597	43	6	our	our	PRON
ijassa-1597	43	7	motivation	motivation	NOUN
ijassa-1597	43	8	and	and	CCONJ
ijassa-1597	43	9	approach	approach	NOUN
ijassa-1597	43	10	for	for	ADP
ijassa-1597	43	11	the	the	DET
ijassa-1597	43	12	problem	problem	NOUN
ijassa-1597	43	13	.	.	PUNCT
ijassa-1597	44	1	in	in	ADP
ijassa-1597	44	2	section	section	NOUN
ijassa-1597	44	3	5	5	NUM
ijassa-1597	44	4	the	the	DET
ijassa-1597	44	5	experiment	experiment	NOUN
ijassa-1597	44	6	’s	’s	PART
ijassa-1597	44	7	result	result	NOUN
ijassa-1597	44	8	is	be	AUX
ijassa-1597	44	9	given	give	VERB
ijassa-1597	44	10	.	.	PUNCT
ijassa-1597	45	1	2	2	X
ijassa-1597	45	2	.	.	X
ijassa-1597	45	3	the	the	DET
ijassa-1597	45	4	problem	problem	NOUN
ijassa-1597	45	5	definition	definition	NOUN
ijassa-1597	45	6	we	we	PRON
ijassa-1597	45	7	consider	consider	VERB
ijassa-1597	45	8	scheduling	schedule	VERB
ijassa-1597	45	9	the	the	DET
ijassa-1597	45	10	problem	problem	NOUN
ijassa-1597	45	11	p2	p2	NOUN
ijassa-1597	45	12	|	|	ADV
ijassa-1597	45	13	prec	prec	X
ijassa-1597	45	14	,	,	PUNCT
ijassa-1597	45	15	pj	pj	PROPN
ijassa-1597	45	16	∈	∈	PROPN
ijassa-1597	45	17	{	{	PUNCT
ijassa-1597	45	18	1	1	NUM
ijassa-1597	45	19	,	,	PUNCT
ijassa-1597	45	20	2	2	NUM
ijassa-1597	45	21	}	}	PUNCT
ijassa-1597	45	22	|	|	ADV
ijassa-1597	45	23	cmax	cmax	VERB
ijassa-1597	45	24	.	.	PUNCT
ijassa-1597	46	1	each	each	DET
ijassa-1597	46	2	instance	instance	NOUN
ijassa-1597	46	3	a	a	PRON
ijassa-1597	46	4	has	have	VERB
ijassa-1597	46	5	a	a	DET
ijassa-1597	46	6	set	set	NOUN
ijassa-1597	46	7	of	of	ADP
ijassa-1597	46	8	n	n	NOUN
ijassa-1597	46	9	jobs	job	NOUN
ijassa-1597	46	10	na	na	NOUN
ijassa-1597	46	11	=	=	SYM
ijassa-1597	46	12	n	n	NOUN
ijassa-1597	46	13	and	and	CCONJ
ijassa-1597	46	14	set	set	VERB
ijassa-1597	46	15	of	of	ADP
ijassa-1597	46	16	m	m	PROPN
ijassa-1597	46	17	machines	machine	NOUN
ijassa-1597	46	18	ma	ma	PROPN
ijassa-1597	47	1	=	=	PROPN
ijassa-1597	47	2	m	m	PROPN
ijassa-1597	47	3	.	.	PUNCT
ijassa-1597	48	1	each	each	DET
ijassa-1597	48	2	job	job	NOUN
ijassa-1597	48	3	j	j	PROPN
ijassa-1597	48	4	∈	∈	PROPN
ijassa-1597	48	5	n	n	CCONJ
ijassa-1597	48	6	can	can	AUX
ijassa-1597	48	7	be	be	AUX
ijassa-1597	48	8	processed	process	VERB
ijassa-1597	48	9	on	on	ADP
ijassa-1597	48	10	one	one	NUM
ijassa-1597	48	11	machine	machine	NOUN
ijassa-1597	48	12	during	during	ADP
ijassa-1597	48	13	pj	pj	PROPN
ijassa-1597	48	14	time	time	NOUN
ijassa-1597	48	15	units	unit	NOUN
ijassa-1597	48	16	.	.	PUNCT
ijassa-1597	49	1	each	each	DET
ijassa-1597	49	2	machine	machine	NOUN
ijassa-1597	49	3	can	can	AUX
ijassa-1597	49	4	process	process	VERB
ijassa-1597	49	5	only	only	ADV
ijassa-1597	49	6	one	one	NUM
ijassa-1597	49	7	job	job	NOUN
ijassa-1597	49	8	at	at	ADP
ijassa-1597	49	9	a	a	DET
ijassa-1597	49	10	time	time	NOUN
ijassa-1597	49	11	.	.	PUNCT
ijassa-1597	50	1	set	set	VERB
ijassa-1597	50	2	copyright	copyright	NOUN
ijassa-1597	50	3	©	©	PROPN
ijassa-1597	50	4	2024	2024	NUM
ijassa-1597	50	5	assa	assa	NOUN
ijassa-1597	50	6	.	.	PUNCT
ijassa-1597	51	1	adv	adv	PROPN
ijassa-1597	51	2	syst	syst	PROPN
ijassa-1597	51	3	sci	sci	PROPN
ijassa-1597	51	4	appl	appl	PROPN
ijassa-1597	51	5	(	(	PUNCT
ijassa-1597	51	6	2024	2024	NUM
ijassa-1597	51	7	)	)	PUNCT
ijassa-1597	51	8	96	96	NUM
ijassa-1597	51	9	a.	a.	NOUN
ijassa-1597	51	10	lazarev	lazarev	PROPN
ijassa-1597	51	11	,	,	PUNCT
ijassa-1597	51	12	d.	d.	PROPN
ijassa-1597	51	13	levtyuzhnikova	levtyuzhnikova	PROPN
ijassa-1597	51	14	,	,	PUNCT
ijassa-1597	51	15	i.	i.	PROPN
ijassa-1597	51	16	kudinov	kudinov	PROPN
ijassa-1597	51	17	n	n	PRON
ijassa-1597	51	18	has	have	VERB
ijassa-1597	51	19	a	a	DET
ijassa-1597	51	20	partial	partial	ADJ
ijassa-1597	51	21	order	order	NOUN
ijassa-1597	51	22	≺	≺	NOUN
ijassa-1597	51	23	that	that	SCONJ
ijassa-1597	51	24	from	from	ADP
ijassa-1597	51	25	j1	j1	PROPN
ijassa-1597	51	26	≺	≺	NOUN
ijassa-1597	51	27	j2	j2	PROPN
ijassa-1597	51	28	follows	follow	VERB
ijassa-1597	51	29	j2	j2	PROPN
ijassa-1597	51	30	can	can	AUX
ijassa-1597	51	31	not	not	PART
ijassa-1597	51	32	be	be	AUX
ijassa-1597	51	33	started	start	VERB
ijassa-1597	51	34	processing	process	VERB
ijassa-1597	51	35	until	until	SCONJ
ijassa-1597	51	36	j1	j1	PROPN
ijassa-1597	51	37	be	be	AUX
ijassa-1597	51	38	complete	complete	ADJ
ijassa-1597	51	39	.	.	PUNCT
ijassa-1597	52	1	the	the	DET
ijassa-1597	52	2	partial	partial	ADJ
ijassa-1597	52	3	order	order	NOUN
ijassa-1597	52	4	is	be	AUX
ijassa-1597	52	5	defined	define	VERB
ijassa-1597	52	6	by	by	ADP
ijassa-1597	52	7	a	a	DET
ijassa-1597	52	8	dag	dag	PROPN
ijassa-1597	52	9	(	(	PUNCT
ijassa-1597	52	10	directed	direct	VERB
ijassa-1597	52	11	acyclic	acyclic	ADJ
ijassa-1597	52	12	graph	graph	NOUN
ijassa-1597	52	13	)	)	PUNCT
ijassa-1597	52	14	called	call	VERB
ijassa-1597	52	15	a	a	DET
ijassa-1597	52	16	precedence	precedence	NOUN
ijassa-1597	52	17	graph	graph	NOUN
ijassa-1597	52	18	.	.	PUNCT
ijassa-1597	53	1	we	we	PRON
ijassa-1597	53	2	denote	denote	VERB
ijassa-1597	53	3	πa	πa	ADP
ijassa-1597	53	4	=	=	PUNCT
ijassa-1597	53	5	π	π	PROPN
ijassa-1597	53	6	as	as	ADP
ijassa-1597	53	7	a	a	DET
ijassa-1597	53	8	permutation	permutation	NOUN
ijassa-1597	53	9	(	(	PUNCT
ijassa-1597	53	10	j1	j1	PROPN
ijassa-1597	53	11	,	,	PUNCT
ijassa-1597	53	12	j2	j2	PROPN
ijassa-1597	53	13	,	,	PUNCT
ijassa-1597	53	14	.	.	PUNCT
ijassa-1597	53	15	.	.	PUNCT
ijassa-1597	53	16	.	.	PUNCT
ijassa-1597	54	1	,	,	PUNCT
ijassa-1597	54	2	jn	jn	PROPN
ijassa-1597	54	3	)	)	PUNCT
ijassa-1597	54	4	over	over	ADP
ijassa-1597	54	5	the	the	DET
ijassa-1597	54	6	job	job	NOUN
ijassa-1597	54	7	set	set	NOUN
ijassa-1597	54	8	n	n	ADV
ijassa-1597	54	9	.	.	PUNCT
ijassa-1597	55	1	in	in	ADP
ijassa-1597	55	2	order	order	NOUN
ijassa-1597	55	3	of	of	ADP
ijassa-1597	55	4	constructing	construct	VERB
ijassa-1597	55	5	a	a	DET
ijassa-1597	55	6	schedule	schedule	NOUN
ijassa-1597	55	7	we	we	PRON
ijassa-1597	55	8	put	put	VERB
ijassa-1597	55	9	each	each	DET
ijassa-1597	55	10	job	job	NOUN
ijassa-1597	55	11	from	from	ADP
ijassa-1597	55	12	π	π	PROPN
ijassa-1597	55	13	sequentially	sequentially	ADV
ijassa-1597	55	14	to	to	ADP
ijassa-1597	55	15	the	the	DET
ijassa-1597	55	16	earliest	early	ADJ
ijassa-1597	55	17	possible	possible	ADJ
ijassa-1597	55	18	place	place	NOUN
ijassa-1597	55	19	of	of	ADP
ijassa-1597	55	20	processing	processing	NOUN
ijassa-1597	55	21	in	in	ADP
ijassa-1597	55	22	the	the	DET
ijassa-1597	55	23	schedule	schedule	NOUN
ijassa-1597	55	24	.	.	PUNCT
ijassa-1597	56	1	for	for	ADP
ijassa-1597	56	2	simplicity	simplicity	NOUN
ijassa-1597	56	3	,	,	PUNCT
ijassa-1597	56	4	we	we	PRON
ijassa-1597	56	5	call	call	VERB
ijassa-1597	56	6	π	π	PROPN
ijassa-1597	56	7	a	a	DET
ijassa-1597	56	8	schedule	schedule	NOUN
ijassa-1597	56	9	as	as	ADV
ijassa-1597	56	10	well	well	ADV
ijassa-1597	56	11	.	.	PUNCT
ijassa-1597	57	1	if	if	SCONJ
ijassa-1597	57	2	saj	saj	PROPN
ijassa-1597	57	3	(	(	PUNCT
ijassa-1597	57	4	π	π	NOUN
ijassa-1597	57	5	)	)	PUNCT
ijassa-1597	57	6	is	be	AUX
ijassa-1597	57	7	a	a	DET
ijassa-1597	57	8	starting	starting	NOUN
ijassa-1597	57	9	time	time	NOUN
ijassa-1597	57	10	of	of	ADP
ijassa-1597	57	11	job	job	NOUN
ijassa-1597	57	12	j	j	PROPN
ijassa-1597	57	13	∈	∈	PROPN
ijassa-1597	57	14	n	n	NOUN
ijassa-1597	57	15	processing	processing	NOUN
ijassa-1597	57	16	and	and	CCONJ
ijassa-1597	57	17	ca	ca	PROPN
ijassa-1597	57	18	j	j	PROPN
ijassa-1597	57	19	(	(	PUNCT
ijassa-1597	57	20	π	π	PROPN
ijassa-1597	57	21	)	)	PUNCT
ijassa-1597	57	22	=	=	SYM
ijassa-1597	57	23	saj	saj	X
ijassa-1597	57	24	(	(	PUNCT
ijassa-1597	57	25	π	π	NOUN
ijassa-1597	57	26	)	)	PUNCT
ijassa-1597	57	27	+	+	CCONJ
ijassa-1597	57	28	pj	pj	PROPN
ijassa-1597	57	29	is	be	AUX
ijassa-1597	57	30	the	the	DET
ijassa-1597	57	31	completion	completion	NOUN
ijassa-1597	57	32	one	one	NUM
ijassa-1597	57	33	,	,	PUNCT
ijassa-1597	57	34	the	the	DET
ijassa-1597	57	35	schedule	schedule	NOUN
ijassa-1597	57	36	π	π	PROPN
ijassa-1597	57	37	has	have	VERB
ijassa-1597	57	38	the	the	DET
ijassa-1597	57	39	following	follow	VERB
ijassa-1597	57	40	features	feature	NOUN
ijassa-1597	57	41	:	:	PUNCT
ijassa-1597	58	1	1	1	X
ijassa-1597	58	2	.	.	X
ijassa-1597	59	1	if	if	SCONJ
ijassa-1597	59	2	mj1	mj1	PROPN
ijassa-1597	59	3	=	=	PUNCT
ijassa-1597	59	4	mj2	mj2	PROPN
ijassa-1597	59	5	then	then	ADV
ijassa-1597	59	6	[	[	X
ijassa-1597	59	7	sj1(π	sj1(π	NOUN
ijassa-1597	59	8	)	)	PUNCT
ijassa-1597	59	9	,	,	PUNCT
ijassa-1597	59	10	cj1(π	cj1(π	NOUN
ijassa-1597	59	11	)	)	PUNCT
ijassa-1597	59	12	)	)	PUNCT
ijassa-1597	60	1	∩	∩	NOUN
ijassa-1597	60	2	[	[	X
ijassa-1597	60	3	sj2(π	sj2(π	NOUN
ijassa-1597	60	4	)	)	PUNCT
ijassa-1597	60	5	,	,	PUNCT
ijassa-1597	60	6	cj2(π	cj2(π	PROPN
ijassa-1597	60	7	)	)	PUNCT
ijassa-1597	60	8	)	)	PUNCT
ijassa-1597	61	1	=	=	NOUN
ijassa-1597	61	2	∅	∅	NOUN
ijassa-1597	61	3	for	for	ADP
ijassa-1597	61	4	j1	j1	PROPN
ijassa-1597	61	5	,	,	PUNCT
ijassa-1597	61	6	j2	j2	PROPN
ijassa-1597	61	7	∈	∈	PROPN
ijassa-1597	61	8	n	n	NOUN
ijassa-1597	61	9	.	.	PUNCT
ijassa-1597	62	1	2	2	X
ijassa-1597	62	2	.	.	X
ijassa-1597	63	1	if	if	SCONJ
ijassa-1597	63	2	j1	j1	PROPN
ijassa-1597	63	3	≺	≺	NOUN
ijassa-1597	63	4	j2	j2	PROPN
ijassa-1597	63	5	then	then	ADV
ijassa-1597	63	6	cj1(π	cj1(π	PROPN
ijassa-1597	63	7	)	)	PUNCT
ijassa-1597	63	8	≤	≤	NUM
ijassa-1597	63	9	sj2(π	sj2(π	NOUN
ijassa-1597	63	10	)	)	PUNCT
ijassa-1597	63	11	.	.	PUNCT
ijassa-1597	64	1	the	the	DET
ijassa-1597	64	2	first	first	ADJ
ijassa-1597	64	3	condition	condition	NOUN
ijassa-1597	64	4	means	mean	VERB
ijassa-1597	64	5	that	that	SCONJ
ijassa-1597	64	6	a	a	DET
ijassa-1597	64	7	machine	machine	NOUN
ijassa-1597	64	8	can	can	AUX
ijassa-1597	64	9	not	not	PART
ijassa-1597	64	10	process	process	VERB
ijassa-1597	64	11	more	more	ADJ
ijassa-1597	64	12	than	than	ADP
ijassa-1597	64	13	one	one	NUM
ijassa-1597	64	14	job	job	NOUN
ijassa-1597	64	15	at	at	ADP
ijassa-1597	64	16	a	a	DET
ijassa-1597	64	17	time	time	NOUN
ijassa-1597	64	18	.	.	PUNCT
ijassa-1597	65	1	the	the	DET
ijassa-1597	65	2	second	second	ADJ
ijassa-1597	65	3	condition	condition	NOUN
ijassa-1597	65	4	is	be	AUX
ijassa-1597	65	5	nothing	nothing	PRON
ijassa-1597	65	6	more	more	ADJ
ijassa-1597	65	7	than	than	ADP
ijassa-1597	65	8	the	the	DET
ijassa-1597	65	9	fulfilltime	fulfilltime	NOUN
ijassa-1597	65	10	of	of	ADP
ijassa-1597	65	11	precedence	precedence	NOUN
ijassa-1597	65	12	relations	relation	NOUN
ijassa-1597	65	13	between	between	ADP
ijassa-1597	65	14	jobs	job	NOUN
ijassa-1597	65	15	.	.	PUNCT
ijassa-1597	66	1	a	a	DET
ijassa-1597	66	2	schedule	schedule	NOUN
ijassa-1597	66	3	π	π	NOUN
ijassa-1597	66	4	of	of	ADP
ijassa-1597	66	5	an	an	DET
ijassa-1597	66	6	instance	instance	NOUN
ijassa-1597	66	7	a	a	PRON
ijassa-1597	66	8	is	be	AUX
ijassa-1597	66	9	feasible	feasible	ADJ
ijassa-1597	66	10	if	if	SCONJ
ijassa-1597	66	11	it	it	PRON
ijassa-1597	66	12	does	do	AUX
ijassa-1597	66	13	not	not	PART
ijassa-1597	66	14	disrupt	disrupt	VERB
ijassa-1597	66	15	the	the	DET
ijassa-1597	66	16	conditions	condition	NOUN
ijassa-1597	66	17	above	above	ADV
ijassa-1597	66	18	.	.	PUNCT
ijassa-1597	67	1	one	one	NUM
ijassa-1597	67	2	schedule	schedule	NOUN
ijassa-1597	67	3	π	π	NOUN
ijassa-1597	67	4	can	can	AUX
ijassa-1597	67	5	be	be	AUX
ijassa-1597	67	6	feasible	feasible	ADJ
ijassa-1597	67	7	for	for	ADP
ijassa-1597	67	8	a	a	DET
ijassa-1597	67	9	number	number	NOUN
ijassa-1597	67	10	of	of	ADP
ijassa-1597	67	11	instances	instance	NOUN
ijassa-1597	67	12	with	with	ADP
ijassa-1597	67	13	the	the	DET
ijassa-1597	67	14	same	same	ADJ
ijassa-1597	67	15	precedence	precedence	NOUN
ijassa-1597	67	16	graphs	graph	NOUN
ijassa-1597	67	17	.	.	PUNCT
ijassa-1597	68	1	as	as	SCONJ
ijassa-1597	68	2	is	be	AUX
ijassa-1597	68	3	usually	usually	ADV
ijassa-1597	68	4	denoted	denote	VERB
ijassa-1597	68	5	in	in	ADP
ijassa-1597	68	6	scheduling	scheduling	NOUN
ijassa-1597	68	7	theory	theory	NOUN
ijassa-1597	68	8	,	,	PUNCT
ijassa-1597	68	9	we	we	PRON
ijassa-1597	68	10	will	will	AUX
ijassa-1597	68	11	denote	denote	VERB
ijassa-1597	68	12	makespane	makespane	NOUN
ijassa-1597	68	13	by	by	ADP
ijassa-1597	68	14	cmax(π	cmax(π	PROPN
ijassa-1597	68	15	):	):	PUNCT
ijassa-1597	68	16	cmax(π	cmax(π	PROPN
ijassa-1597	68	17	)	)	PUNCT
ijassa-1597	68	18	=	=	SYM
ijassa-1597	68	19	max	max	PROPN
ijassa-1597	68	20	j∈n	j∈n	PROPN
ijassa-1597	68	21	cj(π	cj(π	PROPN
ijassa-1597	68	22	)	)	PUNCT
ijassa-1597	68	23	.	.	PUNCT
ijassa-1597	69	1	a	a	DET
ijassa-1597	69	2	schedule	schedule	NOUN
ijassa-1597	69	3	π∗	π∗	NOUN
ijassa-1597	69	4	is	be	AUX
ijassa-1597	69	5	called	call	VERB
ijassa-1597	69	6	an	an	DET
ijassa-1597	69	7	optimal	optimal	ADJ
ijassa-1597	69	8	schedule	schedule	NOUN
ijassa-1597	69	9	for	for	ADP
ijassa-1597	69	10	an	an	DET
ijassa-1597	69	11	instance	instance	NOUN
ijassa-1597	69	12	a	a	PRON
ijassa-1597	69	13	of	of	ADP
ijassa-1597	69	14	the	the	DET
ijassa-1597	69	15	problem	problem	NOUN
ijassa-1597	69	16	p2	p2	NOUN
ijassa-1597	69	17	|	|	ADV
ijassa-1597	69	18	prec	prec	X
ijassa-1597	69	19	,	,	PUNCT
ijassa-1597	69	20	pj	pj	PROPN
ijassa-1597	69	21	∈	∈	PROPN
ijassa-1597	69	22	{	{	PUNCT
ijassa-1597	69	23	1	1	NUM
ijassa-1597	69	24	,	,	PUNCT
ijassa-1597	69	25	2	2	NUM
ijassa-1597	69	26	}	}	PUNCT
ijassa-1597	69	27	|	|	ADV
ijassa-1597	69	28	cmax	cmax	VERB
ijassa-1597	69	29	if	if	SCONJ
ijassa-1597	69	30	cmax(π	cmax(π	PROPN
ijassa-1597	69	31	∗	∗	NOUN
ijassa-1597	69	32	)	)	PUNCT
ijassa-1597	69	33	≤	≤	NUM
ijassa-1597	69	34	cmax(π	cmax(π	PROPN
ijassa-1597	69	35	)	)	PUNCT
ijassa-1597	69	36	for	for	ADP
ijassa-1597	69	37	each	each	DET
ijassa-1597	69	38	feasible	feasible	ADJ
ijassa-1597	69	39	π	π	PROPN
ijassa-1597	69	40	.	.	PUNCT
ijassa-1597	70	1	as	as	SCONJ
ijassa-1597	70	2	indicated	indicate	VERB
ijassa-1597	70	3	[	[	X
ijassa-1597	70	4	9	9	NUM
ijassa-1597	70	5	]	]	PUNCT
ijassa-1597	70	6	,	,	PUNCT
ijassa-1597	70	7	the	the	DET
ijassa-1597	70	8	problem	problem	NOUN
ijassa-1597	70	9	p2	p2	VERB
ijassa-1597	70	10	|	|	ADV
ijassa-1597	70	11	prec	prec	X
ijassa-1597	70	12	,	,	PUNCT
ijassa-1597	70	13	pj	pj	PROPN
ijassa-1597	70	14	∈	∈	PROPN
ijassa-1597	70	15	{	{	PUNCT
ijassa-1597	70	16	1	1	NUM
ijassa-1597	70	17	,	,	PUNCT
ijassa-1597	70	18	2	2	NUM
ijassa-1597	70	19	}	}	PUNCT
ijassa-1597	70	20	|	|	ADV
ijassa-1597	70	21	cmax	cmax	NOUN
ijassa-1597	70	22	is	be	AUX
ijassa-1597	70	23	np	np	INTJ
ijassa-1597	70	24	-	-	NOUN
ijassa-1597	70	25	complete	complete	ADJ
ijassa-1597	70	26	with	with	ADP
ijassa-1597	70	27	respect	respect	NOUN
ijassa-1597	70	28	to	to	ADP
ijassa-1597	70	29	the	the	DET
ijassa-1597	70	30	width	width	NOUN
ijassa-1597	70	31	of	of	ADP
ijassa-1597	70	32	the	the	DET
ijassa-1597	70	33	partial	partial	ADJ
ijassa-1597	70	34	order	order	NOUN
ijassa-1597	70	35	.	.	PUNCT
ijassa-1597	71	1	therefore	therefore	ADV
ijassa-1597	71	2	,	,	PUNCT
ijassa-1597	71	3	this	this	PRON
ijassa-1597	71	4	is	be	AUX
ijassa-1597	71	5	the	the	DET
ijassa-1597	71	6	reason	reason	NOUN
ijassa-1597	71	7	why	why	SCONJ
ijassa-1597	71	8	approximate	approximate	ADJ
ijassa-1597	71	9	solutions	solution	NOUN
ijassa-1597	71	10	of	of	ADP
ijassa-1597	71	11	the	the	DET
ijassa-1597	71	12	problem	problem	NOUN
ijassa-1597	71	13	are	be	AUX
ijassa-1597	71	14	considered	consider	VERB
ijassa-1597	71	15	.	.	PUNCT
ijassa-1597	72	1	3	3	X
ijassa-1597	72	2	.	.	X
ijassa-1597	72	3	metric	metric	ADJ
ijassa-1597	72	4	over	over	ADP
ijassa-1597	72	5	the	the	DET
ijassa-1597	72	6	set	set	NOUN
ijassa-1597	72	7	of	of	ADP
ijassa-1597	72	8	instances	instance	NOUN
ijassa-1597	72	9	of	of	ADP
ijassa-1597	72	10	the	the	DET
ijassa-1597	72	11	problem	problem	NOUN
ijassa-1597	72	12	p2	p2	PROPN
ijassa-1597	72	13	|	|	ADV
ijassa-1597	72	14	prec	prec	X
ijassa-1597	72	15	,	,	PUNCT
ijassa-1597	72	16	pj	pj	PROPN
ijassa-1597	72	17	∈	∈	PROPN
ijassa-1597	72	18	{	{	PUNCT
ijassa-1597	72	19	1	1	NUM
ijassa-1597	72	20	,	,	PUNCT
ijassa-1597	72	21	2	2	NUM
ijassa-1597	72	22	}	}	PUNCT
ijassa-1597	72	23	|	|	ADV
ijassa-1597	72	24	cmax	cmax	NOUN
ijassa-1597	72	25	we	we	PRON
ijassa-1597	72	26	consider	consider	VERB
ijassa-1597	72	27	the	the	DET
ijassa-1597	72	28	metric	metric	ADJ
ijassa-1597	72	29	approach	approach	NOUN
ijassa-1597	72	30	application	application	NOUN
ijassa-1597	72	31	for	for	ADP
ijassa-1597	72	32	the	the	DET
ijassa-1597	72	33	problem	problem	NOUN
ijassa-1597	72	34	p2	p2	PROPN
ijassa-1597	72	35	|	|	ADV
ijassa-1597	72	36	prec	prec	X
ijassa-1597	72	37	,	,	PUNCT
ijassa-1597	72	38	pj	pj	PROPN
ijassa-1597	72	39	∈	∈	PROPN
ijassa-1597	72	40	{	{	PUNCT
ijassa-1597	72	41	1	1	NUM
ijassa-1597	72	42	,	,	PUNCT
ijassa-1597	72	43	2	2	NUM
ijassa-1597	72	44	}	}	PUNCT
ijassa-1597	72	45	|	|	ADV
ijassa-1597	72	46	cmax	cmax	NOUN
ijassa-1597	72	47	.	.	PUNCT
ijassa-1597	73	1	let	let	VERB
ijassa-1597	73	2	π∗	π∗	PROPN
ijassa-1597	73	3	a	a	DET
ijassa-1597	73	4	be	be	AUX
ijassa-1597	73	5	an	an	DET
ijassa-1597	73	6	optimal	optimal	ADJ
ijassa-1597	73	7	solution	solution	NOUN
ijassa-1597	73	8	of	of	ADP
ijassa-1597	73	9	instance	instance	NOUN
ijassa-1597	73	10	a	a	PRON
ijassa-1597	73	11	,	,	PUNCT
ijassa-1597	73	12	and	and	CCONJ
ijassa-1597	73	13	π∗	π∗	PROPN
ijassa-1597	73	14	b	b	PROPN
ijassa-1597	73	15	is	be	AUX
ijassa-1597	73	16	that	that	PRON
ijassa-1597	73	17	of	of	ADP
ijassa-1597	73	18	instance	instance	NOUN
ijassa-1597	73	19	b.	b.	PROPN
ijassa-1597	73	20	using	use	VERB
ijassa-1597	73	21	cmax	cmax	NOUN
ijassa-1597	73	22	instead	instead	ADV
ijassa-1597	73	23	of	of	ADP
ijassa-1597	73	24	f	f	PROPN
ijassa-1597	73	25	into	into	ADP
ijassa-1597	73	26	(	(	PUNCT
ijassa-1597	73	27	1.1	1.1	NUM
ijassa-1597	73	28	)	)	PUNCT
ijassa-1597	73	29	gives	give	VERB
ijassa-1597	73	30	us	we	PRON
ijassa-1597	73	31	,	,	PUNCT
ijassa-1597	73	32	the	the	DET
ijassa-1597	73	33	following	follow	VERB
ijassa-1597	73	34	:	:	PUNCT
ijassa-1597	73	35	ρ(a	ρ(a	PROPN
ijassa-1597	73	36	,	,	PUNCT
ijassa-1597	73	37	b	b	NOUN
ijassa-1597	73	38	)	)	PUNCT
ijassa-1597	73	39	≥	≥	NOUN
ijassa-1597	73	40	ca	can	AUX
ijassa-1597	73	41	max(π	max(π	PROPN
ijassa-1597	73	42	∗	∗	VERB
ijassa-1597	73	43	b)−	b)−	PROPN
ijassa-1597	73	44	ca	can	AUX
ijassa-1597	73	45	max(π	max(π	PROPN
ijassa-1597	73	46	∗	∗	NOUN
ijassa-1597	73	47	a	a	PRON
ijassa-1597	73	48	)	)	PUNCT
ijassa-1597	73	49	.	.	PUNCT
ijassa-1597	74	1	(	(	PUNCT
ijassa-1597	74	2	3.2	3.2	NUM
ijassa-1597	74	3	)	)	PUNCT
ijassa-1597	74	4	there	there	PRON
ijassa-1597	74	5	is	be	VERB
ijassa-1597	74	6	a	a	DET
ijassa-1597	74	7	metric	metric	NOUN
ijassa-1597	74	8	for	for	ADP
ijassa-1597	74	9	the	the	DET
ijassa-1597	74	10	problem	problem	NOUN
ijassa-1597	74	11	p2	p2	VERB
ijassa-1597	75	1	|	|	ADV
ijassa-1597	75	2	pj	pj	PROPN
ijassa-1597	75	3	|	|	ADV
ijassa-1597	75	4	cmax	cmax	VERB
ijassa-1597	75	5	[	[	X
ijassa-1597	75	6	3	3	NUM
ijassa-1597	75	7	]	]	X
ijassa-1597	75	8	:	:	PUNCT
ijassa-1597	75	9	ρ(a	ρ(a	PROPN
ijassa-1597	75	10	,	,	PUNCT
ijassa-1597	75	11	b	b	NOUN
ijassa-1597	75	12	)	)	PUNCT
ijassa-1597	75	13	=	=	SYM
ijassa-1597	75	14	∑	∑	PUNCT
ijassa-1597	75	15	j∈n	j∈n	NOUN
ijassa-1597	76	1	|paj	|paj	NOUN
ijassa-1597	76	2	−	−	PROPN
ijassa-1597	76	3	pbj	pbj	PROPN
ijassa-1597	76	4	|	|	ADV
ijassa-1597	76	5	,	,	PUNCT
ijassa-1597	76	6	(	(	PUNCT
ijassa-1597	76	7	3.3	3.3	NUM
ijassa-1597	76	8	)	)	PUNCT
ijassa-1597	76	9	where	where	SCONJ
ijassa-1597	76	10	instances	instance	NOUN
ijassa-1597	76	11	a	a	PRON
ijassa-1597	76	12	and	and	CCONJ
ijassa-1597	76	13	b	b	NOUN
ijassa-1597	76	14	have	have	VERB
ijassa-1597	76	15	the	the	DET
ijassa-1597	76	16	same	same	ADJ
ijassa-1597	76	17	number	number	NOUN
ijassa-1597	76	18	of	of	ADP
ijassa-1597	76	19	jobs	job	NOUN
ijassa-1597	76	20	n.	n.	VERB
ijassa-1597	76	21	this	this	PRON
ijassa-1597	76	22	is	be	AUX
ijassa-1597	76	23	minkowski	minkowski	ADJ
ijassa-1597	76	24	of	of	ADP
ijassa-1597	76	25	order	order	NOUN
ijassa-1597	76	26	1	1	X
ijassa-1597	76	27	.	.	PUNCT
ijassa-1597	77	1	in	in	ADP
ijassa-1597	77	2	case	case	NOUN
ijassa-1597	77	3	of	of	ADP
ijassa-1597	77	4	the	the	DET
ijassa-1597	77	5	problem	problem	NOUN
ijassa-1597	77	6	p2	p2	PROPN
ijassa-1597	77	7	|	|	ADV
ijassa-1597	77	8	prec	prec	X
ijassa-1597	77	9	,	,	PUNCT
ijassa-1597	77	10	pj	pj	PROPN
ijassa-1597	77	11	∈	∈	PROPN
ijassa-1597	77	12	{	{	PUNCT
ijassa-1597	77	13	1	1	NUM
ijassa-1597	77	14	,	,	PUNCT
ijassa-1597	77	15	2	2	NUM
ijassa-1597	77	16	}	}	PUNCT
ijassa-1597	77	17	|	|	ADV
ijassa-1597	77	18	cmax	cmax	VERB
ijassa-1597	77	19	there	there	PRON
ijassa-1597	77	20	is	be	VERB
ijassa-1597	77	21	no	no	DET
ijassa-1597	77	22	known	know	VERB
ijassa-1597	77	23	metric	metric	NOUN
ijassa-1597	77	24	for	for	ADP
ijassa-1597	77	25	the	the	DET
ijassa-1597	77	26	problem	problem	NOUN
ijassa-1597	77	27	with	with	ADP
ijassa-1597	77	28	partial	partial	ADJ
ijassa-1597	77	29	ordered	order	VERB
ijassa-1597	77	30	over	over	ADP
ijassa-1597	77	31	n	n	PROPN
ijassa-1597	77	32	.	.	PUNCT
ijassa-1597	78	1	so	so	ADV
ijassa-1597	78	2	we	we	PRON
ijassa-1597	78	3	believe	believe	VERB
ijassa-1597	78	4	that	that	SCONJ
ijassa-1597	78	5	for	for	ADP
ijassa-1597	78	6	pairs	pair	NOUN
ijassa-1597	78	7	of	of	ADP
ijassa-1597	78	8	instances	instance	NOUN
ijassa-1597	78	9	a	a	PRON
ijassa-1597	78	10	and	and	CCONJ
ijassa-1597	78	11	b	b	NOUN
ijassa-1597	78	12	that	that	PRON
ijassa-1597	78	13	do	do	AUX
ijassa-1597	78	14	not	not	PART
ijassa-1597	78	15	differ	differ	VERB
ijassa-1597	78	16	otherwise	otherwise	ADV
ijassa-1597	78	17	than	than	SCONJ
ijassa-1597	78	18	a	a	DET
ijassa-1597	78	19	partial	partial	ADJ
ijassa-1597	78	20	order	order	NOUN
ijassa-1597	78	21	over	over	ADP
ijassa-1597	78	22	n	n	CCONJ
ijassa-1597	78	23	the	the	DET
ijassa-1597	78	24	metric	metric	NOUN
ijassa-1597	78	25	takes	take	VERB
ijassa-1597	78	26	the	the	DET
ijassa-1597	78	27	minimal	minimal	ADJ
ijassa-1597	78	28	solution	solution	NOUN
ijassa-1597	78	29	only	only	ADV
ijassa-1597	78	30	when	when	SCONJ
ijassa-1597	78	31	the	the	DET
ijassa-1597	78	32	partial	partial	ADJ
ijassa-1597	78	33	order	order	NOUN
ijassa-1597	78	34	of	of	ADP
ijassa-1597	78	35	both	both	CCONJ
ijassa-1597	78	36	a	a	PRON
ijassa-1597	78	37	and	and	CCONJ
ijassa-1597	78	38	b	b	NOUN
ijassa-1597	78	39	is	be	AUX
ijassa-1597	78	40	the	the	DET
ijassa-1597	78	41	same	same	ADJ
ijassa-1597	78	42	.	.	PUNCT
ijassa-1597	79	1	lemma	lemma	PROPN
ijassa-1597	79	2	3.1	3.1	NUM
ijassa-1597	79	3	:	:	PUNCT
ijassa-1597	79	4	let	let	VERB
ijassa-1597	79	5	a	a	PRON
ijassa-1597	79	6	and	and	CCONJ
ijassa-1597	79	7	b	b	NOUN
ijassa-1597	79	8	be	be	AUX
ijassa-1597	79	9	instances	instance	NOUN
ijassa-1597	79	10	of	of	ADP
ijassa-1597	79	11	the	the	DET
ijassa-1597	79	12	problem	problem	NOUN
ijassa-1597	79	13	p2	p2	PROPN
ijassa-1597	79	14	|	|	ADV
ijassa-1597	79	15	prec	prec	X
ijassa-1597	79	16	,	,	PUNCT
ijassa-1597	79	17	pj	pj	PROPN
ijassa-1597	79	18	∈	∈	PROPN
ijassa-1597	79	19	{	{	PUNCT
ijassa-1597	79	20	1	1	NUM
ijassa-1597	79	21	,	,	PUNCT
ijassa-1597	79	22	2	2	NUM
ijassa-1597	79	23	}	}	PUNCT
ijassa-1597	79	24	|	|	ADV
ijassa-1597	79	25	cmax	cmax	VERB
ijassa-1597	79	26	,	,	PUNCT
ijassa-1597	79	27	and	and	CCONJ
ijassa-1597	79	28	π∗	π∗	PROPN
ijassa-1597	79	29	a	a	PRON
ijassa-1597	79	30	,	,	PUNCT
ijassa-1597	79	31	π∗	π∗	PROPN
ijassa-1597	79	32	b	b	PROPN
ijassa-1597	79	33	are	be	AUX
ijassa-1597	79	34	optimal	optimal	ADJ
ijassa-1597	79	35	solutions	solution	NOUN
ijassa-1597	79	36	of	of	ADP
ijassa-1597	79	37	a	a	DET
ijassa-1597	79	38	,	,	PUNCT
ijassa-1597	79	39	b	b	NOUN
ijassa-1597	79	40	corresponding	corresponding	NOUN
ijassa-1597	79	41	.	.	PUNCT
ijassa-1597	80	1	then	then	ADV
ijassa-1597	80	2	:	:	PUNCT
ijassa-1597	80	3	ca	can	AUX
ijassa-1597	80	4	max(π	max(π	PROPN
ijassa-1597	80	5	∗	∗	VERB
ijassa-1597	80	6	b)−	b)−	PROPN
ijassa-1597	80	7	ca	can	AUX
ijassa-1597	80	8	max(π	max(π	PROPN
ijassa-1597	80	9	∗	∗	X
ijassa-1597	80	10	a	a	PRON
ijassa-1597	80	11	)	)	PUNCT
ijassa-1597	80	12	≤	≤	NOUN
ijassa-1597	80	13	∑	∑	PUNCT
ijassa-1597	80	14	j∈n	j∈n	VERB
ijassa-1597	80	15	|paj	|paj	NOUN
ijassa-1597	80	16	−	−	PROPN
ijassa-1597	80	17	pbj	pbj	PROPN
ijassa-1597	81	1	|	|	INTJ
ijassa-1597	81	2	.	.	PUNCT
ijassa-1597	82	1	(	(	PUNCT
ijassa-1597	82	2	3.4	3.4	NUM
ijassa-1597	82	3	)	)	PUNCT
ijassa-1597	82	4	copyright	copyright	NOUN
ijassa-1597	82	5	©	©	PROPN
ijassa-1597	82	6	2024	2024	NUM
ijassa-1597	82	7	assa	assa	NOUN
ijassa-1597	82	8	.	.	PUNCT
ijassa-1597	83	1	adv	adv	PROPN
ijassa-1597	83	2	syst	syst	PROPN
ijassa-1597	83	3	sci	sci	PROPN
ijassa-1597	83	4	appl	appl	PROPN
ijassa-1597	83	5	(	(	PUNCT
ijassa-1597	83	6	2024	2024	NUM
ijassa-1597	83	7	)	)	PUNCT
ijassa-1597	83	8	practical	practical	ADJ
ijassa-1597	83	9	applicability	applicability	NOUN
ijassa-1597	83	10	of	of	ADP
ijassa-1597	83	11	the	the	DET
ijassa-1597	83	12	metric	metric	ADJ
ijassa-1597	83	13	approach	approach	NOUN
ijassa-1597	83	14	...	...	PUNCT
ijassa-1597	83	15	97	97	NUM
ijassa-1597	83	16	proof	proof	NOUN
ijassa-1597	83	17	let	let	VERB
ijassa-1597	83	18	’s	’s	NOUN
ijassa-1597	83	19	consider	consider	VERB
ijassa-1597	83	20	the	the	DET
ijassa-1597	83	21	following	follow	VERB
ijassa-1597	83	22	difference	difference	NOUN
ijassa-1597	83	23	:	:	PUNCT
ijassa-1597	83	24	|ca	|ca	PUNCT
ijassa-1597	83	25	max(π)−	max(π)−	PROPN
ijassa-1597	83	26	cb	cb	PROPN
ijassa-1597	83	27	max(π)|	max(π)|	PROPN
ijassa-1597	83	28	(	(	PUNCT
ijassa-1597	83	29	3.5	3.5	NUM
ijassa-1597	83	30	)	)	PUNCT
ijassa-1597	83	31	for	for	ADP
ijassa-1597	83	32	any	any	DET
ijassa-1597	83	33	a	a	DET
ijassa-1597	83	34	,	,	PUNCT
ijassa-1597	83	35	b	b	NOUN
ijassa-1597	83	36	,	,	PUNCT
ijassa-1597	83	37	π	π	PROPN
ijassa-1597	83	38	and	and	CCONJ
ijassa-1597	83	39	give	give	VERB
ijassa-1597	83	40	an	an	DET
ijassa-1597	83	41	upper	upper	ADJ
ijassa-1597	83	42	bound	bound	NOUN
ijassa-1597	83	43	of	of	ADP
ijassa-1597	83	44	this	this	PRON
ijassa-1597	83	45	.	.	PUNCT
ijassa-1597	84	1	now	now	ADV
ijassa-1597	84	2	we	we	PRON
ijassa-1597	84	3	prove	prove	VERB
ijassa-1597	84	4	that	that	SCONJ
ijassa-1597	84	5	the	the	DET
ijassa-1597	84	6	maximum	maximum	NOUN
ijassa-1597	84	7	of	of	ADP
ijassa-1597	84	8	(	(	PUNCT
ijassa-1597	84	9	3.5	3.5	NUM
ijassa-1597	84	10	)	)	PUNCT
ijassa-1597	84	11	reaches	reach	VERB
ijassa-1597	84	12	on	on	ADP
ijassa-1597	84	13	π	π	PROPN
ijassa-1597	84	14	on	on	ADP
ijassa-1597	84	15	which	which	PRON
ijassa-1597	84	16	every	every	DET
ijassa-1597	84	17	job	job	NOUN
ijassa-1597	84	18	is	be	AUX
ijassa-1597	84	19	processed	process	VERB
ijassa-1597	84	20	on	on	ADP
ijassa-1597	84	21	only	only	ADV
ijassa-1597	84	22	one	one	NUM
ijassa-1597	84	23	machine	machine	NOUN
ijassa-1597	84	24	,	,	PUNCT
ijassa-1597	84	25	so	so	SCONJ
ijassa-1597	84	26	the	the	DET
ijassa-1597	84	27	other	other	ADJ
ijassa-1597	84	28	one	one	NUM
ijassa-1597	84	29	processes	process	VERB
ijassa-1597	84	30	no	no	DET
ijassa-1597	84	31	one	one	NUM
ijassa-1597	84	32	job	job	NOUN
ijassa-1597	84	33	.	.	PUNCT
ijassa-1597	85	1	obviously	obviously	ADV
ijassa-1597	85	2	,	,	PUNCT
ijassa-1597	85	3	the	the	DET
ijassa-1597	85	4	decrease	decrease	NOUN
ijassa-1597	85	5	value	value	NOUN
ijassa-1597	85	6	of	of	ADP
ijassa-1597	85	7	the	the	DET
ijassa-1597	85	8	target	target	NOUN
ijassa-1597	85	9	function	function	NOUN
ijassa-1597	85	10	value	value	NOUN
ijassa-1597	85	11	is	be	AUX
ijassa-1597	85	12	not	not	PART
ijassa-1597	85	13	greater	great	ADJ
ijassa-1597	85	14	than	than	ADP
ijassa-1597	85	15	the	the	DET
ijassa-1597	85	16	difference	difference	NOUN
ijassa-1597	85	17	between	between	ADP
ijassa-1597	85	18	sums	sum	NOUN
ijassa-1597	85	19	of	of	ADP
ijassa-1597	85	20	processing	processing	NOUN
ijassa-1597	85	21	times	time	NOUN
ijassa-1597	85	22	of	of	ADP
ijassa-1597	85	23	all	all	DET
ijassa-1597	85	24	jobs	job	NOUN
ijassa-1597	85	25	in	in	ADP
ijassa-1597	85	26	terms	term	NOUN
ijassa-1597	85	27	of	of	ADP
ijassa-1597	85	28	each	each	DET
ijassa-1597	85	29	instances	instance	NOUN
ijassa-1597	85	30	a	a	PRON
ijassa-1597	85	31	and	and	CCONJ
ijassa-1597	85	32	b	b	NOUN
ijassa-1597	85	33	:	:	PUNCT
ijassa-1597	85	34	|ca	|ca	PROPN
ijassa-1597	85	35	max(π)−	max(π)−	PROPN
ijassa-1597	85	36	cb	cb	PROPN
ijassa-1597	85	37	max(π)|	max(π)|	PROPN
ijassa-1597	85	38	≤	≤	PROPN
ijassa-1597	85	39	∣∣∣∣∣∑	∣∣∣∣∣∑	PROPN
ijassa-1597	85	40	j∈n	j∈n	NOUN
ijassa-1597	85	41	paj	paj	NOUN
ijassa-1597	85	42	−	−	PROPN
ijassa-1597	85	43	∑	∑	PROPN
ijassa-1597	85	44	j∈n	j∈n	PROPN
ijassa-1597	85	45	pbj	pbj	PROPN
ijassa-1597	85	46	∣∣∣∣∣	∣∣∣∣∣	PROPN
ijassa-1597	85	47	.	.	PUNCT
ijassa-1597	86	1	using	use	VERB
ijassa-1597	86	2	the	the	DET
ijassa-1597	86	3	following	follow	VERB
ijassa-1597	86	4	commonly	commonly	ADV
ijassa-1597	86	5	known	know	VERB
ijassa-1597	86	6	inequality	inequality	NOUN
ijassa-1597	86	7	:	:	PUNCT
ijassa-1597	86	8	|a+	|a+	NOUN
ijassa-1597	86	9	b|	b|	NOUN
ijassa-1597	86	10	≤	≤	NUM
ijassa-1597	86	11	|a|+	|a|+	NOUN
ijassa-1597	86	12	|b|	|b|	NUM
ijassa-1597	86	13	,	,	PUNCT
ijassa-1597	86	14	we	we	PRON
ijassa-1597	86	15	obtain	obtain	VERB
ijassa-1597	86	16	|ca	|ca	PUNCT
ijassa-1597	86	17	max(π)−	max(π)−	PROPN
ijassa-1597	86	18	cb	cb	PROPN
ijassa-1597	86	19	max(π)|	max(π)|	PROPN
ijassa-1597	86	20	≤	≤	PROPN
ijassa-1597	86	21	∣∣∣∣∣∑	∣∣∣∣∣∑	PROPN
ijassa-1597	86	22	j∈n	j∈n	NOUN
ijassa-1597	86	23	paj	paj	NOUN
ijassa-1597	86	24	−	−	PROPN
ijassa-1597	87	1	∑	∑	PROPN
ijassa-1597	87	2	j∈n	j∈n	PROPN
ijassa-1597	87	3	pbj	pbj	PROPN
ijassa-1597	88	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ijassa-1597	88	2	≤	≤	ADV
ijassa-1597	88	3	∑	∑	PUNCT
ijassa-1597	88	4	j∈n	j∈n	VERB
ijassa-1597	88	5	|paj	|paj	NOUN
ijassa-1597	88	6	−	−	PROPN
ijassa-1597	88	7	pbj	pbj	PROPN
ijassa-1597	89	1	|	|	INTJ
ijassa-1597	89	2	.	.	PUNCT
ijassa-1597	90	1	(	(	PUNCT
ijassa-1597	90	2	3.6	3.6	NUM
ijassa-1597	90	3	)	)	PUNCT
ijassa-1597	90	4	finally	finally	ADV
ijassa-1597	90	5	,	,	PUNCT
ijassa-1597	90	6	using	use	VERB
ijassa-1597	90	7	(	(	PUNCT
ijassa-1597	90	8	3.6	3.6	NUM
ijassa-1597	90	9	)	)	PUNCT
ijassa-1597	90	10	,	,	PUNCT
ijassa-1597	90	11	we	we	PRON
ijassa-1597	90	12	get	get	VERB
ijassa-1597	90	13	ca	can	AUX
ijassa-1597	90	14	max(π	max(π	PROPN
ijassa-1597	90	15	∗	∗	NOUN
ijassa-1597	90	16	b)−	b)−	PROPN
ijassa-1597	91	1	ca	can	AUX
ijassa-1597	91	2	max(π	max(π	PROPN
ijassa-1597	91	3	∗	∗	NOUN
ijassa-1597	91	4	a	a	NOUN
ijassa-1597	91	5	)	)	PUNCT
ijassa-1597	91	6	=	=	SYM
ijassa-1597	92	1	=	=	PUNCT
ijassa-1597	92	2	(	(	PUNCT
ijassa-1597	92	3	ca	can	AUX
ijassa-1597	92	4	max(π	max(π	PROPN
ijassa-1597	92	5	∗	∗	VERB
ijassa-1597	92	6	b)−	b)−	PROPN
ijassa-1597	92	7	cb	cb	NOUN
ijassa-1597	92	8	max(π	max(π	PROPN
ijassa-1597	92	9	∗	∗	NOUN
ijassa-1597	92	10	b	b	NOUN
ijassa-1597	92	11	)	)	PUNCT
ijassa-1597	92	12	)	)	PUNCT
ijassa-1597	93	1	+	+	CCONJ
ijassa-1597	93	2	(	(	PUNCT
ijassa-1597	93	3	cb	cb	PROPN
ijassa-1597	93	4	max(π	max(π	PROPN
ijassa-1597	93	5	∗	∗	VERB
ijassa-1597	93	6	b)−	b)−	PROPN
ijassa-1597	93	7	cb	cb	NOUN
ijassa-1597	93	8	max(π	max(π	PROPN
ijassa-1597	93	9	∗	∗	VERB
ijassa-1597	93	10	a	a	NOUN
ijassa-1597	93	11	)	)	PUNCT
ijassa-1597	93	12	)	)	PUNCT
ijassa-1597	94	1	+	+	CCONJ
ijassa-1597	94	2	(	(	PUNCT
ijassa-1597	94	3	cb	cb	PROPN
ijassa-1597	94	4	max(π	max(π	PROPN
ijassa-1597	94	5	∗	∗	VERB
ijassa-1597	94	6	a)−	a)−	ADV
ijassa-1597	94	7	ca	can	AUX
ijassa-1597	94	8	max(π	max(π	PROPN
ijassa-1597	94	9	∗	∗	X
ijassa-1597	94	10	a	a	NOUN
ijassa-1597	94	11	)	)	PUNCT
ijassa-1597	94	12	)	)	PUNCT
ijassa-1597	94	13	≤	≤	ADJ
ijassa-1597	94	14	≤	≤	NUM
ijassa-1597	94	15	(	(	PUNCT
ijassa-1597	94	16	cb	cb	PROPN
ijassa-1597	94	17	max(π	max(π	PROPN
ijassa-1597	94	18	∗	∗	VERB
ijassa-1597	94	19	b)−	b)−	PROPN
ijassa-1597	94	20	cb	cb	NOUN
ijassa-1597	94	21	max(π	max(π	PROPN
ijassa-1597	94	22	∗	∗	VERB
ijassa-1597	94	23	a	a	NOUN
ijassa-1597	94	24	)	)	PUNCT
ijassa-1597	94	25	)	)	PUNCT
ijassa-1597	95	1	+	+	CCONJ
ijassa-1597	95	2	2	2	NUM
ijassa-1597	95	3	∑	∑	NOUN
ijassa-1597	95	4	j∈n	j∈n	VERB
ijassa-1597	95	5	|paj	|paj	NOUN
ijassa-1597	95	6	−	−	PROPN
ijassa-1597	95	7	pbj	pbj	PROPN
ijassa-1597	96	1	|	|	INTJ
ijassa-1597	96	2	.	.	PUNCT
ijassa-1597	97	1	that	that	PRON
ijassa-1597	97	2	is	is	ADV
ijassa-1597	97	3	(	(	PUNCT
ijassa-1597	97	4	ca	can	AUX
ijassa-1597	97	5	max(π	max(π	PROPN
ijassa-1597	97	6	∗	∗	VERB
ijassa-1597	97	7	b)−	b)−	PROPN
ijassa-1597	97	8	ca	can	AUX
ijassa-1597	97	9	max(π	max(π	PROPN
ijassa-1597	97	10	∗	∗	NOUN
ijassa-1597	97	11	a	a	NOUN
ijassa-1597	97	12	)	)	PUNCT
ijassa-1597	97	13	)	)	PUNCT
ijassa-1597	98	1	+	+	CCONJ
ijassa-1597	98	2	(	(	PUNCT
ijassa-1597	98	3	cb	cb	PROPN
ijassa-1597	98	4	max(π	max(π	PROPN
ijassa-1597	98	5	∗	∗	VERB
ijassa-1597	98	6	b)−	b)−	PROPN
ijassa-1597	98	7	cb	cb	NOUN
ijassa-1597	98	8	max(π	max(π	PROPN
ijassa-1597	98	9	∗	∗	VERB
ijassa-1597	98	10	a	a	NOUN
ijassa-1597	98	11	)	)	PUNCT
ijassa-1597	98	12	)	)	PUNCT
ijassa-1597	98	13	≤	≤	ADV
ijassa-1597	98	14	2	2	NUM
ijassa-1597	98	15	∑	∑	NOUN
ijassa-1597	98	16	j∈n	j∈n	VERB
ijassa-1597	98	17	|paj	|paj	NOUN
ijassa-1597	98	18	−	−	PROPN
ijassa-1597	98	19	pbj	pbj	PROPN
ijassa-1597	98	20	|	|	INTJ
ijassa-1597	98	21	.	.	PUNCT
ijassa-1597	99	1	from	from	ADP
ijassa-1597	99	2	symmetry	symmetry	NOUN
ijassa-1597	99	3	considerations	consideration	NOUN
ijassa-1597	99	4	,	,	PUNCT
ijassa-1597	99	5	we	we	PRON
ijassa-1597	99	6	finally	finally	ADV
ijassa-1597	99	7	obtain	obtain	VERB
ijassa-1597	99	8	the	the	DET
ijassa-1597	99	9	following	follow	VERB
ijassa-1597	99	10	result	result	NOUN
ijassa-1597	99	11	:	:	PUNCT
ijassa-1597	99	12	ca	can	AUX
ijassa-1597	99	13	max(π	max(π	PROPN
ijassa-1597	99	14	∗	∗	VERB
ijassa-1597	99	15	b)−	b)−	PROPN
ijassa-1597	99	16	ca	can	AUX
ijassa-1597	99	17	max(π	max(π	PROPN
ijassa-1597	99	18	∗	∗	X
ijassa-1597	99	19	a	a	PRON
ijassa-1597	99	20	)	)	PUNCT
ijassa-1597	99	21	≤	≤	NOUN
ijassa-1597	99	22	∑	∑	PUNCT
ijassa-1597	99	23	j∈n	j∈n	VERB
ijassa-1597	99	24	|paj	|paj	NOUN
ijassa-1597	99	25	−	−	PROPN
ijassa-1597	99	26	pbj	pbj	PROPN
ijassa-1597	99	27	|	|	INTJ
ijassa-1597	99	28	.	.	PUNCT
ijassa-1597	100	1	theorem	theorem	VERB
ijassa-1597	100	2	3.1	3.1	NUM
ijassa-1597	100	3	:	:	PUNCT
ijassa-1597	100	4	the	the	DET
ijassa-1597	100	5	function	function	NOUN
ijassa-1597	100	6	ρ	ρ	NOUN
ijassa-1597	100	7	from	from	ADP
ijassa-1597	100	8	(	(	PUNCT
ijassa-1597	100	9	3.3	3.3	NUM
ijassa-1597	100	10	)	)	PUNCT
ijassa-1597	100	11	is	be	AUX
ijassa-1597	100	12	a	a	DET
ijassa-1597	100	13	metric	metric	NOUN
ijassa-1597	100	14	over	over	ADP
ijassa-1597	100	15	the	the	DET
ijassa-1597	100	16	sets	set	NOUN
ijassa-1597	100	17	of	of	ADP
ijassa-1597	100	18	instances	instance	NOUN
ijassa-1597	100	19	of	of	ADP
ijassa-1597	100	20	the	the	DET
ijassa-1597	100	21	problem	problem	NOUN
ijassa-1597	100	22	p2	p2	PROPN
ijassa-1597	100	23	|	|	ADV
ijassa-1597	100	24	prec	prec	X
ijassa-1597	100	25	,	,	PUNCT
ijassa-1597	100	26	pj	pj	PROPN
ijassa-1597	100	27	∈	∈	PROPN
ijassa-1597	100	28	{	{	PUNCT
ijassa-1597	100	29	1	1	NUM
ijassa-1597	100	30	,	,	PUNCT
ijassa-1597	100	31	2	2	NUM
ijassa-1597	100	32	}	}	PUNCT
ijassa-1597	100	33	|	|	ADV
ijassa-1597	100	34	cmax	cmax	NOUN
ijassa-1597	100	35	.	.	PUNCT
ijassa-1597	101	1	proof	proof	NOUN
ijassa-1597	101	2	that	that	SCONJ
ijassa-1597	101	3	(	(	PUNCT
ijassa-1597	101	4	3.4	3.4	NUM
ijassa-1597	101	5	)	)	PUNCT
ijassa-1597	101	6	corresponds	correspond	VERB
ijassa-1597	101	7	to	to	ADP
ijassa-1597	101	8	the	the	DET
ijassa-1597	101	9	axioms	axiom	NOUN
ijassa-1597	101	10	of	of	ADP
ijassa-1597	101	11	the	the	DET
ijassa-1597	101	12	metric	metric	NOUN
ijassa-1597	101	13	is	be	AUX
ijassa-1597	101	14	obvious	obvious	ADJ
ijassa-1597	101	15	:	:	PUNCT
ijassa-1597	101	16	1	1	X
ijassa-1597	101	17	.	.	X
ijassa-1597	102	1	ρ(a	ρ(a	ADJ
ijassa-1597	102	2	,	,	PUNCT
ijassa-1597	102	3	b	b	NOUN
ijassa-1597	102	4	)	)	PUNCT
ijassa-1597	102	5	=	=	SYM
ijassa-1597	102	6	0	0	NUM
ijassa-1597	102	7	⇐	⇐	ADJ
ijassa-1597	102	8	⇒	⇒	PROPN
ijassa-1597	102	9	a	a	DET
ijassa-1597	102	10	=	=	SYM
ijassa-1597	102	11	b	b	NOUN
ijassa-1597	102	12	:	:	PUNCT
ijassa-1597	102	13	ρ(a	ρ(a	PROPN
ijassa-1597	102	14	,	,	PUNCT
ijassa-1597	102	15	b	b	NOUN
ijassa-1597	102	16	)	)	PUNCT
ijassa-1597	102	17	=	=	SYM
ijassa-1597	102	18	∑	∑	PUNCT
ijassa-1597	102	19	j∈n	j∈n	NOUN
ijassa-1597	102	20	|paj	|paj	NOUN
ijassa-1597	102	21	−	−	PROPN
ijassa-1597	103	1	pbj	pbj	INTJ
ijassa-1597	104	1	|	|	NOUN
ijassa-1597	104	2	=	=	NOUN
ijassa-1597	104	3	0	0	NUM
ijassa-1597	105	1	⇐	⇐	ADJ
ijassa-1597	105	2	⇒	⇒	PROPN
ijassa-1597	105	3	paj	paj	PROPN
ijassa-1597	105	4	=	=	PUNCT
ijassa-1597	105	5	pbj	pbj	PROPN
ijassa-1597	105	6	,	,	PUNCT
ijassa-1597	105	7	∀j	∀j	PROPN
ijassa-1597	105	8	∈	∈	PROPN
ijassa-1597	105	9	n.	n.	NOUN
ijassa-1597	105	10	copyright	copyright	NOUN
ijassa-1597	105	11	©	©	PROPN
ijassa-1597	105	12	2024	2024	NUM
ijassa-1597	105	13	assa	assa	NOUN
ijassa-1597	105	14	.	.	PUNCT
ijassa-1597	106	1	adv	adv	PROPN
ijassa-1597	106	2	syst	syst	PROPN
ijassa-1597	106	3	sci	sci	PROPN
ijassa-1597	106	4	appl	appl	PROPN
ijassa-1597	106	5	(	(	PUNCT
ijassa-1597	106	6	2024	2024	NUM
ijassa-1597	106	7	)	)	PUNCT
ijassa-1597	106	8	98	98	NUM
ijassa-1597	106	9	a.	a.	NOUN
ijassa-1597	106	10	lazarev	lazarev	PROPN
ijassa-1597	106	11	,	,	PUNCT
ijassa-1597	106	12	d.	d.	PROPN
ijassa-1597	106	13	levtyuzhnikova	levtyuzhnikova	PROPN
ijassa-1597	106	14	,	,	PUNCT
ijassa-1597	106	15	i.	i.	PROPN
ijassa-1597	106	16	kudinov	kudinov	PROPN
ijassa-1597	106	17	2	2	NUM
ijassa-1597	106	18	.	.	PUNCT
ijassa-1597	107	1	ρ(a	ρ(a	ADJ
ijassa-1597	107	2	,	,	PUNCT
ijassa-1597	107	3	b	b	NOUN
ijassa-1597	107	4	)	)	PUNCT
ijassa-1597	107	5	≥	≥	NOUN
ijassa-1597	107	6	0	0	NUM
ijassa-1597	107	7	:	:	PUNCT
ijassa-1597	107	8	ρ(a	ρ(a	PROPN
ijassa-1597	107	9	,	,	PUNCT
ijassa-1597	107	10	b	b	NOUN
ijassa-1597	107	11	)	)	PUNCT
ijassa-1597	107	12	=	=	SYM
ijassa-1597	107	13	∑	∑	PUNCT
ijassa-1597	107	14	j∈n	j∈n	NOUN
ijassa-1597	107	15	|paj	|paj	NOUN
ijassa-1597	107	16	−	−	PROPN
ijassa-1597	108	1	pbj	pbj	INTJ
ijassa-1597	109	1	|	|	INTJ
ijassa-1597	109	2	≥	≥	NOUN
ijassa-1597	109	3	0	0	NUM
ijassa-1597	109	4	.	.	NOUN
ijassa-1597	110	1	3	3	NUM
ijassa-1597	110	2	.	.	X
ijassa-1597	111	1	ρ(a	ρ(a	ADJ
ijassa-1597	111	2	,	,	PUNCT
ijassa-1597	111	3	b	b	NOUN
ijassa-1597	111	4	)	)	PUNCT
ijassa-1597	111	5	=	=	SYM
ijassa-1597	111	6	ρ(b	ρ(b	NOUN
ijassa-1597	111	7	,	,	PUNCT
ijassa-1597	111	8	a	a	PRON
ijassa-1597	111	9	):	):	PUNCT
ijassa-1597	111	10	ρ(a	ρ(a	PROPN
ijassa-1597	111	11	,	,	PUNCT
ijassa-1597	111	12	b	b	NOUN
ijassa-1597	111	13	)	)	PUNCT
ijassa-1597	111	14	=	=	SYM
ijassa-1597	111	15	∑	∑	PUNCT
ijassa-1597	111	16	j∈n	j∈n	NOUN
ijassa-1597	111	17	|paj	|paj	NOUN
ijassa-1597	111	18	−	−	PROPN
ijassa-1597	111	19	pbj	pbj	INTJ
ijassa-1597	112	1	|	|	NOUN
ijassa-1597	112	2	=	=	SYM
ijassa-1597	112	3	∑	∑	PUNCT
ijassa-1597	112	4	j∈n	j∈n	NOUN
ijassa-1597	113	1	|	|	ADV
ijassa-1597	113	2	−	−	PROPN
ijassa-1597	113	3	paj	paj	PROPN
ijassa-1597	113	4	+	+	CCONJ
ijassa-1597	113	5	pbj	pbj	PROPN
ijassa-1597	113	6	|	|	PROPN
ijassa-1597	113	7	=	=	SYM
ijassa-1597	113	8	ρ(b	ρ(b	PROPN
ijassa-1597	113	9	,	,	PUNCT
ijassa-1597	113	10	a	a	PRON
ijassa-1597	113	11	)	)	PUNCT
ijassa-1597	113	12	=	=	SYM
ijassa-1597	113	13	4	4	X
ijassa-1597	113	14	.	.	X
ijassa-1597	114	1	ρ(a	ρ(a	ADJ
ijassa-1597	114	2	,	,	PUNCT
ijassa-1597	114	3	c	c	NOUN
ijassa-1597	114	4	)	)	PUNCT
ijassa-1597	114	5	≤	≤	NOUN
ijassa-1597	115	1	ρ(a	ρ(a	PROPN
ijassa-1597	115	2	,	,	PUNCT
ijassa-1597	115	3	b	b	NOUN
ijassa-1597	115	4	)	)	PUNCT
ijassa-1597	115	5	+	+	PUNCT
ijassa-1597	115	6	ρ(b	ρ(b	NOUN
ijassa-1597	115	7	,	,	PUNCT
ijassa-1597	115	8	c	c	NOUN
ijassa-1597	115	9	):	):	PUNCT
ijassa-1597	115	10	since	since	SCONJ
ijassa-1597	115	11	|a+	|a+	PROPN
ijassa-1597	115	12	b|	b|	VERB
ijassa-1597	115	13	≤	≤	NUM
ijassa-1597	115	14	|a|+	|a|+	NOUN
ijassa-1597	115	15	|b|	|b|	PROPN
ijassa-1597	115	16	,	,	PUNCT
ijassa-1597	115	17	ρ(a	ρ(a	PROPN
ijassa-1597	115	18	,	,	PUNCT
ijassa-1597	115	19	c	c	NOUN
ijassa-1597	115	20	)	)	PUNCT
ijassa-1597	116	1	=	=	NOUN
ijassa-1597	116	2	∑	∑	AUX
ijassa-1597	116	3	j∈n	j∈n	NOUN
ijassa-1597	116	4	|paj	|paj	NOUN
ijassa-1597	116	5	−	−	PROPN
ijassa-1597	117	1	pcj	pcj	PROPN
ijassa-1597	118	1	|	|	ADV
ijassa-1597	118	2	=	=	SYM
ijassa-1597	118	3	∑	∑	PUNCT
ijassa-1597	118	4	j∈n	j∈n	NOUN
ijassa-1597	118	5	|paj	|paj	NOUN
ijassa-1597	118	6	−	−	PROPN
ijassa-1597	119	1	pbj	pbj	PROPN
ijassa-1597	120	1	+	+	CCONJ
ijassa-1597	120	2	pbj	pbj	PROPN
ijassa-1597	120	3	−	−	PROPN
ijassa-1597	120	4	pcj	pcj	PROPN
ijassa-1597	120	5	|	|	ADV
ijassa-1597	120	6	≤	≤	PROPN
ijassa-1597	120	7	∑	∑	PUNCT
ijassa-1597	120	8	j∈n	j∈n	VERB
ijassa-1597	120	9	|paj	|paj	NOUN
ijassa-1597	120	10	−	−	PROPN
ijassa-1597	120	11	pbj	pbj	PROPN
ijassa-1597	120	12	|+	|+	PROPN
ijassa-1597	120	13	∑	∑	PROPN
ijassa-1597	120	14	j∈n	j∈n	NOUN
ijassa-1597	120	15	|pbj	|pbj	PROPN
ijassa-1597	120	16	−	−	PROPN
ijassa-1597	121	1	pcj	pcj	PROPN
ijassa-1597	121	2	|	|	ADV
ijassa-1597	121	3	=	=	SYM
ijassa-1597	121	4	ρ(a	ρ(a	PROPN
ijassa-1597	121	5	,	,	PUNCT
ijassa-1597	121	6	b	b	NOUN
ijassa-1597	121	7	)	)	PUNCT
ijassa-1597	121	8	+	+	PUNCT
ijassa-1597	121	9	ρ(b	ρ(b	NOUN
ijassa-1597	121	10	,	,	PUNCT
ijassa-1597	121	11	c	c	NOUN
ijassa-1597	121	12	)	)	PUNCT
ijassa-1597	121	13	.	.	PUNCT
ijassa-1597	122	1	4	4	X
ijassa-1597	122	2	.	.	X
ijassa-1597	122	3	the	the	DET
ijassa-1597	122	4	polynomial	polynomial	ADJ
ijassa-1597	122	5	-	-	PUNCT
ijassa-1597	122	6	time	time	NOUN
ijassa-1597	122	7	approximation	approximation	NOUN
ijassa-1597	122	8	scheme	scheme	NOUN
ijassa-1597	122	9	as	as	SCONJ
ijassa-1597	122	10	stated	state	VERB
ijassa-1597	122	11	above	above	ADV
ijassa-1597	122	12	,	,	PUNCT
ijassa-1597	122	13	an	an	DET
ijassa-1597	122	14	instance	instance	NOUN
ijassa-1597	122	15	of	of	ADP
ijassa-1597	122	16	the	the	DET
ijassa-1597	122	17	problem	problem	NOUN
ijassa-1597	122	18	p2	p2	PROPN
ijassa-1597	122	19	|	|	ADV
ijassa-1597	122	20	prec	prec	X
ijassa-1597	122	21	,	,	PUNCT
ijassa-1597	122	22	pj	pj	PROPN
ijassa-1597	122	23	=	=	SYM
ijassa-1597	122	24	1	1	NUM
ijassa-1597	122	25	|	|	ADV
ijassa-1597	122	26	cmax	cmax	NOUN
ijassa-1597	122	27	can	can	AUX
ijassa-1597	122	28	be	be	AUX
ijassa-1597	122	29	solved	solve	VERB
ijassa-1597	122	30	by	by	ADP
ijassa-1597	122	31	polynomial	polynomial	ADJ
ijassa-1597	122	32	algorithms	algorithm	NOUN
ijassa-1597	122	33	.	.	PUNCT
ijassa-1597	123	1	it	it	PRON
ijassa-1597	123	2	is	be	AUX
ijassa-1597	123	3	possible	possible	ADJ
ijassa-1597	123	4	to	to	PART
ijassa-1597	123	5	convert	convert	VERB
ijassa-1597	123	6	an	an	DET
ijassa-1597	123	7	instance	instance	NOUN
ijassa-1597	123	8	a	a	PRON
ijassa-1597	123	9	of	of	ADP
ijassa-1597	123	10	the	the	DET
ijassa-1597	123	11	problem	problem	NOUN
ijassa-1597	123	12	p2	p2	NOUN
ijassa-1597	123	13	|	|	ADV
ijassa-1597	123	14	prec	prec	X
ijassa-1597	123	15	,	,	PUNCT
ijassa-1597	123	16	pj	pj	PROPN
ijassa-1597	123	17	∈	∈	PROPN
ijassa-1597	123	18	{	{	PUNCT
ijassa-1597	123	19	1	1	NUM
ijassa-1597	123	20	,	,	PUNCT
ijassa-1597	123	21	2	2	NUM
ijassa-1597	123	22	}	}	PUNCT
ijassa-1597	123	23	|	|	ADV
ijassa-1597	123	24	cmax	cmax	VERB
ijassa-1597	123	25	to	to	ADP
ijassa-1597	123	26	an	an	DET
ijassa-1597	123	27	instance	instance	NOUN
ijassa-1597	123	28	b	b	PROPN
ijassa-1597	123	29	of	of	ADP
ijassa-1597	123	30	the	the	DET
ijassa-1597	123	31	problem	problem	NOUN
ijassa-1597	123	32	p2	p2	PROPN
ijassa-1597	123	33	|	|	ADV
ijassa-1597	123	34	prec	prec	X
ijassa-1597	123	35	,	,	PUNCT
ijassa-1597	123	36	pj	pj	PROPN
ijassa-1597	123	37	=	=	SYM
ijassa-1597	123	38	1	1	NUM
ijassa-1597	123	39	|	|	ADV
ijassa-1597	123	40	cmax	cmax	NOUN
ijassa-1597	123	41	by	by	ADP
ijassa-1597	123	42	setting	set	VERB
ijassa-1597	123	43	pj	pj	PROPN
ijassa-1597	123	44	=	=	PUNCT
ijassa-1597	123	45	1	1	NUM
ijassa-1597	123	46	for	for	ADP
ijassa-1597	123	47	all	all	DET
ijassa-1597	123	48	j	j	PROPN
ijassa-1597	123	49	∈	∈	PROPN
ijassa-1597	123	50	n	n	ADV
ijassa-1597	123	51	.	.	PUNCT
ijassa-1597	124	1	this	this	PRON
ijassa-1597	124	2	leads	lead	VERB
ijassa-1597	124	3	to	to	ADP
ijassa-1597	124	4	a	a	DET
ijassa-1597	124	5	polynomial	polynomial	ADJ
ijassa-1597	124	6	-	-	PUNCT
ijassa-1597	124	7	time	time	NOUN
ijassa-1597	124	8	approximation	approximation	NOUN
ijassa-1597	124	9	scheme	scheme	NOUN
ijassa-1597	124	10	(	(	PUNCT
ijassa-1597	124	11	ptas	pta	NOUN
ijassa-1597	124	12	)	)	PUNCT
ijassa-1597	124	13	that	that	PRON
ijassa-1597	124	14	can	can	AUX
ijassa-1597	124	15	be	be	AUX
ijassa-1597	124	16	seen	see	VERB
ijassa-1597	124	17	on	on	ADP
ijassa-1597	124	18	fig	fig	NOUN
ijassa-1597	124	19	.	.	PUNCT
ijassa-1597	125	1	4.1	4.1	NUM
ijassa-1597	125	2	.	.	PUNCT
ijassa-1597	126	1	b	b	X
ijassa-1597	126	2	π∗	π∗	PROPN
ijassa-1597	126	3	b	b	PROPN
ijassa-1597	126	4	πa	πa	ADP
ijassa-1597	126	5	a	a	DET
ijassa-1597	126	6	π∗	π∗	NOUN
ijassa-1597	126	7	a	a	DET
ijassa-1597	126	8	o(n	o(n	PROPN
ijassa-1597	126	9	)	)	PUNCT
ijassa-1597	126	10	o(n	o(n	NOUN
ijassa-1597	126	11	)	)	PUNCT
ijassa-1597	126	12	o(n	o(n	NOUN
ijassa-1597	126	13	)	)	PUNCT
ijassa-1597	126	14	o(2n	o(2n	NOUN
ijassa-1597	126	15	)	)	PUNCT
ijassa-1597	126	16	fig	fig	NOUN
ijassa-1597	126	17	.	.	PUNCT
ijassa-1597	127	1	4.1	4.1	NUM
ijassa-1597	127	2	.	.	PUNCT
ijassa-1597	128	1	the	the	DET
ijassa-1597	128	2	ptas	pta	NOUN
ijassa-1597	128	3	scheme	scheme	NOUN
ijassa-1597	128	4	for	for	ADP
ijassa-1597	128	5	the	the	DET
ijassa-1597	128	6	problem	problem	NOUN
ijassa-1597	128	7	p2	p2	PROPN
ijassa-1597	128	8	|	|	ADV
ijassa-1597	128	9	prec	prec	X
ijassa-1597	128	10	,	,	PUNCT
ijassa-1597	128	11	pj	pj	PROPN
ijassa-1597	128	12	∈	∈	PROPN
ijassa-1597	128	13	{	{	PUNCT
ijassa-1597	128	14	1	1	NUM
ijassa-1597	128	15	,	,	PUNCT
ijassa-1597	128	16	2	2	NUM
ijassa-1597	128	17	}	}	PUNCT
ijassa-1597	128	18	|	|	ADV
ijassa-1597	128	19	cmax	cmax	VERB
ijassa-1597	128	20	.	.	PUNCT
ijassa-1597	129	1	an	an	DET
ijassa-1597	129	2	instance	instance	NOUN
ijassa-1597	129	3	of	of	ADP
ijassa-1597	129	4	the	the	DET
ijassa-1597	129	5	problem	problem	NOUN
ijassa-1597	129	6	p2	p2	PROPN
ijassa-1597	129	7	|	|	ADV
ijassa-1597	129	8	prec	prec	X
ijassa-1597	129	9	,	,	PUNCT
ijassa-1597	129	10	pj	pj	PROPN
ijassa-1597	129	11	∈	∈	PROPN
ijassa-1597	129	12	{	{	PUNCT
ijassa-1597	129	13	1	1	NUM
ijassa-1597	129	14	,	,	PUNCT
ijassa-1597	129	15	2	2	NUM
ijassa-1597	129	16	}	}	PUNCT
ijassa-1597	130	1	|	|	ADV
ijassa-1597	130	2	cmax	cmax	NOUN
ijassa-1597	130	3	has	have	VERB
ijassa-1597	130	4	a	a	DET
ijassa-1597	130	5	set	set	NOUN
ijassa-1597	130	6	of	of	ADP
ijassa-1597	130	7	feasible	feasible	ADJ
ijassa-1597	130	8	schedules	schedule	NOUN
ijassa-1597	130	9	.	.	PUNCT
ijassa-1597	131	1	but	but	CCONJ
ijassa-1597	131	2	some	some	PRON
ijassa-1597	131	3	of	of	ADP
ijassa-1597	131	4	them	they	PRON
ijassa-1597	131	5	differs	differ	VERB
ijassa-1597	131	6	from	from	ADP
ijassa-1597	131	7	the	the	DET
ijassa-1597	131	8	other	other	ADJ
ijassa-1597	131	9	only	only	ADV
ijassa-1597	131	10	by	by	ADP
ijassa-1597	131	11	the	the	DET
ijassa-1597	131	12	order	order	NOUN
ijassa-1597	131	13	of	of	ADP
ijassa-1597	131	14	jobs	job	NOUN
ijassa-1597	131	15	on	on	ADP
ijassa-1597	131	16	each	each	DET
ijassa-1597	131	17	machine	machine	NOUN
ijassa-1597	131	18	,	,	PUNCT
ijassa-1597	131	19	not	not	PART
ijassa-1597	131	20	by	by	ADP
ijassa-1597	131	21	the	the	DET
ijassa-1597	131	22	makespan	makespan	ADJ
ijassa-1597	131	23	value	value	NOUN
ijassa-1597	131	24	.	.	PUNCT
ijassa-1597	132	1	since	since	SCONJ
ijassa-1597	132	2	we	we	PRON
ijassa-1597	132	3	aim	aim	VERB
ijassa-1597	132	4	to	to	PART
ijassa-1597	132	5	minimize	minimize	VERB
ijassa-1597	132	6	target	target	NOUN
ijassa-1597	132	7	function	function	NOUN
ijassa-1597	132	8	cmax	cmax	NOUN
ijassa-1597	132	9	,	,	PUNCT
ijassa-1597	132	10	we	we	PRON
ijassa-1597	132	11	take	take	VERB
ijassa-1597	132	12	only	only	ADV
ijassa-1597	132	13	those	those	DET
ijassa-1597	132	14	schedules	schedule	NOUN
ijassa-1597	132	15	that	that	PRON
ijassa-1597	132	16	have	have	VERB
ijassa-1597	132	17	the	the	DET
ijassa-1597	132	18	minimal	minimal	ADJ
ijassa-1597	132	19	value	value	NOUN
ijassa-1597	132	20	of	of	ADP
ijassa-1597	132	21	cmax	cmax	NOUN
ijassa-1597	132	22	.	.	PUNCT
ijassa-1597	133	1	no	no	DET
ijassa-1597	133	2	solving	solving	NOUN
ijassa-1597	133	3	instance	instance	NOUN
ijassa-1597	133	4	b	b	PROPN
ijassa-1597	133	5	algorithm	algorithm	NOUN
ijassa-1597	133	6	from	from	ADP
ijassa-1597	133	7	the	the	DET
ijassa-1597	133	8	ones	one	NOUN
ijassa-1597	133	9	above	above	ADV
ijassa-1597	133	10	must	must	AUX
ijassa-1597	133	11	be	be	AUX
ijassa-1597	133	12	better	well	ADJ
ijassa-1597	133	13	than	than	ADP
ijassa-1597	133	14	others	other	NOUN
ijassa-1597	133	15	in	in	ADP
ijassa-1597	133	16	general	general	ADJ
ijassa-1597	133	17	case	case	NOUN
ijassa-1597	133	18	.	.	PUNCT
ijassa-1597	134	1	indeed	indeed	ADV
ijassa-1597	134	2	,	,	PUNCT
ijassa-1597	134	3	let	let	VERB
ijassa-1597	134	4	f∗(a	f∗(a	NOUN
ijassa-1597	134	5	)	)	PUNCT
ijassa-1597	134	6	⊆	⊆	NUM
ijassa-1597	134	7	f(a	f(a	NOUN
ijassa-1597	134	8	)	)	PUNCT
ijassa-1597	134	9	be	be	VERB
ijassa-1597	134	10	a	a	DET
ijassa-1597	134	11	subset	subset	NOUN
ijassa-1597	134	12	of	of	ADP
ijassa-1597	134	13	optimal	optimal	ADJ
ijassa-1597	134	14	schedules	schedule	NOUN
ijassa-1597	134	15	from	from	ADP
ijassa-1597	134	16	f(a	f(a	PROPN
ijassa-1597	134	17	)	)	PUNCT
ijassa-1597	134	18	.	.	PUNCT
ijassa-1597	135	1	since	since	SCONJ
ijassa-1597	135	2	g(a	g(a	PROPN
ijassa-1597	135	3	)	)	PUNCT
ijassa-1597	135	4	=	=	PUNCT
ijassa-1597	136	1	g(b	g(b	NOUN
ijassa-1597	136	2	)	)	PUNCT
ijassa-1597	136	3	,	,	PUNCT
ijassa-1597	136	4	the	the	DET
ijassa-1597	136	5	sets	set	NOUN
ijassa-1597	136	6	f(a	f(a	PROPN
ijassa-1597	136	7	)	)	PUNCT
ijassa-1597	136	8	and	and	CCONJ
ijassa-1597	136	9	f(b	f(b	PROPN
ijassa-1597	136	10	)	)	PUNCT
ijassa-1597	136	11	are	be	AUX
ijassa-1597	136	12	equal	equal	ADJ
ijassa-1597	136	13	too	too	ADV
ijassa-1597	136	14	.	.	PUNCT
ijassa-1597	137	1	but	but	CCONJ
ijassa-1597	137	2	sets	set	VERB
ijassa-1597	137	3	f∗(a	f∗(a	NOUN
ijassa-1597	137	4	)	)	PUNCT
ijassa-1597	137	5	and	and	CCONJ
ijassa-1597	137	6	f∗(b	f∗(b	PROPN
ijassa-1597	137	7	)	)	PUNCT
ijassa-1597	137	8	are	be	AUX
ijassa-1597	137	9	completely	completely	ADV
ijassa-1597	137	10	different	different	ADJ
ijassa-1597	137	11	in	in	ADP
ijassa-1597	137	12	general	general	ADJ
ijassa-1597	137	13	case	case	NOUN
ijassa-1597	137	14	.	.	PUNCT
ijassa-1597	138	1	it	it	PRON
ijassa-1597	138	2	means	mean	VERB
ijassa-1597	138	3	that	that	SCONJ
ijassa-1597	138	4	the	the	DET
ijassa-1597	138	5	polynomial	polynomial	ADJ
ijassa-1597	138	6	algorithms	algorithms	NOUN
ijassa-1597	138	7	one	one	NUM
ijassa-1597	138	8	use	use	NOUN
ijassa-1597	138	9	for	for	ADP
ijassa-1597	138	10	the	the	DET
ijassa-1597	138	11	instance	instance	PROPN
ijassa-1597	138	12	b	b	PROPN
ijassa-1597	138	13	of	of	ADP
ijassa-1597	138	14	the	the	DET
ijassa-1597	138	15	problem	problem	NOUN
ijassa-1597	138	16	p2	p2	PROPN
ijassa-1597	138	17	|	|	ADV
ijassa-1597	138	18	prec	prec	X
ijassa-1597	138	19	,	,	PUNCT
ijassa-1597	138	20	pj	pj	PROPN
ijassa-1597	138	21	=	=	SYM
ijassa-1597	138	22	1	1	NUM
ijassa-1597	138	23	|	|	ADV
ijassa-1597	138	24	cmax	cmax	VERB
ijassa-1597	138	25	generally	generally	ADV
ijassa-1597	138	26	just	just	ADV
ijassa-1597	138	27	take	take	VERB
ijassa-1597	138	28	a	a	DET
ijassa-1597	138	29	random	random	ADJ
ijassa-1597	138	30	schedule	schedule	NOUN
ijassa-1597	138	31	from	from	ADP
ijassa-1597	138	32	f(a	f(a	PROPN
ijassa-1597	138	33	)	)	PUNCT
ijassa-1597	138	34	as	as	ADP
ijassa-1597	138	35	an	an	DET
ijassa-1597	138	36	approximate	approximate	ADJ
ijassa-1597	138	37	solution	solution	NOUN
ijassa-1597	138	38	πa	πa	ADP
ijassa-1597	138	39	for	for	ADP
ijassa-1597	138	40	the	the	DET
ijassa-1597	138	41	instance	instance	NOUN
ijassa-1597	138	42	a.	a.	NOUN
ijassa-1597	138	43	5	5	NUM
ijassa-1597	138	44	.	.	PUNCT
ijassa-1597	139	1	computer	computer	NOUN
ijassa-1597	139	2	experiments	experiment	NOUN
ijassa-1597	139	3	four	four	NUM
ijassa-1597	139	4	polynomial	polynomial	ADJ
ijassa-1597	139	5	algorithms	algorithm	NOUN
ijassa-1597	139	6	for	for	ADP
ijassa-1597	139	7	the	the	DET
ijassa-1597	139	8	problem	problem	NOUN
ijassa-1597	139	9	p2	p2	PROPN
ijassa-1597	139	10	|	|	ADV
ijassa-1597	139	11	prec	prec	X
ijassa-1597	139	12	,	,	PUNCT
ijassa-1597	139	13	pj	pj	PROPN
ijassa-1597	139	14	=	=	SYM
ijassa-1597	139	15	1	1	NUM
ijassa-1597	139	16	|	|	ADV
ijassa-1597	139	17	cmax	cmax	NOUN
ijassa-1597	139	18	:	:	PUNCT
ijassa-1597	139	19	fujii	fujii	PROPN
ijassa-1597	139	20	’s	’s	PART
ijassa-1597	139	21	algorithm	algorithm	NOUN
ijassa-1597	140	1	[	[	X
ijassa-1597	140	2	4	4	NUM
ijassa-1597	140	3	]	]	PUNCT
ijassa-1597	140	4	,	,	PUNCT
ijassa-1597	140	5	coffman	coffman	PROPN
ijassa-1597	140	6	’s	’s	PART
ijassa-1597	140	7	algorithm	algorithm	NOUN
ijassa-1597	141	1	[	[	X
ijassa-1597	141	2	5	5	NUM
ijassa-1597	141	3	]	]	PUNCT
ijassa-1597	141	4	,	,	PUNCT
ijassa-1597	141	5	sethi	sethi	PROPN
ijassa-1597	141	6	’s	’s	PART
ijassa-1597	141	7	algorithm	algorithm	NOUN
ijassa-1597	142	1	[	[	X
ijassa-1597	142	2	6	6	NUM
ijassa-1597	142	3	]	]	PUNCT
ijassa-1597	142	4	and	and	CCONJ
ijassa-1597	142	5	gabow	gabow	NOUN
ijassa-1597	142	6	’s	’s	PART
ijassa-1597	142	7	algorithm	algorithm	NOUN
ijassa-1597	142	8	[	[	X
ijassa-1597	142	9	7	7	NUM
ijassa-1597	142	10	]	]	PUNCT
ijassa-1597	142	11	were	be	AUX
ijassa-1597	142	12	copyright	copyright	NOUN
ijassa-1597	142	13	©	©	PROPN
ijassa-1597	142	14	2024	2024	NUM
ijassa-1597	142	15	assa	assa	NOUN
ijassa-1597	142	16	.	.	PUNCT
ijassa-1597	143	1	adv	adv	PROPN
ijassa-1597	143	2	syst	syst	PROPN
ijassa-1597	143	3	sci	sci	PROPN
ijassa-1597	143	4	appl	appl	PROPN
ijassa-1597	143	5	(	(	PUNCT
ijassa-1597	143	6	2024	2024	NUM
ijassa-1597	143	7	)	)	PUNCT
ijassa-1597	143	8	practical	practical	ADJ
ijassa-1597	143	9	applicability	applicability	NOUN
ijassa-1597	143	10	of	of	ADP
ijassa-1597	143	11	the	the	DET
ijassa-1597	143	12	metric	metric	ADJ
ijassa-1597	143	13	approach	approach	NOUN
ijassa-1597	143	14	...	...	PUNCT
ijassa-1597	143	15	99	99	NUM
ijassa-1597	143	16	implemented	implement	VERB
ijassa-1597	143	17	.	.	PUNCT
ijassa-1597	144	1	optimal	optimal	ADJ
ijassa-1597	144	2	solution	solution	NOUN
ijassa-1597	144	3	of	of	ADP
ijassa-1597	144	4	np	np	PRON
ijassa-1597	144	5	-hard	-hard	NOUN
ijassa-1597	144	6	problem	problem	NOUN
ijassa-1597	144	7	p2	p2	NOUN
ijassa-1597	144	8	|	|	ADV
ijassa-1597	144	9	prec	prec	X
ijassa-1597	144	10	,	,	PUNCT
ijassa-1597	144	11	pj	pj	PROPN
ijassa-1597	144	12	∈	∈	PROPN
ijassa-1597	144	13	{	{	PUNCT
ijassa-1597	144	14	1	1	NUM
ijassa-1597	144	15	,	,	PUNCT
ijassa-1597	144	16	2	2	NUM
ijassa-1597	144	17	}	}	PUNCT
ijassa-1597	144	18	|	|	ADV
ijassa-1597	144	19	cmax	cmax	NOUN
ijassa-1597	144	20	was	be	AUX
ijassa-1597	144	21	obtained	obtain	VERB
ijassa-1597	144	22	by	by	ADP
ijassa-1597	144	23	glpk	glpk	PROPN
ijassa-1597	144	24	solver†.	solver†.	NUM
ijassa-1597	144	25	the	the	DET
ijassa-1597	144	26	following	follow	VERB
ijassa-1597	144	27	indicators	indicator	NOUN
ijassa-1597	144	28	were	be	AUX
ijassa-1597	144	29	chosen	choose	VERB
ijassa-1597	144	30	as	as	ADP
ijassa-1597	144	31	efficiency	efficiency	NOUN
ijassa-1597	144	32	evaluation	evaluation	NOUN
ijassa-1597	144	33	criteria	criterion	NOUN
ijassa-1597	144	34	:	:	PUNCT
ijassa-1597	145	1	1	1	X
ijassa-1597	145	2	.	.	X
ijassa-1597	145	3	µ	µ	NOUN
ijassa-1597	145	4	determines	determine	VERB
ijassa-1597	145	5	the	the	DET
ijassa-1597	145	6	share	share	NOUN
ijassa-1597	145	7	of	of	ADP
ijassa-1597	145	8	cases	case	NOUN
ijassa-1597	145	9	for	for	ADP
ijassa-1597	145	10	which	which	PRON
ijassa-1597	145	11	no	no	DET
ijassa-1597	145	12	optimal	optimal	ADJ
ijassa-1597	145	13	solution	solution	NOUN
ijassa-1597	145	14	was	be	AUX
ijassa-1597	145	15	obtained	obtain	VERB
ijassa-1597	145	16	by	by	ADP
ijassa-1597	145	17	the	the	DET
ijassa-1597	145	18	approximate	approximate	ADJ
ijassa-1597	145	19	algorithm	algorithm	NOUN
ijassa-1597	145	20	:	:	PUNCT
ijassa-1597	145	21	µ	µ	X
ijassa-1597	145	22	=	=	PUNCT
ijassa-1597	145	23	k̄	k̄	INTJ
ijassa-1597	145	24	k	k	NOUN
ijassa-1597	145	25	,	,	PUNCT
ijassa-1597	145	26	where	where	SCONJ
ijassa-1597	145	27	k	k	PROPN
ijassa-1597	145	28	is	be	AUX
ijassa-1597	145	29	the	the	DET
ijassa-1597	145	30	number	number	NOUN
ijassa-1597	145	31	of	of	ADP
ijassa-1597	145	32	generated	generate	VERB
ijassa-1597	145	33	examples	example	NOUN
ijassa-1597	145	34	,	,	PUNCT
ijassa-1597	145	35	and	and	CCONJ
ijassa-1597	145	36	k̄	k̄	PRON
ijassa-1597	145	37	is	be	AUX
ijassa-1597	145	38	the	the	DET
ijassa-1597	145	39	one	one	NUM
ijassa-1597	145	40	for	for	ADP
ijassa-1597	145	41	which	which	PRON
ijassa-1597	145	42	the	the	DET
ijassa-1597	145	43	found	find	VERB
ijassa-1597	145	44	solution	solution	NOUN
ijassa-1597	145	45	was	be	AUX
ijassa-1597	145	46	not	not	PART
ijassa-1597	145	47	optimal	optimal	ADJ
ijassa-1597	145	48	,	,	PUNCT
ijassa-1597	145	49	i.e	i.e	X
ijassa-1597	145	50	:	:	PUNCT
ijassa-1597	145	51	cmax(πi)−	cmax(πi)−	NOUN
ijassa-1597	145	52	cmax(π	cmax(π	PROPN
ijassa-1597	145	53	∗	∗	X
ijassa-1597	145	54	i	i	PRON
ijassa-1597	145	55	)	)	PUNCT
ijassa-1597	145	56	>	>	X
ijassa-1597	145	57	0	0	NUM
ijassa-1597	145	58	;	;	PUNCT
ijassa-1597	145	59	2	2	NUM
ijassa-1597	145	60	.	.	X
ijassa-1597	145	61	average	average	ADJ
ijassa-1597	145	62	relative	relative	ADJ
ijassa-1597	145	63	non	non	ADJ
ijassa-1597	145	64	-	-	ADJ
ijassa-1597	145	65	zero	zero	NUM
ijassa-1597	145	66	error	error	NOUN
ijassa-1597	145	67	βnre	βnre	NOUN
ijassa-1597	145	68	:	:	PUNCT
ijassa-1597	145	69	βnre	βnre	X
ijassa-1597	145	70	=	=	SYM
ijassa-1597	146	1	1	1	NUM
ijassa-1597	147	1	k̄	k̄	INTJ
ijassa-1597	147	2	k̄∑	k̄∑	PROPN
ijassa-1597	147	3	i=1	i=1	PROPN
ijassa-1597	148	1	cmax(πi)−	cmax(πi)−	PROPN
ijassa-1597	148	2	cmax(π	cmax(π	PROPN
ijassa-1597	148	3	∗	∗	NOUN
ijassa-1597	148	4	i	i	NOUN
ijassa-1597	148	5	)	)	PUNCT
ijassa-1597	148	6	cmax(π∗	cmax(π∗	PROPN
ijassa-1597	148	7	i	i	PROPN
ijassa-1597	148	8	)	)	PUNCT
ijassa-1597	148	9	;	;	PUNCT
ijassa-1597	148	10	3	3	X
ijassa-1597	148	11	.	.	X
ijassa-1597	148	12	average	average	ADJ
ijassa-1597	148	13	absolute	absolute	ADJ
ijassa-1597	148	14	non	non	ADJ
ijassa-1597	148	15	-	-	ADJ
ijassa-1597	148	16	zero	zero	NUM
ijassa-1597	148	17	error	error	NOUN
ijassa-1597	148	18	βnae	βnae	NOUN
ijassa-1597	148	19	:	:	PUNCT
ijassa-1597	148	20	βnae	βnae	ADJ
ijassa-1597	148	21	=	=	SYM
ijassa-1597	148	22	1	1	NUM
ijassa-1597	149	1	k̄	k̄	INTJ
ijassa-1597	150	1	k̄∑	k̄∑	PROPN
ijassa-1597	150	2	i=1	i=1	PROPN
ijassa-1597	150	3	(	(	PUNCT
ijassa-1597	150	4	cmax(πi	cmax(πi	VERB
ijassa-1597	150	5	,	,	PUNCT
ijassa-1597	150	6	a)−	a)−	PROPN
ijassa-1597	150	7	cmax(π	cmax(π	PROPN
ijassa-1597	150	8	∗	∗	NOUN
ijassa-1597	150	9	i	i	PRON
ijassa-1597	150	10	,	,	PUNCT
ijassa-1597	150	11	a	a	PRON
ijassa-1597	150	12	)	)	PUNCT
ijassa-1597	150	13	)	)	PUNCT
ijassa-1597	150	14	;	;	PUNCT
ijassa-1597	150	15	4	4	X
ijassa-1597	150	16	.	.	X
ijassa-1597	150	17	average	average	ADJ
ijassa-1597	150	18	relative	relative	ADJ
ijassa-1597	150	19	error	error	NOUN
ijassa-1597	150	20	βre	βre	NOUN
ijassa-1597	150	21	:	:	PUNCT
ijassa-1597	150	22	βre	βre	PROPN
ijassa-1597	150	23	=	=	SYM
ijassa-1597	150	24	1	1	NUM
ijassa-1597	150	25	k	k	NOUN
ijassa-1597	150	26	k∑	k∑	PROPN
ijassa-1597	150	27	i=1	i=1	PROPN
ijassa-1597	151	1	cmax(πi)−	cmax(πi)−	PROPN
ijassa-1597	151	2	cmax(π	cmax(π	PROPN
ijassa-1597	151	3	∗	∗	NOUN
ijassa-1597	151	4	i	i	NOUN
ijassa-1597	151	5	)	)	PUNCT
ijassa-1597	151	6	cmax(π∗	cmax(π∗	PROPN
ijassa-1597	151	7	i	i	PROPN
ijassa-1597	151	8	)	)	PUNCT
ijassa-1597	151	9	;	;	PUNCT
ijassa-1597	151	10	5	5	X
ijassa-1597	151	11	.	.	X
ijassa-1597	151	12	average	average	ADJ
ijassa-1597	151	13	absolute	absolute	ADJ
ijassa-1597	151	14	error	error	NOUN
ijassa-1597	151	15	βae	βae	NOUN
ijassa-1597	151	16	:	:	PUNCT
ijassa-1597	151	17	βae	βae	X
ijassa-1597	152	1	=	=	NOUN
ijassa-1597	152	2	1	1	NUM
ijassa-1597	152	3	k	k	NOUN
ijassa-1597	152	4	k∑	k∑	PROPN
ijassa-1597	152	5	i=1	i=1	PROPN
ijassa-1597	153	1	(	(	PUNCT
ijassa-1597	153	2	cmax(πi	cmax(πi	VERB
ijassa-1597	153	3	,	,	PUNCT
ijassa-1597	153	4	a)−	a)−	PROPN
ijassa-1597	153	5	cmax(π	cmax(π	PROPN
ijassa-1597	153	6	∗	∗	NOUN
ijassa-1597	153	7	i	i	PRON
ijassa-1597	153	8	,	,	PUNCT
ijassa-1597	153	9	a	a	PRON
ijassa-1597	153	10	)	)	PUNCT
ijassa-1597	153	11	)	)	PUNCT
ijassa-1597	153	12	.	.	PUNCT
ijassa-1597	154	1	there	there	PRON
ijassa-1597	154	2	were	be	AUX
ijassa-1597	154	3	calculated	calculate	VERB
ijassa-1597	154	4	1000	1000	NUM
ijassa-1597	154	5	of	of	ADP
ijassa-1597	154	6	uniformly	uniformly	ADV
ijassa-1597	154	7	distributed	distribute	VERB
ijassa-1597	154	8	random	random	ADJ
ijassa-1597	154	9	instances	instance	NOUN
ijassa-1597	154	10	of	of	ADP
ijassa-1597	154	11	the	the	DET
ijassa-1597	154	12	problem	problem	NOUN
ijassa-1597	154	13	p2	p2	PROPN
ijassa-1597	154	14	|	|	ADV
ijassa-1597	154	15	prec	prec	X
ijassa-1597	154	16	,	,	PUNCT
ijassa-1597	154	17	pj	pj	PROPN
ijassa-1597	154	18	=	=	PUNCT
ijassa-1597	154	19	{	{	PUNCT
ijassa-1597	154	20	1	1	NUM
ijassa-1597	154	21	,	,	PUNCT
ijassa-1597	154	22	2	2	NUM
ijassa-1597	154	23	}	}	PUNCT
ijassa-1597	154	24	|	|	ADV
ijassa-1597	154	25	cmax	cmax	VERB
ijassa-1597	154	26	for	for	ADP
ijassa-1597	154	27	instance	instance	NOUN
ijassa-1597	154	28	with	with	ADP
ijassa-1597	154	29	number	number	NOUN
ijassa-1597	154	30	of	of	ADP
ijassa-1597	154	31	jobs	job	NOUN
ijassa-1597	154	32	n	n	PRON
ijassa-1597	154	33	∈	∈	PROPN
ijassa-1597	154	34	{	{	PUNCT
ijassa-1597	154	35	3	3	NUM
ijassa-1597	154	36	,	,	PUNCT
ijassa-1597	154	37	4	4	NUM
ijassa-1597	154	38	,	,	PUNCT
ijassa-1597	154	39	.	.	PUNCT
ijassa-1597	154	40	.	.	PUNCT
ijassa-1597	154	41	.	.	PUNCT
ijassa-1597	155	1	,	,	PUNCT
ijassa-1597	155	2	13	13	NUM
ijassa-1597	155	3	}	}	PUNCT
ijassa-1597	155	4	with	with	ADP
ijassa-1597	155	5	the	the	DET
ijassa-1597	155	6	density	density	NOUN
ijassa-1597	156	1	d	d	NOUN
ijassa-1597	156	2	=	=	SYM
ijassa-1597	156	3	0.3	0.3	NUM
ijassa-1597	156	4	,	,	PUNCT
ijassa-1597	156	5	where	where	SCONJ
ijassa-1597	156	6	the	the	DET
ijassa-1597	156	7	density	density	NOUN
ijassa-1597	156	8	is	be	AUX
ijassa-1597	156	9	the	the	DET
ijassa-1597	156	10	ratio	ratio	NOUN
ijassa-1597	156	11	of	of	ADP
ijassa-1597	156	12	the	the	DET
ijassa-1597	156	13	number	number	NOUN
ijassa-1597	156	14	of	of	ADP
ijassa-1597	156	15	edges	edge	NOUN
ijassa-1597	156	16	of	of	ADP
ijassa-1597	156	17	the	the	DET
ijassa-1597	156	18	given	give	VERB
ijassa-1597	156	19	graph	graph	NOUN
ijassa-1597	156	20	to	to	ADP
ijassa-1597	156	21	the	the	DET
ijassa-1597	156	22	one	one	NUM
ijassa-1597	156	23	of	of	ADP
ijassa-1597	156	24	the	the	DET
ijassa-1597	156	25	complete	complete	ADJ
ijassa-1597	156	26	graph	graph	NOUN
ijassa-1597	156	27	,	,	PUNCT
ijassa-1597	156	28	and	and	CCONJ
ijassa-1597	156	29	250	250	NUM
ijassa-1597	156	30	of	of	ADP
ijassa-1597	156	31	uniformly	uniformly	ADV
ijassa-1597	156	32	distributed	distribute	VERB
ijassa-1597	156	33	random	random	ADJ
ijassa-1597	156	34	instances	instance	NOUN
ijassa-1597	156	35	for	for	ADP
ijassa-1597	156	36	each	each	DET
ijassa-1597	156	37	problem	problem	NOUN
ijassa-1597	156	38	for	for	ADP
ijassa-1597	156	39	density	density	NOUN
ijassa-1597	156	40	values	value	NOUN
ijassa-1597	156	41	d	d	X
ijassa-1597	156	42	∈	∈	PROPN
ijassa-1597	156	43	{	{	PUNCT
ijassa-1597	156	44	0.1	0.1	NUM
ijassa-1597	156	45	,	,	PUNCT
ijassa-1597	156	46	0.2	0.2	NUM
ijassa-1597	156	47	,	,	PUNCT
ijassa-1597	156	48	.	.	PUNCT
ijassa-1597	156	49	.	.	PUNCT
ijassa-1597	157	1	.	.	PUNCT
ijassa-1597	158	1	,	,	PUNCT
ijassa-1597	158	2	1.0	1.0	NUM
ijassa-1597	158	3	}	}	PUNCT
ijassa-1597	158	4	for	for	ADP
ijassa-1597	158	5	problems	problem	NOUN
ijassa-1597	158	6	with	with	ADP
ijassa-1597	158	7	number	number	NOUN
ijassa-1597	158	8	of	of	ADP
ijassa-1597	158	9	jobs	job	NOUN
ijassa-1597	158	10	n	n	PRON
ijassa-1597	158	11	∈	∈	PROPN
ijassa-1597	158	12	{	{	PUNCT
ijassa-1597	158	13	3	3	NUM
ijassa-1597	158	14	,	,	PUNCT
ijassa-1597	158	15	4	4	NUM
ijassa-1597	158	16	,	,	PUNCT
ijassa-1597	158	17	.	.	PUNCT
ijassa-1597	158	18	.	.	PUNCT
ijassa-1597	159	1	.	.	PUNCT
ijassa-1597	160	1	,	,	PUNCT
ijassa-1597	160	2	13	13	NUM
ijassa-1597	160	3	}	}	PUNCT
ijassa-1597	160	4	.	.	PUNCT
ijassa-1597	161	1	as	as	SCONJ
ijassa-1597	161	2	can	can	AUX
ijassa-1597	161	3	be	be	AUX
ijassa-1597	161	4	seen	see	VERB
ijassa-1597	161	5	from	from	ADP
ijassa-1597	161	6	fig	fig	NOUN
ijassa-1597	161	7	.	.	PUNCT
ijassa-1597	162	1	5.2	5.2	NUM
ijassa-1597	162	2	,	,	PUNCT
ijassa-1597	162	3	the	the	DET
ijassa-1597	162	4	share	share	NOUN
ijassa-1597	162	5	of	of	ADP
ijassa-1597	162	6	cases	case	NOUN
ijassa-1597	162	7	for	for	ADP
ijassa-1597	162	8	which	which	PRON
ijassa-1597	162	9	the	the	DET
ijassa-1597	162	10	algorithm	algorithm	NOUN
ijassa-1597	162	11	obtained	obtain	VERB
ijassa-1597	162	12	a	a	DET
ijassa-1597	162	13	nonoptimal	nonoptimal	ADJ
ijassa-1597	162	14	solution	solution	NOUN
ijassa-1597	162	15	,	,	PUNCT
ijassa-1597	162	16	µ	µ	X
ijassa-1597	162	17	grows	grow	VERB
ijassa-1597	162	18	no	no	PRON
ijassa-1597	162	19	more	more	ADJ
ijassa-1597	162	20	than	than	ADP
ijassa-1597	162	21	linearly	linearly	ADV
ijassa-1597	162	22	with	with	ADP
ijassa-1597	162	23	increasing	increase	VERB
ijassa-1597	162	24	the	the	DET
ijassa-1597	162	25	number	number	NOUN
ijassa-1597	162	26	of	of	ADP
ijassa-1597	162	27	vertices	vertex	NOUN
ijassa-1597	162	28	(	(	PUNCT
ijassa-1597	162	29	jobs	job	NOUN
ijassa-1597	162	30	)	)	PUNCT
ijassa-1597	162	31	n.	n.	NOUN
ijassa-1597	162	32	the	the	DET
ijassa-1597	162	33	fluctuations	fluctuation	NOUN
ijassa-1597	162	34	in	in	ADP
ijassa-1597	162	35	the	the	DET
ijassa-1597	162	36	graph	graph	NOUN
ijassa-1597	162	37	at	at	ADP
ijassa-1597	162	38	odd	odd	ADJ
ijassa-1597	162	39	n	n	NOUN
ijassa-1597	162	40	are	be	AUX
ijassa-1597	162	41	caused	cause	VERB
ijassa-1597	162	42	by	by	ADP
ijassa-1597	162	43	the	the	DET
ijassa-1597	162	44	fact	fact	NOUN
ijassa-1597	162	45	that	that	SCONJ
ijassa-1597	162	46	there	there	PRON
ijassa-1597	162	47	are	be	VERB
ijassa-1597	162	48	two	two	NUM
ijassa-1597	162	49	machines	machine	NOUN
ijassa-1597	162	50	in	in	ADP
ijassa-1597	162	51	the	the	DET
ijassa-1597	162	52	problem	problem	NOUN
ijassa-1597	162	53	p2	p2	PROPN
ijassa-1597	162	54	|	|	ADV
ijassa-1597	162	55	prec	prec	X
ijassa-1597	162	56	,	,	PUNCT
ijassa-1597	162	57	pj	pj	PROPN
ijassa-1597	162	58	∈	∈	PROPN
ijassa-1597	162	59	{	{	PUNCT
ijassa-1597	162	60	1	1	NUM
ijassa-1597	162	61	,	,	PUNCT
ijassa-1597	162	62	2	2	NUM
ijassa-1597	162	63	}	}	PUNCT
ijassa-1597	162	64	|	|	ADV
ijassa-1597	162	65	cmax	cmax	VERB
ijassa-1597	162	66	.	.	PUNCT
ijassa-1597	163	1	when	when	SCONJ
ijassa-1597	163	2	a	a	DET
ijassa-1597	163	3	number	number	NOUN
ijassa-1597	163	4	of	of	ADP
ijassa-1597	163	5	jobs	job	NOUN
ijassa-1597	163	6	n	n	VERB
ijassa-1597	163	7	is	be	AUX
ijassa-1597	163	8	odd	odd	ADJ
ijassa-1597	163	9	,	,	PUNCT
ijassa-1597	163	10	on	on	ADP
ijassa-1597	163	11	average	average	ADJ
ijassa-1597	163	12	the	the	DET
ijassa-1597	163	13	last	last	ADJ
ijassa-1597	163	14	job	job	NOUN
ijassa-1597	163	15	can	can	AUX
ijassa-1597	163	16	be	be	AUX
ijassa-1597	163	17	put	put	VERB
ijassa-1597	163	18	into	into	ADP
ijassa-1597	163	19	the	the	DET
ijassa-1597	163	20	schedule	schedule	NOUN
ijassa-1597	163	21	,	,	PUNCT
ijassa-1597	163	22	leaving	leave	VERB
ijassa-1597	163	23	an	an	DET
ijassa-1597	163	24	empty	empty	ADJ
ijassa-1597	163	25	space	space	NOUN
ijassa-1597	163	26	on	on	ADP
ijassa-1597	163	27	another	another	DET
ijassa-1597	163	28	machine	machine	NOUN
ijassa-1597	163	29	.	.	PUNCT
ijassa-1597	164	1	an	an	DET
ijassa-1597	164	2	important	important	ADJ
ijassa-1597	164	3	result	result	NOUN
ijassa-1597	164	4	is	be	AUX
ijassa-1597	164	5	the	the	DET
ijassa-1597	164	6	dependence	dependence	NOUN
ijassa-1597	164	7	of	of	ADP
ijassa-1597	164	8	the	the	DET
ijassa-1597	164	9	relative	relative	ADJ
ijassa-1597	164	10	non	non	ADJ
ijassa-1597	164	11	-	-	ADJ
ijassa-1597	164	12	zero	zero	NUM
ijassa-1597	164	13	error	error	NOUN
ijassa-1597	164	14	βnre	βnre	NOUN
ijassa-1597	164	15	and	and	CCONJ
ijassa-1597	164	16	the	the	DET
ijassa-1597	164	17	absolute	absolute	ADJ
ijassa-1597	164	18	non	non	ADJ
ijassa-1597	164	19	-	-	ADJ
ijassa-1597	164	20	zero	zero	NUM
ijassa-1597	164	21	error	error	NOUN
ijassa-1597	164	22	βnae	βnae	NOUN
ijassa-1597	164	23	on	on	ADP
ijassa-1597	164	24	the	the	DET
ijassa-1597	164	25	number	number	NOUN
ijassa-1597	164	26	of	of	ADP
ijassa-1597	164	27	vertices	vertex	NOUN
ijassa-1597	164	28	n.	n.	ADJ
ijassa-1597	164	29	as	as	SCONJ
ijassa-1597	164	30	can	can	AUX
ijassa-1597	164	31	be	be	AUX
ijassa-1597	164	32	seen	see	VERB
ijassa-1597	164	33	from	from	ADP
ijassa-1597	164	34	fig	fig	NOUN
ijassa-1597	164	35	.	.	PUNCT
ijassa-1597	165	1	5.3	5.3	NUM
ijassa-1597	165	2	,	,	PUNCT
ijassa-1597	165	3	respectively	respectively	ADV
ijassa-1597	165	4	,	,	PUNCT
ijassa-1597	165	5	βnre	βnre	NOUN
ijassa-1597	165	6	decreases	decrease	VERB
ijassa-1597	165	7	with	with	ADP
ijassa-1597	165	8	increasing	increase	VERB
ijassa-1597	165	9	number	number	NOUN
ijassa-1597	165	10	of	of	ADP
ijassa-1597	165	11	vertices	vertex	NOUN
ijassa-1597	165	12	,	,	PUNCT
ijassa-1597	165	13	and	and	CCONJ
ijassa-1597	165	14	βnae	βnae	NOUN
ijassa-1597	165	15	grows	grow	VERB
ijassa-1597	165	16	slowly	slowly	ADV
ijassa-1597	165	17	,	,	PUNCT
ijassa-1597	165	18	which	which	PRON
ijassa-1597	165	19	makes	make	VERB
ijassa-1597	165	20	it	it	PRON
ijassa-1597	165	21	possible	possible	ADJ
ijassa-1597	165	22	to	to	PART
ijassa-1597	165	23	apply	apply	VERB
ijassa-1597	165	24	the	the	DET
ijassa-1597	165	25	method	method	NOUN
ijassa-1597	165	26	to	to	PART
ijassa-1597	165	27	graphs	graph	NOUN
ijassa-1597	165	28	with	with	ADP
ijassa-1597	165	29	a	a	DET
ijassa-1597	165	30	large	large	ADJ
ijassa-1597	165	31	number	number	NOUN
ijassa-1597	165	32	of	of	ADP
ijassa-1597	165	33	vertices	vertex	NOUN
ijassa-1597	165	34	.	.	PUNCT
ijassa-1597	166	1	the	the	DET
ijassa-1597	166	2	absolute	absolute	ADJ
ijassa-1597	166	3	error	error	NOUN
ijassa-1597	166	4	βnae	βnae	NOUN
ijassa-1597	166	5	remains	remain	VERB
ijassa-1597	166	6	approximately	approximately	ADV
ijassa-1597	166	7	at	at	ADP
ijassa-1597	166	8	the	the	DET
ijassa-1597	166	9	same	same	ADJ
ijassa-1597	166	10	level	level	NOUN
ijassa-1597	166	11	for	for	ADP
ijassa-1597	166	12	all	all	DET
ijassa-1597	166	13	n.	n.	NOUN
ijassa-1597	166	14	this	this	PRON
ijassa-1597	166	15	is	be	AUX
ijassa-1597	166	16	a	a	DET
ijassa-1597	166	17	consequence	consequence	NOUN
ijassa-1597	166	18	of	of	ADP
ijassa-1597	166	19	the	the	DET
ijassa-1597	166	20	fact	fact	NOUN
ijassa-1597	166	21	that	that	SCONJ
ijassa-1597	166	22	copyright	copyright	NOUN
ijassa-1597	166	23	©	©	PROPN
ijassa-1597	166	24	2024	2024	NUM
ijassa-1597	166	25	assa	assa	NOUN
ijassa-1597	166	26	.	.	PUNCT
ijassa-1597	167	1	adv	adv	PROPN
ijassa-1597	167	2	syst	syst	PROPN
ijassa-1597	167	3	sci	sci	PROPN
ijassa-1597	167	4	appl	appl	PROPN
ijassa-1597	167	5	(	(	PUNCT
ijassa-1597	167	6	2024	2024	NUM
ijassa-1597	167	7	)	)	PUNCT
ijassa-1597	167	8	100	100	NUM
ijassa-1597	167	9	a.	a.	NOUN
ijassa-1597	167	10	lazarev	lazarev	PROPN
ijassa-1597	167	11	,	,	PUNCT
ijassa-1597	167	12	d.	d.	PROPN
ijassa-1597	167	13	levtyuzhnikova	levtyuzhnikova	PROPN
ijassa-1597	167	14	,	,	PUNCT
ijassa-1597	167	15	i.	i.	PROPN
ijassa-1597	167	16	kudinov	kudinov	PROPN
ijassa-1597	167	17	fig	fig	PROPN
ijassa-1597	167	18	.	.	PUNCT
ijassa-1597	168	1	5.2	5.2	NUM
ijassa-1597	168	2	.	.	PUNCT
ijassa-1597	169	1	graph	graph	NOUN
ijassa-1597	169	2	of	of	ADP
ijassa-1597	169	3	the	the	DET
ijassa-1597	169	4	dependence	dependence	NOUN
ijassa-1597	169	5	of	of	ADP
ijassa-1597	169	6	the	the	DET
ijassa-1597	169	7	share	share	NOUN
ijassa-1597	169	8	of	of	ADP
ijassa-1597	169	9	cases	case	NOUN
ijassa-1597	169	10	µ	µ	VERB
ijassa-1597	169	11	for	for	ADP
ijassa-1597	169	12	which	which	PRON
ijassa-1597	169	13	the	the	DET
ijassa-1597	169	14	algorithm	algorithm	NOUN
ijassa-1597	169	15	obtained	obtain	VERB
ijassa-1597	169	16	a	a	DET
ijassa-1597	169	17	non	non	ADJ
ijassa-1597	169	18	-	-	ADJ
ijassa-1597	169	19	optimal	optimal	ADJ
ijassa-1597	169	20	solution	solution	NOUN
ijassa-1597	169	21	on	on	ADP
ijassa-1597	169	22	the	the	DET
ijassa-1597	169	23	number	number	NOUN
ijassa-1597	169	24	of	of	ADP
ijassa-1597	169	25	vertices	vertex	NOUN
ijassa-1597	169	26	n.	n.	VERB
ijassa-1597	169	27	it	it	PRON
ijassa-1597	169	28	slowly	slowly	ADV
ijassa-1597	169	29	grows	grow	VERB
ijassa-1597	169	30	with	with	ADP
ijassa-1597	169	31	the	the	DET
ijassa-1597	169	32	growth	growth	NOUN
ijassa-1597	169	33	of	of	ADP
ijassa-1597	169	34	n.	n.	NOUN
ijassa-1597	169	35	fluctuations	fluctuation	NOUN
ijassa-1597	169	36	between	between	ADP
ijassa-1597	169	37	even	even	ADV
ijassa-1597	169	38	and	and	CCONJ
ijassa-1597	169	39	odd	odd	ADJ
ijassa-1597	169	40	values	value	NOUN
ijassa-1597	169	41	of	of	ADP
ijassa-1597	169	42	n	n	X
ijassa-1597	169	43	is	be	AUX
ijassa-1597	169	44	due	due	ADJ
ijassa-1597	169	45	to	to	ADP
ijassa-1597	169	46	the	the	DET
ijassa-1597	169	47	fact	fact	NOUN
ijassa-1597	169	48	that	that	SCONJ
ijassa-1597	169	49	there	there	PRON
ijassa-1597	169	50	are	be	VERB
ijassa-1597	169	51	two	two	NUM
ijassa-1597	169	52	machines	machine	NOUN
ijassa-1597	169	53	in	in	ADP
ijassa-1597	169	54	considered	considered	ADJ
ijassa-1597	169	55	problem	problem	NOUN
ijassa-1597	169	56	(	(	PUNCT
ijassa-1597	169	57	a	a	X
ijassa-1597	169	58	)	)	PUNCT
ijassa-1597	169	59	(	(	PUNCT
ijassa-1597	169	60	b	b	X
ijassa-1597	169	61	)	)	PUNCT
ijassa-1597	169	62	fig	fig	NOUN
ijassa-1597	169	63	.	.	PUNCT
ijassa-1597	170	1	5.3	5.3	NUM
ijassa-1597	170	2	.	.	PUNCT
ijassa-1597	170	3	graphs	graph	NOUN
ijassa-1597	170	4	of	of	ADP
ijassa-1597	170	5	the	the	DET
ijassa-1597	170	6	dependence	dependence	NOUN
ijassa-1597	170	7	of	of	ADP
ijassa-1597	170	8	the	the	DET
ijassa-1597	170	9	relative	relative	ADJ
ijassa-1597	170	10	non	non	ADJ
ijassa-1597	170	11	-	-	ADJ
ijassa-1597	170	12	zero	zero	NUM
ijassa-1597	170	13	error	error	NOUN
ijassa-1597	170	14	βnre	βnre	NOUN
ijassa-1597	170	15	(	(	PUNCT
ijassa-1597	170	16	a	a	X
ijassa-1597	170	17	)	)	PUNCT
ijassa-1597	170	18	and	and	CCONJ
ijassa-1597	170	19	the	the	DET
ijassa-1597	170	20	absolute	absolute	ADJ
ijassa-1597	170	21	non	non	ADJ
ijassa-1597	170	22	-	-	ADJ
ijassa-1597	170	23	zero	zero	NUM
ijassa-1597	170	24	error	error	NOUN
ijassa-1597	170	25	βnae	βnae	NOUN
ijassa-1597	170	26	(	(	PUNCT
ijassa-1597	170	27	b	b	NOUN
ijassa-1597	170	28	)	)	PUNCT
ijassa-1597	170	29	indicators	indicator	NOUN
ijassa-1597	170	30	on	on	ADP
ijassa-1597	170	31	the	the	DET
ijassa-1597	170	32	number	number	NOUN
ijassa-1597	170	33	of	of	ADP
ijassa-1597	170	34	vertices	vertex	NOUN
ijassa-1597	170	35	n	n	X
ijassa-1597	170	36	at	at	ADP
ijassa-1597	170	37	1000	1000	NUM
ijassa-1597	170	38	generations	generation	NOUN
ijassa-1597	170	39	.	.	PUNCT
ijassa-1597	171	1	the	the	DET
ijassa-1597	171	2	cases	case	NOUN
ijassa-1597	171	3	n	n	CCONJ
ijassa-1597	171	4	≤	≤	NUM
ijassa-1597	171	5	4	4	NUM
ijassa-1597	171	6	are	be	AUX
ijassa-1597	171	7	trivial	trivial	ADJ
ijassa-1597	171	8	,	,	PUNCT
ijassa-1597	171	9	and	and	CCONJ
ijassa-1597	171	10	the	the	DET
ijassa-1597	171	11	polynomial	polynomial	ADJ
ijassa-1597	171	12	algorithms	algorithm	NOUN
ijassa-1597	171	13	always	always	ADV
ijassa-1597	171	14	get	get	VERB
ijassa-1597	171	15	an	an	DET
ijassa-1597	171	16	optimal	optimal	ADJ
ijassa-1597	171	17	solution	solution	NOUN
ijassa-1597	171	18	the	the	DET
ijassa-1597	171	19	polynomial	polynomial	ADJ
ijassa-1597	171	20	algorithms	algorithm	NOUN
ijassa-1597	171	21	absolute	absolute	ADJ
ijassa-1597	171	22	errors	error	NOUN
ijassa-1597	171	23	do	do	AUX
ijassa-1597	171	24	not	not	PART
ijassa-1597	171	25	tend	tend	VERB
ijassa-1597	171	26	to	to	PART
ijassa-1597	171	27	accumulate	accumulate	VERB
ijassa-1597	171	28	overtime	overtime	NOUN
ijassa-1597	171	29	and	and	CCONJ
ijassa-1597	171	30	”	"	PUNCT
ijassa-1597	171	31	fixes	fix	NOUN
ijassa-1597	171	32	”	"	PUNCT
ijassa-1597	171	33	each	each	DET
ijassa-1597	171	34	other	other	ADJ
ijassa-1597	171	35	due	due	ADP
ijassa-1597	171	36	to	to	ADP
ijassa-1597	171	37	the	the	DET
ijassa-1597	171	38	presence	presence	NOUN
ijassa-1597	171	39	of	of	ADP
ijassa-1597	171	40	two	two	NUM
ijassa-1597	171	41	machines	machine	NOUN
ijassa-1597	171	42	.	.	PUNCT
ijassa-1597	172	1	but	but	CCONJ
ijassa-1597	172	2	if	if	SCONJ
ijassa-1597	172	3	we	we	PRON
ijassa-1597	172	4	start	start	VERB
ijassa-1597	172	5	count	count	NOUN
ijassa-1597	172	6	cases	case	NOUN
ijassa-1597	172	7	of	of	ADP
ijassa-1597	172	8	zero	zero	NUM
ijassa-1597	172	9	error	error	NOUN
ijassa-1597	172	10	,	,	PUNCT
ijassa-1597	172	11	the	the	DET
ijassa-1597	172	12	full	full	ADJ
ijassa-1597	172	13	picture	picture	NOUN
ijassa-1597	172	14	changes	change	NOUN
ijassa-1597	172	15	.	.	PUNCT
ijassa-1597	173	1	as	as	SCONJ
ijassa-1597	173	2	can	can	AUX
ijassa-1597	173	3	be	be	AUX
ijassa-1597	173	4	seen	see	VERB
ijassa-1597	173	5	from	from	ADP
ijassa-1597	173	6	fig	fig	NOUN
ijassa-1597	173	7	.	.	PUNCT
ijassa-1597	174	1	5.4	5.4	NUM
ijassa-1597	174	2	,	,	PUNCT
ijassa-1597	174	3	the	the	DET
ijassa-1597	174	4	graphs	graph	NOUN
ijassa-1597	174	5	of	of	ADP
ijassa-1597	174	6	relative	relative	ADJ
ijassa-1597	174	7	and	and	CCONJ
ijassa-1597	174	8	absolute	absolute	ADJ
ijassa-1597	174	9	errors	error	NOUN
ijassa-1597	174	10	on	on	ADP
ijassa-1597	174	11	the	the	DET
ijassa-1597	174	12	number	number	NOUN
ijassa-1597	174	13	of	of	ADP
ijassa-1597	174	14	vertices	vertex	NOUN
ijassa-1597	174	15	show	show	VERB
ijassa-1597	174	16	a	a	DET
ijassa-1597	174	17	pairwise	pairwise	NOUN
ijassa-1597	174	18	relationship	relationship	NOUN
ijassa-1597	174	19	between	between	ADP
ijassa-1597	174	20	the	the	DET
ijassa-1597	174	21	algorithms	algorithm	NOUN
ijassa-1597	174	22	.	.	PUNCT
ijassa-1597	175	1	during	during	ADP
ijassa-1597	175	2	the	the	DET
ijassa-1597	175	3	near	near	ADV
ijassa-1597	175	4	-	-	PUNCT
ijassa-1597	175	5	constant	constant	ADJ
ijassa-1597	175	6	graph	graph	NOUN
ijassa-1597	175	7	of	of	ADP
ijassa-1597	175	8	βnae	βnae	NOUN
ijassa-1597	175	9	,	,	PUNCT
ijassa-1597	175	10	the	the	DET
ijassa-1597	175	11	growth	growth	NOUN
ijassa-1597	175	12	of	of	ADP
ijassa-1597	175	13	βae	βae	PROPN
ijassa-1597	175	14	means	mean	VERB
ijassa-1597	175	15	growth	growth	NOUN
ijassa-1597	175	16	of	of	ADP
ijassa-1597	175	17	the	the	DET
ijassa-1597	175	18	rate	rate	NOUN
ijassa-1597	175	19	of	of	ADP
ijassa-1597	175	20	errors	error	NOUN
ijassa-1597	175	21	.	.	PUNCT
ijassa-1597	176	1	all	all	DET
ijassa-1597	176	2	indicators	indicator	NOUN
ijassa-1597	176	3	show	show	VERB
ijassa-1597	176	4	a	a	DET
ijassa-1597	176	5	decrease	decrease	NOUN
ijassa-1597	176	6	in	in	ADP
ijassa-1597	176	7	the	the	DET
ijassa-1597	176	8	value	value	NOUN
ijassa-1597	176	9	of	of	ADP
ijassa-1597	176	10	the	the	DET
ijassa-1597	176	11	error	error	NOUN
ijassa-1597	176	12	when	when	SCONJ
ijassa-1597	176	13	the	the	DET
ijassa-1597	176	14	density	density	NOUN
ijassa-1597	176	15	of	of	ADP
ijassa-1597	176	16	the	the	DET
ijassa-1597	176	17	graph	graph	NOUN
ijassa-1597	176	18	d	d	NOUN
ijassa-1597	176	19	increases	increase	NOUN
ijassa-1597	176	20	,	,	PUNCT
ijassa-1597	176	21	as	as	SCONJ
ijassa-1597	176	22	look	look	VERB
ijassa-1597	176	23	in	in	ADP
ijassa-1597	176	24	fig	fig	NOUN
ijassa-1597	176	25	.	.	PUNCT
ijassa-1597	177	1	5.5	5.5	NUM
ijassa-1597	177	2	.	.	PUNCT
ijassa-1597	178	1	it	it	PRON
ijassa-1597	178	2	seems	seem	VERB
ijassa-1597	178	3	that	that	SCONJ
ijassa-1597	178	4	the	the	PRON
ijassa-1597	178	5	less	less	ADJ
ijassa-1597	178	6	the	the	DET
ijassa-1597	178	7	graph	graph	NOUN
ijassa-1597	178	8	density	density	NOUN
ijassa-1597	178	9	d	d	PROPN
ijassa-1597	178	10	,	,	PUNCT
ijassa-1597	178	11	the	the	PRON
ijassa-1597	178	12	smaller	small	ADJ
ijassa-1597	178	13	a	a	DET
ijassa-1597	178	14	space	space	NOUN
ijassa-1597	178	15	of	of	ADP
ijassa-1597	178	16	feasible	feasible	ADJ
ijassa-1597	178	17	schedules	schedule	NOUN
ijassa-1597	178	18	,	,	PUNCT
ijassa-1597	178	19	and	and	CCONJ
ijassa-1597	178	20	the	the	DET
ijassa-1597	178	21	remain	remain	NOUN
ijassa-1597	178	22	are	be	AUX
ijassa-1597	178	23	closer	close	ADJ
ijassa-1597	178	24	to	to	ADP
ijassa-1597	178	25	an	an	DET
ijassa-1597	178	26	optimal	optimal	ADJ
ijassa-1597	178	27	one	one	NUM
ijassa-1597	178	28	.	.	PUNCT
ijassa-1597	179	1	†https://www.gnu.org	†https://www.gnu.org	ADJ
ijassa-1597	179	2	/	/	SYM
ijassa-1597	179	3	software	software	NOUN
ijassa-1597	179	4	/	/	SYM
ijassa-1597	179	5	glpk	glpk	NOUN
ijassa-1597	179	6	/	/	SYM
ijassa-1597	179	7	glpk.html	glpk.html	PROPN
ijassa-1597	179	8	copyright	copyright	NOUN
ijassa-1597	179	9	©	©	PROPN
ijassa-1597	179	10	2024	2024	NUM
ijassa-1597	179	11	assa	assa	NOUN
ijassa-1597	179	12	.	.	PUNCT
ijassa-1597	180	1	adv	adv	PROPN
ijassa-1597	180	2	syst	syst	PROPN
ijassa-1597	180	3	sci	sci	PROPN
ijassa-1597	180	4	appl	appl	PROPN
ijassa-1597	180	5	(	(	PUNCT
ijassa-1597	180	6	2024	2024	NUM
ijassa-1597	180	7	)	)	PUNCT
ijassa-1597	180	8	practical	practical	ADJ
ijassa-1597	180	9	applicability	applicability	NOUN
ijassa-1597	180	10	of	of	ADP
ijassa-1597	180	11	the	the	DET
ijassa-1597	180	12	metric	metric	ADJ
ijassa-1597	180	13	approach	approach	NOUN
ijassa-1597	180	14	...	...	PUNCT
ijassa-1597	181	1	101	101	NUM
ijassa-1597	181	2	(	(	PUNCT
ijassa-1597	181	3	a	a	NOUN
ijassa-1597	181	4	)	)	PUNCT
ijassa-1597	181	5	(	(	PUNCT
ijassa-1597	181	6	b	b	X
ijassa-1597	181	7	)	)	PUNCT
ijassa-1597	181	8	fig	fig	NOUN
ijassa-1597	181	9	.	.	PUNCT
ijassa-1597	182	1	5.4	5.4	NUM
ijassa-1597	182	2	.	.	PUNCT
ijassa-1597	182	3	graph	graph	NOUN
ijassa-1597	182	4	of	of	ADP
ijassa-1597	182	5	the	the	DET
ijassa-1597	182	6	dependence	dependence	NOUN
ijassa-1597	182	7	of	of	ADP
ijassa-1597	182	8	the	the	DET
ijassa-1597	182	9	relative	relative	ADJ
ijassa-1597	182	10	error	error	NOUN
ijassa-1597	182	11	βre	βre	NOUN
ijassa-1597	182	12	(	(	PUNCT
ijassa-1597	182	13	a	a	NOUN
ijassa-1597	182	14	)	)	PUNCT
ijassa-1597	182	15	and	and	CCONJ
ijassa-1597	182	16	the	the	DET
ijassa-1597	182	17	absolute	absolute	ADJ
ijassa-1597	182	18	error	error	NOUN
ijassa-1597	182	19	βae	βae	NOUN
ijassa-1597	182	20	(	(	PUNCT
ijassa-1597	182	21	b	b	NOUN
ijassa-1597	182	22	)	)	PUNCT
ijassa-1597	182	23	on	on	ADP
ijassa-1597	182	24	the	the	DET
ijassa-1597	182	25	number	number	NOUN
ijassa-1597	182	26	of	of	ADP
ijassa-1597	182	27	vertices	vertex	NOUN
ijassa-1597	182	28	n	n	X
ijassa-1597	182	29	at	at	ADP
ijassa-1597	182	30	1000	1000	NUM
ijassa-1597	182	31	generations	generation	NOUN
ijassa-1597	182	32	fig	fig	NOUN
ijassa-1597	182	33	.	.	PUNCT
ijassa-1597	183	1	5.5	5.5	NUM
ijassa-1597	183	2	.	.	PUNCT
ijassa-1597	183	3	graph	graph	NOUN
ijassa-1597	183	4	of	of	ADP
ijassa-1597	183	5	the	the	DET
ijassa-1597	183	6	dependence	dependence	NOUN
ijassa-1597	183	7	of	of	ADP
ijassa-1597	183	8	the	the	DET
ijassa-1597	183	9	absolute	absolute	ADJ
ijassa-1597	183	10	error	error	NOUN
ijassa-1597	183	11	βae	βae	NOUN
ijassa-1597	183	12	on	on	ADP
ijassa-1597	183	13	the	the	DET
ijassa-1597	183	14	density	density	NOUN
ijassa-1597	183	15	d	d	PROPN
ijassa-1597	183	16	of	of	ADP
ijassa-1597	183	17	the	the	DET
ijassa-1597	183	18	graph	graph	NOUN
ijassa-1597	183	19	at	at	ADP
ijassa-1597	183	20	250	250	NUM
ijassa-1597	183	21	generations	generation	NOUN
ijassa-1597	183	22	6	6	NUM
ijassa-1597	183	23	.	.	PUNCT
ijassa-1597	184	1	conclusions	conclusion	NOUN
ijassa-1597	184	2	in	in	ADP
ijassa-1597	184	3	this	this	DET
ijassa-1597	184	4	paper	paper	NOUN
ijassa-1597	184	5	we	we	PRON
ijassa-1597	184	6	consider	consider	VERB
ijassa-1597	184	7	the	the	DET
ijassa-1597	184	8	possibility	possibility	NOUN
ijassa-1597	184	9	of	of	ADP
ijassa-1597	184	10	applying	apply	VERB
ijassa-1597	184	11	the	the	DET
ijassa-1597	184	12	metric	metric	ADJ
ijassa-1597	184	13	approach	approach	NOUN
ijassa-1597	184	14	to	to	PART
ijassa-1597	184	15	solve	solve	VERB
ijassa-1597	184	16	the	the	DET
ijassa-1597	184	17	np	np	ADV
ijassa-1597	184	18	-complete	-complete	ADJ
ijassa-1597	184	19	problem	problem	NOUN
ijassa-1597	184	20	p2	p2	NOUN
ijassa-1597	184	21	|	|	ADV
ijassa-1597	184	22	prec	prec	X
ijassa-1597	184	23	,	,	PUNCT
ijassa-1597	184	24	pj	pj	PROPN
ijassa-1597	184	25	∈	∈	PROPN
ijassa-1597	184	26	{	{	PUNCT
ijassa-1597	184	27	1	1	NUM
ijassa-1597	184	28	,	,	PUNCT
ijassa-1597	184	29	2	2	NUM
ijassa-1597	184	30	}	}	PUNCT
ijassa-1597	184	31	|	|	ADV
ijassa-1597	184	32	cmax	cmax	VERB
ijassa-1597	184	33	.	.	PUNCT
ijassa-1597	185	1	it	it	PRON
ijassa-1597	185	2	was	be	AUX
ijassa-1597	185	3	shown	show	VERB
ijassa-1597	185	4	that	that	SCONJ
ijassa-1597	185	5	if	if	SCONJ
ijassa-1597	185	6	the	the	DET
ijassa-1597	185	7	number	number	NOUN
ijassa-1597	185	8	of	of	ADP
ijassa-1597	185	9	restrictions	restriction	NOUN
ijassa-1597	185	10	increases	increase	NOUN
ijassa-1597	185	11	,	,	PUNCT
ijassa-1597	185	12	the	the	DET
ijassa-1597	185	13	absolute	absolute	ADJ
ijassa-1597	185	14	and	and	CCONJ
ijassa-1597	185	15	relative	relative	ADJ
ijassa-1597	185	16	error	error	NOUN
ijassa-1597	185	17	of	of	ADP
ijassa-1597	185	18	cmax	cmax	NOUN
ijassa-1597	185	19	change	change	VERB
ijassa-1597	185	20	slowly	slowly	ADV
ijassa-1597	185	21	.	.	PUNCT
ijassa-1597	186	1	besides	besides	SCONJ
ijassa-1597	186	2	,	,	PUNCT
ijassa-1597	186	3	the	the	DET
ijassa-1597	186	4	relative	relative	ADJ
ijassa-1597	186	5	non	non	ADJ
ijassa-1597	186	6	-	-	ADJ
ijassa-1597	186	7	zero	zero	NUM
ijassa-1597	186	8	error	error	NOUN
ijassa-1597	186	9	value	value	NOUN
ijassa-1597	186	10	decreases	decrease	VERB
ijassa-1597	186	11	,	,	PUNCT
ijassa-1597	186	12	if	if	SCONJ
ijassa-1597	186	13	the	the	DET
ijassa-1597	186	14	number	number	NOUN
ijassa-1597	186	15	of	of	ADP
ijassa-1597	186	16	vertices	vertex	NOUN
ijassa-1597	186	17	in	in	ADP
ijassa-1597	186	18	the	the	DET
ijassa-1597	186	19	graph	graph	NOUN
ijassa-1597	186	20	grows	grow	VERB
ijassa-1597	186	21	.	.	PUNCT
ijassa-1597	187	1	in	in	ADP
ijassa-1597	187	2	addition	addition	NOUN
ijassa-1597	187	3	,	,	PUNCT
ijassa-1597	187	4	it	it	PRON
ijassa-1597	187	5	turned	turn	VERB
ijassa-1597	187	6	out	out	ADP
ijassa-1597	187	7	to	to	PART
ijassa-1597	187	8	be	be	AUX
ijassa-1597	187	9	more	more	ADV
ijassa-1597	187	10	efficient	efficient	ADJ
ijassa-1597	187	11	to	to	PART
ijassa-1597	187	12	use	use	VERB
ijassa-1597	187	13	the	the	DET
ijassa-1597	187	14	coffman	coffman	PROPN
ijassa-1597	187	15	’s	’s	PART
ijassa-1597	187	16	and	and	CCONJ
ijassa-1597	187	17	gabow	gabow	VERB
ijassa-1597	187	18	’s	’s	PART
ijassa-1597	187	19	algorithms	algorithm	NOUN
ijassa-1597	187	20	in	in	ADP
ijassa-1597	187	21	finding	find	VERB
ijassa-1597	187	22	an	an	DET
ijassa-1597	187	23	approximate	approximate	ADJ
ijassa-1597	187	24	solution	solution	NOUN
ijassa-1597	187	25	of	of	ADP
ijassa-1597	187	26	this	this	DET
ijassa-1597	187	27	problem	problem	NOUN
ijassa-1597	187	28	by	by	ADP
ijassa-1597	187	29	the	the	DET
ijassa-1597	187	30	method	method	NOUN
ijassa-1597	187	31	discussed	discuss	VERB
ijassa-1597	187	32	in	in	ADP
ijassa-1597	187	33	this	this	DET
ijassa-1597	187	34	paper	paper	NOUN
ijassa-1597	187	35	.	.	PUNCT
ijassa-1597	188	1	the	the	DET
ijassa-1597	188	2	obtained	obtain	VERB
ijassa-1597	188	3	average	average	ADJ
ijassa-1597	188	4	absolute	absolute	ADJ
ijassa-1597	188	5	error	error	NOUN
ijassa-1597	188	6	cmax(πa)−	cmax(πa)−	NOUN
ijassa-1597	188	7	cmax(π	cmax(π	ADP
ijassa-1597	188	8	∗	∗	NOUN
ijassa-1597	188	9	a	a	PRON
ijassa-1597	188	10	)	)	PUNCT
ijassa-1597	188	11	seems	seem	VERB
ijassa-1597	188	12	to	to	PART
ijassa-1597	188	13	be	be	AUX
ijassa-1597	188	14	depends	depend	VERB
ijassa-1597	188	15	only	only	ADV
ijassa-1597	188	16	on	on	ADP
ijassa-1597	188	17	n	n	PRON
ijassa-1597	188	18	and	and	CCONJ
ijassa-1597	188	19	d	d	X
ijassa-1597	188	20	on	on	ADP
ijassa-1597	188	21	sets	set	NOUN
ijassa-1597	188	22	of	of	ADP
ijassa-1597	188	23	all	all	DET
ijassa-1597	188	24	dags	dag	NOUN
ijassa-1597	188	25	of	of	ADP
ijassa-1597	188	26	classes	class	NOUN
ijassa-1597	188	27	considered	consider	VERB
ijassa-1597	188	28	above	above	ADV
ijassa-1597	188	29	.	.	PUNCT
ijassa-1597	189	1	however	however	ADV
ijassa-1597	189	2	,	,	PUNCT
ijassa-1597	189	3	this	this	DET
ijassa-1597	189	4	result	result	NOUN
ijassa-1597	189	5	could	could	AUX
ijassa-1597	189	6	not	not	PART
ijassa-1597	189	7	be	be	AUX
ijassa-1597	189	8	proved	prove	VERB
ijassa-1597	189	9	analytically	analytically	ADV
ijassa-1597	189	10	at	at	ADP
ijassa-1597	189	11	this	this	DET
ijassa-1597	189	12	moment	moment	NOUN
ijassa-1597	189	13	.	.	PUNCT
ijassa-1597	190	1	acknowledgements	acknowledgement	NOUN
ijassa-1597	190	2	copyright	copyright	NOUN
ijassa-1597	190	3	©	©	ADP
ijassa-1597	190	4	2024	2024	NUM
ijassa-1597	190	5	assa	assa	NOUN
ijassa-1597	190	6	.	.	PUNCT
ijassa-1597	191	1	adv	adv	PROPN
ijassa-1597	191	2	syst	syst	PROPN
ijassa-1597	191	3	sci	sci	PROPN
ijassa-1597	191	4	appl	appl	PROPN
ijassa-1597	191	5	(	(	PUNCT
ijassa-1597	191	6	2024	2024	NUM
ijassa-1597	191	7	)	)	PUNCT
ijassa-1597	191	8	102	102	NUM
ijassa-1597	191	9	a.	a.	NOUN
ijassa-1597	191	10	lazarev	lazarev	PROPN
ijassa-1597	191	11	,	,	PUNCT
ijassa-1597	191	12	d.	d.	PROPN
ijassa-1597	191	13	levtyuzhnikova	levtyuzhnikova	PROPN
ijassa-1597	191	14	,	,	PUNCT
ijassa-1597	191	15	i.	i.	PROPN
ijassa-1597	191	16	kudinov	kudinov	VERB
ijassa-1597	191	17	the	the	DET
ijassa-1597	191	18	results	result	NOUN
ijassa-1597	191	19	of	of	ADP
ijassa-1597	191	20	this	this	DET
ijassa-1597	191	21	paper	paper	NOUN
ijassa-1597	191	22	partly	partly	ADV
ijassa-1597	191	23	were	be	AUX
ijassa-1597	191	24	obtained	obtain	VERB
ijassa-1597	191	25	within	within	ADP
ijassa-1597	191	26	the	the	DET
ijassa-1597	191	27	rsf	rsf	PROPN
ijassa-1597	191	28	grant	grant	NOUN
ijassa-1597	191	29	(	(	PUNCT
ijassa-1597	191	30	project	project	VERB
ijassa-1597	191	31	no	no	NOUN
ijassa-1597	191	32	.	.	NOUN
ijassa-1597	192	1	22	22	NUM
ijassa-1597	192	2	-	-	SYM
ijassa-1597	192	3	7110131	7110131	NUM
ijassa-1597	192	4	)	)	PUNCT
ijassa-1597	192	5	.	.	PUNCT
ijassa-1597	193	1	we	we	PRON
ijassa-1597	193	2	thanks	thanks	PROPN
ijassa-1597	193	3	e.	e.	PROPN
ijassa-1597	193	4	bukueva	bukueva	PROPN
ijassa-1597	193	5	for	for	ADP
ijassa-1597	193	6	assistance	assistance	NOUN
ijassa-1597	193	7	on	on	ADP
ijassa-1597	193	8	in	in	ADP
ijassa-1597	193	9	the	the	DET
ijassa-1597	193	10	early	early	ADJ
ijassa-1597	193	11	stages	stage	NOUN
ijassa-1597	193	12	of	of	ADP
ijassa-1597	193	13	the	the	DET
ijassa-1597	193	14	work	work	NOUN
ijassa-1597	193	15	.	.	PUNCT
ijassa-1597	194	1	references	reference	NOUN
ijassa-1597	194	2	1	1	NUM
ijassa-1597	194	3	.	.	PUNCT
ijassa-1597	194	4	lazarev	lazarev	PROPN
ijassa-1597	194	5	,	,	PUNCT
ijassa-1597	194	6	a.	a.	NOUN
ijassa-1597	194	7	(	(	PUNCT
ijassa-1597	194	8	2019	2019	NUM
ijassa-1597	194	9	)	)	PUNCT
ijassa-1597	194	10	scheduling	scheduling	NOUN
ijassa-1597	194	11	theory	theory	NOUN
ijassa-1597	194	12	.	.	PUNCT
ijassa-1597	195	1	methods	method	NOUN
ijassa-1597	195	2	and	and	CCONJ
ijassa-1597	195	3	algorithms	algorithm	NOUN
ijassa-1597	195	4	.	.	PUNCT
ijassa-1597	196	1	moscow	moscow	PROPN
ijassa-1597	196	2	,	,	PUNCT
ijassa-1597	196	3	russia	russia	PROPN
ijassa-1597	196	4	:	:	PUNCT
ijassa-1597	196	5	ics	ics	PROPN
ijassa-1597	196	6	ras	ras	PROPN
ijassa-1597	196	7	.	.	PROPN
ijassa-1597	196	8	2	2	NUM
ijassa-1597	196	9	.	.	X
ijassa-1597	196	10	lazarev	lazarev	PROPN
ijassa-1597	196	11	,	,	PUNCT
ijassa-1597	196	12	a.	a.	PROPN
ijassa-1597	196	13	,	,	PUNCT
ijassa-1597	196	14	lemtyuzhnikova	lemtyuzhnikova	PROPN
ijassa-1597	196	15	,	,	PUNCT
ijassa-1597	196	16	d.	d.	PROPN
ijassa-1597	196	17	&	&	CCONJ
ijassa-1597	196	18	werner	werner	PROPN
ijassa-1597	196	19	f.	f.	PROPN
ijassa-1597	196	20	(	(	PUNCT
ijassa-1597	196	21	2021	2021	NUM
ijassa-1597	196	22	)	)	PUNCT
ijassa-1597	196	23	a	a	DET
ijassa-1597	196	24	metric	metric	ADJ
ijassa-1597	196	25	approach	approach	NOUN
ijassa-1597	196	26	for	for	ADP
ijassa-1597	196	27	scheduling	scheduling	NOUN
ijassa-1597	196	28	problems	problem	NOUN
ijassa-1597	196	29	with	with	ADP
ijassa-1597	196	30	minimizing	minimize	VERB
ijassa-1597	196	31	the	the	DET
ijassa-1597	196	32	maximum	maximum	ADJ
ijassa-1597	196	33	penalty	penalty	NOUN
ijassa-1597	196	34	,	,	PUNCT
ijassa-1597	196	35	applied	apply	VERB
ijassa-1597	196	36	mathematical	mathematical	ADJ
ijassa-1597	196	37	modelling	modelling	NOUN
ijassa-1597	196	38	,	,	PUNCT
ijassa-1597	196	39	89	89	NUM
ijassa-1597	196	40	,	,	PUNCT
ijassa-1597	196	41	1163–1176	1163–1176	NUM
ijassa-1597	196	42	.	.	PUNCT
ijassa-1597	197	1	3	3	X
ijassa-1597	197	2	.	.	X
ijassa-1597	197	3	lazarev	lazarev	PROPN
ijassa-1597	197	4	,	,	PUNCT
ijassa-1597	197	5	a.	a.	PROPN
ijassa-1597	197	6	&	&	CCONJ
ijassa-1597	197	7	arkhipov	arkhipov	PROPN
ijassa-1597	197	8	,	,	PUNCT
ijassa-1597	197	9	b.	b.	PROPN
ijassa-1597	197	10	(	(	PUNCT
ijassa-1597	197	11	2018	2018	NUM
ijassa-1597	197	12	)	)	PUNCT
ijassa-1597	197	13	estimation	estimation	NOUN
ijassa-1597	197	14	of	of	ADP
ijassa-1597	197	15	the	the	DET
ijassa-1597	197	16	absolute	absolute	ADJ
ijassa-1597	197	17	error	error	NOUN
ijassa-1597	197	18	and	and	CCONJ
ijassa-1597	197	19	polynomial	polynomial	ADJ
ijassa-1597	197	20	solvability	solvability	NOUN
ijassa-1597	197	21	for	for	ADP
ijassa-1597	197	22	a	a	DET
ijassa-1597	197	23	classical	classical	ADJ
ijassa-1597	197	24	np	np	ADJ
ijassa-1597	197	25	-	-	PUNCT
ijassa-1597	197	26	hard	hard	ADJ
ijassa-1597	197	27	scheduling	scheduling	NOUN
ijassa-1597	197	28	problem	problem	NOUN
ijassa-1597	197	29	,	,	PUNCT
ijassa-1597	197	30	doklady	doklady	NOUN
ijassa-1597	197	31	mathematics	mathematic	NOUN
ijassa-1597	197	32	,	,	PUNCT
ijassa-1597	197	33	97	97	NUM
ijassa-1597	197	34	,	,	PUNCT
ijassa-1597	197	35	262–265	262–265	NUM
ijassa-1597	197	36	.	.	PUNCT
ijassa-1597	198	1	4	4	NUM
ijassa-1597	198	2	.	.	X
ijassa-1597	198	3	fujii	fujii	PROPN
ijassa-1597	198	4	,	,	PUNCT
ijassa-1597	198	5	m.	m.	NOUN
ijassa-1597	198	6	,	,	PUNCT
ijassa-1597	198	7	kasami	kasami	NOUN
ijassa-1597	198	8	,	,	PUNCT
ijassa-1597	198	9	t.	t.	PROPN
ijassa-1597	198	10	&	&	CCONJ
ijassa-1597	198	11	ninomiya	ninomiya	PROPN
ijassa-1597	198	12	,	,	PUNCT
ijassa-1597	198	13	k.	k.	PROPN
ijassa-1597	198	14	(	(	PUNCT
ijassa-1597	198	15	1969	1969	NUM
ijassa-1597	198	16	)	)	PUNCT
ijassa-1597	198	17	optimal	optimal	ADJ
ijassa-1597	198	18	sequencing	sequencing	NOUN
ijassa-1597	198	19	of	of	ADP
ijassa-1597	198	20	two	two	NUM
ijassa-1597	198	21	equivalent	equivalent	ADJ
ijassa-1597	198	22	processors	processor	NOUN
ijassa-1597	198	23	,	,	PUNCT
ijassa-1597	198	24	siam	siam	ADJ
ijassa-1597	198	25	journal	journal	NOUN
ijassa-1597	198	26	on	on	ADP
ijassa-1597	198	27	applied	apply	VERB
ijassa-1597	198	28	mathematics	mathematic	NOUN
ijassa-1597	198	29	,	,	PUNCT
ijassa-1597	198	30	17(4	17(4	NUM
ijassa-1597	198	31	)	)	PUNCT
ijassa-1597	198	32	,	,	PUNCT
ijassa-1597	198	33	784–789	784–789	NUM
ijassa-1597	198	34	.	.	NOUN
ijassa-1597	199	1	5	5	NUM
ijassa-1597	199	2	.	.	PUNCT
ijassa-1597	199	3	coffman	coffman	PROPN
ijassa-1597	199	4	e.	e.	PROPN
ijassa-1597	199	5	g.	g.	PROPN
ijassa-1597	199	6	&	&	CCONJ
ijassa-1597	199	7	graham	graham	PROPN
ijassa-1597	199	8	r.	r.	PROPN
ijassa-1597	199	9	l.	l.	PROPN
ijassa-1597	199	10	(	(	PUNCT
ijassa-1597	199	11	1972	1972	NUM
ijassa-1597	199	12	)	)	PUNCT
ijassa-1597	199	13	optimal	optimal	ADJ
ijassa-1597	199	14	scheduling	scheduling	NOUN
ijassa-1597	199	15	for	for	ADP
ijassa-1597	199	16	two	two	NUM
ijassa-1597	199	17	-	-	PUNCT
ijassa-1597	199	18	processor	processor	NOUN
ijassa-1597	199	19	systems	system	NOUN
ijassa-1597	199	20	,	,	PUNCT
ijassa-1597	199	21	acta	acta	PROPN
ijassa-1597	199	22	informatica	informatica	PROPN
ijassa-1597	199	23	,	,	PUNCT
ijassa-1597	199	24	1(3	1(3	NUM
ijassa-1597	199	25	)	)	PUNCT
ijassa-1597	199	26	,	,	PUNCT
ijassa-1597	199	27	200–213	200–213	NUM
ijassa-1597	199	28	.	.	NOUN
ijassa-1597	200	1	6	6	NUM
ijassa-1597	200	2	.	.	X
ijassa-1597	201	1	sethi	sethi	PROPN
ijassa-1597	201	2	,	,	PUNCT
ijassa-1597	201	3	r.	r.	PROPN
ijassa-1597	201	4	(	(	PUNCT
ijassa-1597	201	5	1976	1976	NUM
ijassa-1597	201	6	)	)	PUNCT
ijassa-1597	201	7	scheduling	scheduling	NOUN
ijassa-1597	201	8	graphs	graph	NOUN
ijassa-1597	201	9	on	on	ADP
ijassa-1597	201	10	two	two	NUM
ijassa-1597	201	11	processors	processor	NOUN
ijassa-1597	201	12	,	,	PUNCT
ijassa-1597	201	13	siam	siam	ADJ
ijassa-1597	201	14	journal	journal	NOUN
ijassa-1597	201	15	on	on	ADP
ijassa-1597	201	16	computing	computing	NOUN
ijassa-1597	201	17	,	,	PUNCT
ijassa-1597	201	18	5(1	5(1	NUM
ijassa-1597	201	19	)	)	PUNCT
ijassa-1597	201	20	,	,	PUNCT
ijassa-1597	201	21	73–82	73–82	NUM
ijassa-1597	201	22	.	.	NOUN
ijassa-1597	201	23	7	7	NUM
ijassa-1597	201	24	.	.	X
ijassa-1597	201	25	gabow	gabow	PROPN
ijassa-1597	201	26	,	,	PUNCT
ijassa-1597	201	27	h.	h.	PROPN
ijassa-1597	201	28	n.	n.	PROPN
ijassa-1597	201	29	(	(	PUNCT
ijassa-1597	201	30	1982	1982	NUM
ijassa-1597	201	31	)	)	PUNCT
ijassa-1597	201	32	an	an	DET
ijassa-1597	201	33	almost	almost	ADV
ijassa-1597	201	34	-	-	PUNCT
ijassa-1597	201	35	linear	linear	NOUN
ijassa-1597	201	36	algorithm	algorithm	NOUN
ijassa-1597	201	37	for	for	ADP
ijassa-1597	201	38	two	two	NUM
ijassa-1597	201	39	-	-	PUNCT
ijassa-1597	201	40	processor	processor	NOUN
ijassa-1597	201	41	scheduling	scheduling	NOUN
ijassa-1597	201	42	,	,	PUNCT
ijassa-1597	201	43	journal	journal	NOUN
ijassa-1597	201	44	of	of	ADP
ijassa-1597	201	45	the	the	DET
ijassa-1597	201	46	acm	acm	NOUN
ijassa-1597	201	47	(	(	PUNCT
ijassa-1597	201	48	jacm	jacm	PROPN
ijassa-1597	201	49	)	)	PUNCT
ijassa-1597	201	50	,	,	PUNCT
ijassa-1597	201	51	29(3	29(3	NUM
ijassa-1597	201	52	)	)	PUNCT
ijassa-1597	201	53	,	,	PUNCT
ijassa-1597	201	54	766–780	766–780	NUM
ijassa-1597	201	55	.	.	NOUN
ijassa-1597	201	56	8	8	NUM
ijassa-1597	201	57	.	.	X
ijassa-1597	201	58	ullman	ullman	PROPN
ijassa-1597	201	59	,	,	PUNCT
ijassa-1597	201	60	j.	j.	PROPN
ijassa-1597	201	61	d.	d.	PROPN
ijassa-1597	201	62	(	(	PUNCT
ijassa-1597	201	63	1975	1975	NUM
ijassa-1597	201	64	)	)	PUNCT
ijassa-1597	201	65	np	np	X
ijassa-1597	201	66	-	-	PUNCT
ijassa-1597	201	67	complete	complete	ADJ
ijassa-1597	201	68	scheduling	scheduling	NOUN
ijassa-1597	201	69	problems	problem	NOUN
ijassa-1597	201	70	,	,	PUNCT
ijassa-1597	201	71	journal	journal	NOUN
ijassa-1597	201	72	of	of	ADP
ijassa-1597	201	73	computer	computer	NOUN
ijassa-1597	201	74	and	and	CCONJ
ijassa-1597	201	75	system	system	NOUN
ijassa-1597	201	76	sciences	science	NOUN
ijassa-1597	201	77	,	,	PUNCT
ijassa-1597	201	78	10(3	10(3	NUM
ijassa-1597	201	79	)	)	PUNCT
ijassa-1597	201	80	,	,	PUNCT
ijassa-1597	201	81	384–393	384–393	NUM
ijassa-1597	201	82	.	.	PUNCT
ijassa-1597	202	1	9	9	NUM
ijassa-1597	202	2	.	.	X
ijassa-1597	202	3	van	van	PROPN
ijassa-1597	202	4	bevern	bevern	PROPN
ijassa-1597	202	5	,	,	PUNCT
ijassa-1597	202	6	r.	r.	PROPN
ijassa-1597	202	7	,	,	PUNCT
ijassa-1597	202	8	bredereck	bredereck	NOUN
ijassa-1597	202	9	,	,	PUNCT
ijassa-1597	202	10	r.	r.	PROPN
ijassa-1597	202	11	,	,	PUNCT
ijassa-1597	202	12	bulteau	bulteau	PROPN
ijassa-1597	202	13	,	,	PUNCT
ijassa-1597	202	14	l.	l.	PROPN
ijassa-1597	202	15	,	,	PUNCT
ijassa-1597	202	16	komusiewicz	komusiewicz	PROPN
ijassa-1597	202	17	,	,	PUNCT
ijassa-1597	202	18	c.	c.	PROPN
ijassa-1597	202	19	,	,	PUNCT
ijassa-1597	202	20	talmon	talmon	PROPN
ijassa-1597	202	21	,	,	PUNCT
ijassa-1597	202	22	n.	n.	NOUN
ijassa-1597	202	23	,	,	PUNCT
ijassa-1597	202	24	et	et	PROPN
ijassa-1597	202	25	al	al	PROPN
ijassa-1597	202	26	.	.	PUNCT
ijassa-1597	203	1	(	(	PUNCT
ijassa-1597	203	2	2016	2016	NUM
ijassa-1597	203	3	)	)	PUNCT
ijassa-1597	203	4	precedence	precedence	NOUN
ijassa-1597	203	5	-	-	PUNCT
ijassa-1597	203	6	constrained	constrain	VERB
ijassa-1597	203	7	scheduling	scheduling	NOUN
ijassa-1597	203	8	problems	problem	NOUN
ijassa-1597	203	9	parameterized	parameterize	VERB
ijassa-1597	203	10	by	by	ADP
ijassa-1597	203	11	partial	partial	ADJ
ijassa-1597	203	12	order	order	NOUN
ijassa-1597	203	13	width	width	NOUN
ijassa-1597	203	14	,	,	PUNCT
ijassa-1597	203	15	international	international	ADJ
ijassa-1597	203	16	conference	conference	NOUN
ijassa-1597	203	17	on	on	ADP
ijassa-1597	203	18	discrete	discrete	ADJ
ijassa-1597	203	19	optimization	optimization	NOUN
ijassa-1597	203	20	and	and	CCONJ
ijassa-1597	203	21	operations	operation	NOUN
ijassa-1597	203	22	research	research	NOUN
ijassa-1597	203	23	–	–	PUNCT
ijassa-1597	203	24	springer	springer	NOUN
ijassa-1597	203	25	,	,	PUNCT
ijassa-1597	203	26	cham	cham	NOUN
ijassa-1597	203	27	,	,	PUNCT
ijassa-1597	203	28	105–120	105–120	NUM
ijassa-1597	203	29	.	.	NOUN
ijassa-1597	203	30	10	10	NUM
ijassa-1597	203	31	.	.	PUNCT
ijassa-1597	204	1	nakajima	nakajima	PROPN
ijassa-1597	204	2	,	,	PUNCT
ijassa-1597	204	3	k.	k.	PROPN
ijassa-1597	204	4	,	,	PUNCT
ijassa-1597	204	5	leung	leung	PROPN
ijassa-1597	204	6	,	,	PUNCT
ijassa-1597	204	7	j.	j.	PROPN
ijassa-1597	204	8	&	&	CCONJ
ijassa-1597	204	9	hakimi	hakimi	PROPN
ijassa-1597	204	10	,	,	PUNCT
ijassa-1597	204	11	s.	s.	PROPN
ijassa-1597	204	12	l.	l.	PROPN
ijassa-1597	204	13	(	(	PUNCT
ijassa-1597	204	14	1981	1981	NUM
ijassa-1597	204	15	)	)	PUNCT
ijassa-1597	204	16	optimal	optimal	ADJ
ijassa-1597	204	17	two	two	NUM
ijassa-1597	204	18	processor	processor	NOUN
ijassa-1597	204	19	scheduling	scheduling	NOUN
ijassa-1597	204	20	of	of	ADP
ijassa-1597	204	21	tree	tree	NOUN
ijassa-1597	204	22	precedence	precedence	VERB
ijassa-1597	204	23	constrained	constrain	VERB
ijassa-1597	204	24	tasks	task	NOUN
ijassa-1597	204	25	with	with	ADP
ijassa-1597	204	26	two	two	NUM
ijassa-1597	204	27	execution	execution	NOUN
ijassa-1597	204	28	times	time	NOUN
ijassa-1597	204	29	,	,	PUNCT
ijassa-1597	204	30	performance	performance	NOUN
ijassa-1597	204	31	evaluation	evaluation	NOUN
ijassa-1597	204	32	,	,	PUNCT
ijassa-1597	204	33	1(4	1(4	NUM
ijassa-1597	204	34	)	)	PUNCT
ijassa-1597	204	35	,	,	PUNCT
ijassa-1597	204	36	320–330	320–330	NUM
ijassa-1597	204	37	.	.	PUNCT
ijassa-1597	205	1	11	11	NUM
ijassa-1597	205	2	.	.	PUNCT
ijassa-1597	206	1	kaufman	kaufman	PROPN
ijassa-1597	206	2	,	,	PUNCT
ijassa-1597	206	3	m.	m.	NOUN
ijassa-1597	206	4	t.	t.	PROPN
ijassa-1597	206	5	(	(	PUNCT
ijassa-1597	206	6	1974	1974	NUM
ijassa-1597	206	7	)	)	PUNCT
ijassa-1597	206	8	an	an	DET
ijassa-1597	206	9	almost	almost	ADV
ijassa-1597	206	10	-	-	PUNCT
ijassa-1597	206	11	optimal	optimal	ADJ
ijassa-1597	206	12	algorithm	algorithm	NOUN
ijassa-1597	206	13	for	for	ADP
ijassa-1597	206	14	the	the	DET
ijassa-1597	206	15	assembly	assembly	NOUN
ijassa-1597	206	16	line	line	NOUN
ijassa-1597	206	17	scheduling	scheduling	NOUN
ijassa-1597	206	18	problem	problem	NOUN
ijassa-1597	206	19	,	,	PUNCT
ijassa-1597	206	20	ieee	ieee	NOUN
ijassa-1597	206	21	transactions	transaction	NOUN
ijassa-1597	206	22	on	on	ADP
ijassa-1597	206	23	computers	computer	NOUN
ijassa-1597	206	24	,	,	PUNCT
ijassa-1597	206	25	100(11	100(11	NUM
ijassa-1597	206	26	)	)	PUNCT
ijassa-1597	206	27	,	,	PUNCT
ijassa-1597	206	28	1169–1174	1169–1174	NUM
ijassa-1597	206	29	.	.	PUNCT
ijassa-1597	206	30	12	12	NUM
ijassa-1597	206	31	.	.	PUNCT
ijassa-1597	206	32	du	du	PROPN
ijassa-1597	206	33	j.	j.	PROPN
ijassa-1597	206	34	&	&	CCONJ
ijassa-1597	206	35	leung	leung	PROPN
ijassa-1597	206	36	j.	j.	PROPN
ijassa-1597	206	37	y.	y.	PROPN
ijassa-1597	206	38	t.	t.	PROPN
ijassa-1597	206	39	(	(	PUNCT
ijassa-1597	206	40	1989	1989	NUM
ijassa-1597	206	41	)	)	PUNCT
ijassa-1597	206	42	scheduling	scheduling	NOUN
ijassa-1597	206	43	tree	tree	NOUN
ijassa-1597	206	44	-	-	PUNCT
ijassa-1597	206	45	structured	structure	VERB
ijassa-1597	206	46	tasks	task	NOUN
ijassa-1597	206	47	on	on	ADP
ijassa-1597	206	48	two	two	NUM
ijassa-1597	206	49	processors	processor	NOUN
ijassa-1597	206	50	to	to	PART
ijassa-1597	206	51	minimize	minimize	VERB
ijassa-1597	206	52	schedule	schedule	NOUN
ijassa-1597	206	53	length	length	NOUN
ijassa-1597	206	54	,	,	PUNCT
ijassa-1597	206	55	siam	siam	ADJ
ijassa-1597	206	56	journal	journal	NOUN
ijassa-1597	206	57	on	on	ADP
ijassa-1597	206	58	discrete	discrete	ADJ
ijassa-1597	206	59	mathematics	mathematic	NOUN
ijassa-1597	206	60	,	,	PUNCT
ijassa-1597	206	61	2(2	2(2	NUM
ijassa-1597	206	62	)	)	PUNCT
ijassa-1597	206	63	,	,	PUNCT
ijassa-1597	206	64	176–196	176–196	NUM
ijassa-1597	206	65	.	.	PUNCT
ijassa-1597	207	1	13	13	NUM
ijassa-1597	207	2	.	.	PUNCT
ijassa-1597	207	3	hu	hu	PROPN
ijassa-1597	207	4	,	,	PUNCT
ijassa-1597	207	5	t.	t.	PROPN
ijassa-1597	207	6	c.	c.	PROPN
ijassa-1597	207	7	(	(	PUNCT
ijassa-1597	207	8	1961	1961	NUM
ijassa-1597	207	9	)	)	PUNCT
ijassa-1597	207	10	parallel	parallel	ADJ
ijassa-1597	207	11	sequencing	sequencing	NOUN
ijassa-1597	207	12	and	and	CCONJ
ijassa-1597	207	13	assembly	assembly	NOUN
ijassa-1597	207	14	line	line	NOUN
ijassa-1597	207	15	problems	problem	NOUN
ijassa-1597	207	16	,	,	PUNCT
ijassa-1597	207	17	operations	operation	NOUN
ijassa-1597	207	18	research	research	NOUN
ijassa-1597	207	19	,	,	PUNCT
ijassa-1597	207	20	9(6	9(6	NUM
ijassa-1597	207	21	)	)	PUNCT
ijassa-1597	207	22	,	,	PUNCT
ijassa-1597	207	23	841–848	841–848	NUM
ijassa-1597	207	24	.	.	PUNCT
ijassa-1597	208	1	14	14	NUM
ijassa-1597	208	2	.	.	PUNCT
ijassa-1597	209	1	dolev	dolev	PROPN
ijassa-1597	209	2	,	,	PUNCT
ijassa-1597	209	3	d.	d.	PROPN
ijassa-1597	209	4	&	&	CCONJ
ijassa-1597	209	5	warmuth	warmuth	PROPN
ijassa-1597	209	6	,	,	PUNCT
ijassa-1597	209	7	m.	m.	NOUN
ijassa-1597	209	8	(	(	PUNCT
ijassa-1597	209	9	1985	1985	NUM
ijassa-1597	209	10	)	)	PUNCT
ijassa-1597	209	11	scheduling	schedule	VERB
ijassa-1597	209	12	flat	flat	ADJ
ijassa-1597	209	13	graphs	graph	NOUN
ijassa-1597	209	14	,	,	PUNCT
ijassa-1597	209	15	siam	siam	ADJ
ijassa-1597	209	16	journal	journal	NOUN
ijassa-1597	209	17	on	on	ADP
ijassa-1597	209	18	computing	computing	PROPN
ijassa-1597	209	19	,	,	PUNCT
ijassa-1597	209	20	14(3	14(3	NUM
ijassa-1597	209	21	)	)	PUNCT
ijassa-1597	209	22	,	,	PUNCT
ijassa-1597	209	23	638–657	638–657	NUM
ijassa-1597	209	24	.	.	PUNCT
ijassa-1597	210	1	copyright	copyright	NOUN
ijassa-1597	210	2	©	©	PROPN
ijassa-1597	210	3	2024	2024	NUM
ijassa-1597	210	4	assa	assa	NOUN
ijassa-1597	210	5	.	.	PUNCT
ijassa-1597	211	1	adv	adv	PROPN
ijassa-1597	211	2	syst	syst	PROPN
ijassa-1597	211	3	sci	sci	PROPN
ijassa-1597	211	4	appl	appl	PROPN
ijassa-1597	211	5	(	(	PUNCT
ijassa-1597	211	6	2024	2024	NUM
ijassa-1597	211	7	)	)	PUNCT
ijassa-1597	211	8	introduction	introduction	NOUN
ijassa-1597	211	9	the	the	DET
ijassa-1597	211	10	problem	problem	NOUN
ijassa-1597	211	11	definition	definition	NOUN
ijassa-1597	211	12	metric	metric	ADJ
ijassa-1597	211	13	over	over	ADP
ijassa-1597	211	14	the	the	DET
ijassa-1597	211	15	set	set	NOUN
ijassa-1597	211	16	of	of	ADP
ijassa-1597	211	17	instances	instance	NOUN
ijassa-1597	211	18	of	of	ADP
ijassa-1597	211	19	the	the	DET
ijassa-1597	211	20	problem	problem	NOUN
ijassa-1597	211	21	p2	p2	PROPN
ijassa-1597	211	22	prec	prec	PROPN
ijassa-1597	211	23	,	,	PUNCT
ijassa-1597	211	24	pj	pj	PROPN
ijassa-1597	211	25	{	{	PUNCT
ijassa-1597	211	26	1	1	NUM
ijassa-1597	211	27	,	,	PUNCT
ijassa-1597	211	28	2	2	NUM
ijassa-1597	211	29	}	}	PUNCT
ijassa-1597	211	30	cmax	cmax	VERB
ijassa-1597	211	31	the	the	DET
ijassa-1597	211	32	polynomial	polynomial	ADJ
ijassa-1597	211	33	-	-	PUNCT
ijassa-1597	211	34	time	time	NOUN
ijassa-1597	211	35	approximation	approximation	NOUN
ijassa-1597	211	36	scheme	scheme	NOUN
ijassa-1597	211	37	computer	computer	NOUN
ijassa-1597	211	38	experiments	experiment	VERB
ijassa-1597	211	39	conclusions	conclusion	NOUN