id	sid	tid	token	lemma	pos
cana-6180	1	1	communications	communication	NOUN
cana-6180	1	2	on	on	ADP
cana-6180	1	3	applied	apply	VERB
cana-6180	1	4	nonlinear	nonlinear	ADJ
cana-6180	1	5	analysis	analysis	NOUN
cana-6180	1	6	issn	issn	NOUN
cana-6180	1	7	:	:	PUNCT
cana-6180	1	8	1074	1074	NUM
cana-6180	1	9	-	-	PUNCT
cana-6180	1	10	133x	133x	NUM
cana-6180	1	11	vol	vol	NOUN
cana-6180	1	12	32	32	NUM
cana-6180	1	13	no	no	NOUN
cana-6180	1	14	.	.	NOUN
cana-6180	1	15	3	3	NUM
cana-6180	1	16	(	(	PUNCT
cana-6180	1	17	2025	2025	NUM
cana-6180	1	18	)	)	PUNCT
cana-6180	1	19	1131	1131	NUM
cana-6180	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	1	21	comparison	comparison	NOUN
cana-6180	1	22	between	between	ADP
cana-6180	1	23	three	three	NUM
cana-6180	1	24	algorithms	algorithm	NOUN
cana-6180	1	25	to	to	PART
cana-6180	1	26	study	study	VERB
cana-6180	1	27	their	their	PRON
cana-6180	1	28	overall	overall	ADJ
cana-6180	1	29	convergence	convergence	NOUN
cana-6180	1	30	farouk	farouk	PROPN
cana-6180	1	31	benoumelaz	benoumelaz	PROPN
cana-6180	1	32	tsegc	tsegc	PROPN
cana-6180	1	33	department	department	PROPN
cana-6180	1	34	,	,	PUNCT
cana-6180	1	35	university	university	NOUN
cana-6180	1	36	hadj	hadj	PROPN
cana-6180	1	37	lakhdar	lakhdar	PROPN
cana-6180	1	38	,	,	PUNCT
cana-6180	1	39	batna	batna	PROPN
cana-6180	1	40	,	,	PUNCT
cana-6180	1	41	algeria	algeria	PROPN
cana-6180	1	42	,	,	PUNCT
cana-6180	1	43	farouk.benoumelaz@univ-batna.dz	farouk.benoumelaz@univ-batna.dz	PROPN
cana-6180	1	44	article	article	NOUN
cana-6180	1	45	history	history	NOUN
cana-6180	1	46	:	:	PUNCT
cana-6180	1	47	received	receive	VERB
cana-6180	1	48	:	:	PUNCT
cana-6180	1	49	29	29	NUM
cana-6180	1	50	-	-	SYM
cana-6180	1	51	05	05	NUM
cana-6180	1	52	-	-	PUNCT
cana-6180	1	53	2025	2025	NUM
cana-6180	1	54	revised	revise	VERB
cana-6180	1	55	:	:	PUNCT
cana-6180	1	56	14	14	NUM
cana-6180	1	57	-	-	SYM
cana-6180	1	58	09	09	NUM
cana-6180	1	59	-	-	PUNCT
cana-6180	1	60	2025	2025	NUM
cana-6180	1	61	accepted	accept	VERB
cana-6180	1	62	:	:	PUNCT
cana-6180	1	63	13	13	NUM
cana-6180	1	64	-	-	SYM
cana-6180	1	65	10	10	NUM
cana-6180	1	66	-	-	PUNCT
cana-6180	1	67	2025	2025	NUM
cana-6180	1	68	abstract	abstract	NOUN
cana-6180	1	69	:	:	PUNCT
cana-6180	1	70	in	in	ADP
cana-6180	1	71	this	this	DET
cana-6180	1	72	research	research	NOUN
cana-6180	1	73	paper	paper	NOUN
cana-6180	1	74	,	,	PUNCT
cana-6180	1	75	i	i	PRON
cana-6180	1	76	presented	present	VERB
cana-6180	1	77	a	a	DET
cana-6180	1	78	new	new	ADJ
cana-6180	1	79	algorithm	algorithm	NOUN
cana-6180	1	80	for	for	ADP
cana-6180	1	81	solving	solve	VERB
cana-6180	1	82	integer	integer	NOUN
cana-6180	1	83	linear	linear	ADJ
cana-6180	1	84	programming	programming	NOUN
cana-6180	1	85	problems	problem	NOUN
cana-6180	1	86	based	base	VERB
cana-6180	1	87	on	on	ADP
cana-6180	1	88	previous	previous	ADJ
cana-6180	1	89	methods	method	NOUN
cana-6180	1	90	for	for	ADP
cana-6180	1	91	solving	solve	VERB
cana-6180	1	92	such	such	ADJ
cana-6180	1	93	problems	problem	NOUN
cana-6180	1	94	,	,	PUNCT
cana-6180	1	95	including	include	VERB
cana-6180	1	96	the	the	DET
cana-6180	1	97	boundary	boundary	ADJ
cana-6180	1	98	method	method	NOUN
cana-6180	1	99	and	and	CCONJ
cana-6180	1	100	gommari	gommari	NOUN
cana-6180	1	101	’s	’s	PART
cana-6180	1	102	truncation	truncation	NOUN
cana-6180	1	103	algorithm	algorithm	NOUN
cana-6180	1	104	.	.	PUNCT
cana-6180	2	1	the	the	DET
cana-6180	2	2	two	two	NUM
cana-6180	2	3	known	know	VERB
cana-6180	2	4	ones	one	NOUN
cana-6180	2	5	.	.	PUNCT
cana-6180	3	1	the	the	DET
cana-6180	3	2	new	new	ADJ
cana-6180	3	3	algorithm	algorithm	NOUN
cana-6180	3	4	relies	rely	VERB
cana-6180	3	5	on	on	ADP
cana-6180	3	6	a	a	DET
cana-6180	3	7	coupling	coupling	NOUN
cana-6180	3	8	process	process	NOUN
cana-6180	3	9	between	between	ADP
cana-6180	3	10	the	the	DET
cana-6180	3	11	two	two	NUM
cana-6180	3	12	aforementioned	aforementioned	ADJ
cana-6180	3	13	methods	method	NOUN
cana-6180	3	14	.	.	PUNCT
cana-6180	4	1	the	the	DET
cana-6180	4	2	reasons	reason	NOUN
cana-6180	4	3	that	that	PRON
cana-6180	4	4	led	lead	VERB
cana-6180	4	5	to	to	ADP
cana-6180	4	6	the	the	DET
cana-6180	4	7	connection	connection	NOUN
cana-6180	4	8	between	between	ADP
cana-6180	4	9	the	the	DET
cana-6180	4	10	branch	branch	NOUN
cana-6180	4	11	and	and	CCONJ
cana-6180	4	12	node	node	NOUN
cana-6180	4	13	method	method	NOUN
cana-6180	4	14	and	and	CCONJ
cana-6180	4	15	the	the	DET
cana-6180	4	16	cutting	cut	VERB
cana-6180	4	17	planes	plane	NOUN
cana-6180	4	18	method	method	NOUN
cana-6180	4	19	are	be	AUX
cana-6180	4	20	to	to	PART
cana-6180	4	21	overcome	overcome	VERB
cana-6180	4	22	some	some	PRON
cana-6180	4	23	of	of	ADP
cana-6180	4	24	the	the	DET
cana-6180	4	25	disadvantages	disadvantage	NOUN
cana-6180	4	26	of	of	ADP
cana-6180	4	27	the	the	DET
cana-6180	4	28	two	two	NUM
cana-6180	4	29	methods	method	NOUN
cana-6180	4	30	,	,	PUNCT
cana-6180	4	31	especially	especially	ADV
cana-6180	4	32	in	in	ADP
cana-6180	4	33	the	the	DET
cana-6180	4	34	case	case	NOUN
cana-6180	4	35	of	of	ADP
cana-6180	4	36	large	large	ADJ
cana-6180	4	37	repetitions	repetition	NOUN
cana-6180	4	38	and	and	CCONJ
cana-6180	4	39	the	the	DET
cana-6180	4	40	large	large	ADJ
cana-6180	4	41	time	time	NOUN
cana-6180	4	42	spent	spend	VERB
cana-6180	4	43	on	on	ADP
cana-6180	4	44	the	the	DET
cana-6180	4	45	solution	solution	NOUN
cana-6180	4	46	,	,	PUNCT
cana-6180	4	47	and	and	CCONJ
cana-6180	4	48	to	to	PART
cana-6180	4	49	obtain	obtain	VERB
cana-6180	4	50	results	result	NOUN
cana-6180	4	51	that	that	PRON
cana-6180	4	52	are	be	AUX
cana-6180	4	53	superior	superior	ADJ
cana-6180	4	54	to	to	ADP
cana-6180	4	55	the	the	DET
cana-6180	4	56	results	result	NOUN
cana-6180	4	57	of	of	ADP
cana-6180	4	58	each	each	PRON
cana-6180	4	59	of	of	ADP
cana-6180	4	60	the	the	DET
cana-6180	4	61	two	two	NUM
cana-6180	4	62	methods	method	NOUN
cana-6180	4	63	.	.	PUNCT
cana-6180	5	1	it	it	PRON
cana-6180	5	2	can	can	AUX
cana-6180	5	3	be	be	AUX
cana-6180	5	4	said	say	VERB
cana-6180	5	5	that	that	SCONJ
cana-6180	5	6	the	the	DET
cana-6180	5	7	new	new	ADJ
cana-6180	5	8	algorithm	algorithm	NOUN
cana-6180	5	9	was	be	AUX
cana-6180	5	10	characterized	characterize	VERB
cana-6180	5	11	by	by	ADP
cana-6180	5	12	good	good	ADJ
cana-6180	5	13	features	feature	NOUN
cana-6180	5	14	and	and	CCONJ
cana-6180	5	15	excluded	exclude	VERB
cana-6180	5	16	and	and	CCONJ
cana-6180	5	17	eliminated	eliminate	VERB
cana-6180	5	18	many	many	ADJ
cana-6180	5	19	of	of	ADP
cana-6180	5	20	the	the	DET
cana-6180	5	21	bad	bad	ADJ
cana-6180	5	22	qualities	quality	NOUN
cana-6180	5	23	.	.	PUNCT
cana-6180	6	1	keywords	keyword	NOUN
cana-6180	6	2	:	:	PUNCT
cana-6180	6	3	operations	operation	NOUN
cana-6180	6	4	research	research	NOUN
cana-6180	6	5	,	,	PUNCT
cana-6180	6	6	integer	integer	NOUN
cana-6180	6	7	programming	programming	NOUN
cana-6180	6	8	,	,	PUNCT
cana-6180	6	9	gomori	gomori	PROPN
cana-6180	6	10	algorithm	algorithm	PROPN
cana-6180	6	11	,	,	PUNCT
cana-6180	6	12	algorithms	algorithm	NOUN
cana-6180	6	13	.	.	PUNCT
cana-6180	7	1	1	1	X
cana-6180	7	2	.	.	X
cana-6180	7	3	introduction	introduction	NOUN
cana-6180	7	4	algorithms	algorithm	NOUN
cana-6180	7	5	are	be	AUX
cana-6180	7	6	valuable	valuable	ADJ
cana-6180	7	7	to	to	ADP
cana-6180	7	8	us	we	PRON
cana-6180	7	9	because	because	SCONJ
cana-6180	7	10	they	they	PRON
cana-6180	7	11	form	form	VERB
cana-6180	7	12	the	the	DET
cana-6180	7	13	basis	basis	NOUN
cana-6180	7	14	of	of	ADP
cana-6180	7	15	much	much	ADJ
cana-6180	7	16	of	of	ADP
cana-6180	7	17	the	the	DET
cana-6180	7	18	technology	technology	NOUN
cana-6180	7	19	we	we	PRON
cana-6180	7	20	use	use	VERB
cana-6180	7	21	in	in	ADP
cana-6180	7	22	our	our	PRON
cana-6180	7	23	daily	daily	ADJ
cana-6180	7	24	lives	life	NOUN
cana-6180	7	25	,	,	PUNCT
cana-6180	7	26	from	from	ADP
cana-6180	7	27	mobile	mobile	ADJ
cana-6180	7	28	apps	app	NOUN
cana-6180	7	29	to	to	ADP
cana-6180	7	30	search	search	NOUN
cana-6180	7	31	engines	engine	NOUN
cana-6180	7	32	.	.	PUNCT
cana-6180	8	1	powerful	powerful	ADJ
cana-6180	8	2	innovations	innovation	NOUN
cana-6180	8	3	in	in	ADP
cana-6180	8	4	various	various	ADJ
cana-6180	8	5	industries	industry	NOUN
cana-6180	8	6	enhance	enhance	VERB
cana-6180	8	7	our	our	PRON
cana-6180	8	8	capabilities	capability	NOUN
cana-6180	8	9	(	(	PUNCT
cana-6180	8	10	for	for	ADP
cana-6180	8	11	example	example	NOUN
cana-6180	8	12	,	,	PUNCT
cana-6180	8	13	artificial	artificial	ADJ
cana-6180	8	14	intelligence	intelligence	NOUN
cana-6180	8	15	assistants	assistant	NOUN
cana-6180	8	16	or	or	CCONJ
cana-6180	8	17	medical	medical	ADJ
cana-6180	8	18	diagnostics	diagnostic	NOUN
cana-6180	8	19	...	...	PUNCT
cana-6180	8	20	)	)	PUNCT
cana-6180	8	21	.	.	PUNCT
cana-6180	9	1	that	that	PRON
cana-6180	9	2	’s	’	VERB
cana-6180	9	3	why	why	SCONJ
cana-6180	9	4	we	we	PRON
cana-6180	9	5	work	work	VERB
cana-6180	9	6	to	to	PART
cana-6180	9	7	improve	improve	VERB
cana-6180	9	8	them	they	PRON
cana-6180	9	9	.	.	PUNCT
cana-6180	10	1	linear	linear	ADJ
cana-6180	10	2	programming	programming	NOUN
cana-6180	10	3	is	be	AUX
cana-6180	10	4	one	one	NUM
cana-6180	10	5	of	of	ADP
cana-6180	10	6	the	the	DET
cana-6180	10	7	most	most	ADV
cana-6180	10	8	widespread	widespread	ADJ
cana-6180	10	9	optimization	optimization	NOUN
cana-6180	10	10	techniques	technique	NOUN
cana-6180	10	11	in	in	ADP
cana-6180	10	12	operational	operational	ADJ
cana-6180	10	13	research	research	NOUN
cana-6180	10	14	.	.	PUNCT
cana-6180	11	1	this	this	PRON
cana-6180	11	2	is	be	AUX
cana-6180	11	3	mainly	mainly	ADV
cana-6180	11	4	due	due	ADJ
cana-6180	11	5	to	to	ADP
cana-6180	11	6	the	the	DET
cana-6180	11	7	ease	ease	NOUN
cana-6180	11	8	of	of	ADP
cana-6180	11	9	modeling	modeling	NOUN
cana-6180	11	10	,	,	PUNCT
cana-6180	11	11	the	the	DET
cana-6180	11	12	efficiency	efficiency	NOUN
cana-6180	11	13	of	of	ADP
cana-6180	11	14	the	the	DET
cana-6180	11	15	algorithms	algorithm	NOUN
cana-6180	11	16	developed	develop	VERB
cana-6180	11	17	,	,	PUNCT
cana-6180	11	18	and	and	CCONJ
cana-6180	11	19	the	the	DET
cana-6180	11	20	existence	existence	NOUN
cana-6180	11	21	of	of	ADP
cana-6180	11	22	many	many	ADJ
cana-6180	11	23	software	software	NOUN
cana-6180	11	24	programs	program	NOUN
cana-6180	11	25	on	on	ADP
cana-6180	11	26	the	the	DET
cana-6180	11	27	market	market	NOUN
cana-6180	11	28	.	.	PUNCT
cana-6180	12	1	in	in	ADP
cana-6180	12	2	addition	addition	NOUN
cana-6180	12	3	,	,	PUNCT
cana-6180	12	4	the	the	DET
cana-6180	12	5	widespread	widespread	ADJ
cana-6180	12	6	use	use	NOUN
cana-6180	12	7	of	of	ADP
cana-6180	12	8	microcomputing	microcomputing	NOUN
cana-6180	12	9	has	have	AUX
cana-6180	12	10	made	make	VERB
cana-6180	12	11	linear	linear	ADJ
cana-6180	12	12	programming	programming	NOUN
cana-6180	12	13	accessible	accessible	ADJ
cana-6180	12	14	to	to	ADP
cana-6180	12	15	everyone.[1	everyone.[1	VERB
cana-6180	12	16	]	]	PUNCT
cana-6180	12	17	the	the	DET
cana-6180	12	18	importance	importance	NOUN
cana-6180	12	19	of	of	ADP
cana-6180	12	20	linear	linear	PROPN
cana-6180	12	21	programming	programming	NOUN
cana-6180	12	22	is	be	AUX
cana-6180	12	23	attributed	attribute	VERB
cana-6180	12	24	mainly	mainly	ADV
cana-6180	12	25	to	to	ADP
cana-6180	12	26	its	its	PRON
cana-6180	12	27	multiple	multiple	ADJ
cana-6180	12	28	applications	application	NOUN
cana-6180	12	29	,	,	PUNCT
cana-6180	12	30	as	as	ADV
cana-6180	12	31	well	well	ADV
cana-6180	12	32	as	as	ADP
cana-6180	12	33	its	its	PRON
cana-6180	12	34	contribution	contribution	NOUN
cana-6180	12	35	to	to	ADP
cana-6180	12	36	generating	generate	VERB
cana-6180	12	37	techniques	technique	NOUN
cana-6180	12	38	for	for	ADP
cana-6180	12	39	finding	find	VERB
cana-6180	12	40	optimal	optimal	ADJ
cana-6180	12	41	solutions	solution	NOUN
cana-6180	12	42	.	.	PUNCT
cana-6180	13	1	linear	linear	ADJ
cana-6180	13	2	programming	programming	NOUN
cana-6180	13	3	is	be	AUX
cana-6180	13	4	a	a	DET
cana-6180	13	5	decision	decision	NOUN
cana-6180	13	6	making	make	VERB
cana-6180	13	7	tool	tool	NOUN
cana-6180	13	8	,	,	PUNCT
cana-6180	13	9	particularly	particularly	ADV
cana-6180	13	10	in	in	ADP
cana-6180	13	11	quantitative	quantitative	ADJ
cana-6180	13	12	decisions	decision	NOUN
cana-6180	13	13	in	in	ADP
cana-6180	13	14	the	the	DET
cana-6180	13	15	business	business	NOUN
cana-6180	13	16	world	world	NOUN
cana-6180	13	17	,	,	PUNCT
cana-6180	13	18	in	in	ADP
cana-6180	13	19	industrial	industrial	ADJ
cana-6180	13	20	engineering	engineering	NOUN
cana-6180	13	21	companies	company	NOUN
cana-6180	13	22	and	and	CCONJ
cana-6180	13	23	,	,	PUNCT
cana-6180	13	24	to	to	ADP
cana-6180	13	25	a	a	DET
cana-6180	13	26	lesser	less	ADJ
cana-6180	13	27	extent	extent	NOUN
cana-6180	13	28	,	,	PUNCT
cana-6180	13	29	in	in	ADP
cana-6180	13	30	certain	certain	ADJ
cana-6180	13	31	activities	activity	NOUN
cana-6180	13	32	in	in	ADP
cana-6180	13	33	the	the	DET
cana-6180	13	34	life	life	NOUN
cana-6180	13	35	sciences	science	NOUN
cana-6180	13	36	and	and	CCONJ
cana-6180	13	37	social	social	ADJ
cana-6180	13	38	sciences	science	NOUN
cana-6180	13	39	.	.	PUNCT
cana-6180	14	1	the	the	DET
cana-6180	14	2	main	main	ADJ
cana-6180	14	3	objective	objective	NOUN
cana-6180	14	4	of	of	ADP
cana-6180	14	5	linear	linear	PROPN
cana-6180	14	6	programming	programming	NOUN
cana-6180	14	7	is	be	AUX
cana-6180	14	8	to	to	PART
cana-6180	14	9	determine	determine	VERB
cana-6180	14	10	the	the	DET
cana-6180	14	11	optimal	optimal	ADJ
cana-6180	14	12	allocation	allocation	NOUN
cana-6180	14	13	of	of	ADP
cana-6180	14	14	scarce	scarce	ADJ
cana-6180	14	15	resources	resource	NOUN
cana-6180	14	16	between	between	ADP
cana-6180	14	17	competing	compete	VERB
cana-6180	14	18	activities	activity	NOUN
cana-6180	14	19	or	or	CCONJ
cana-6180	14	20	products	product	NOUN
cana-6180	14	21	.	.	PUNCT
cana-6180	15	1	economic	economic	ADJ
cana-6180	15	2	situations	situation	NOUN
cana-6180	15	3	often	often	ADV
cana-6180	15	4	require	require	VERB
cana-6180	15	5	that	that	SCONJ
cana-6180	15	6	a	a	DET
cana-6180	15	7	function	function	NOUN
cana-6180	15	8	be	be	AUX
cana-6180	15	9	optimized	optimize	VERB
cana-6180	15	10	under	under	ADP
cana-6180	15	11	several	several	ADJ
cana-6180	15	12	constraints	constraint	NOUN
cana-6180	15	13	in	in	ADP
cana-6180	15	14	the	the	DET
cana-6180	15	15	form	form	NOUN
cana-6180	15	16	of	of	ADP
cana-6180	15	17	inequalities	inequality	NOUN
cana-6180	15	18	.	.	PUNCT
cana-6180	16	1	mathematical	mathematical	ADJ
cana-6180	16	2	programming	programming	NOUN
cana-6180	16	3	can	can	AUX
cana-6180	16	4	be	be	AUX
cana-6180	16	5	defined	define	VERB
cana-6180	16	6	as	as	ADP
cana-6180	16	7	a	a	DET
cana-6180	16	8	mathematical	mathematical	ADJ
cana-6180	16	9	technique	technique	NOUN
cana-6180	16	10	for	for	ADP
cana-6180	16	11	solving	solve	VERB
cana-6180	16	12	management	management	NOUN
cana-6180	16	13	problems	problem	NOUN
cana-6180	16	14	,	,	PUNCT
cana-6180	16	15	particularly	particularly	ADV
cana-6180	16	16	those	those	PRON
cana-6180	16	17	where	where	SCONJ
cana-6180	16	18	the	the	DET
cana-6180	16	19	manager	manager	NOUN
cana-6180	16	20	must	must	AUX
cana-6180	16	21	determine	determine	VERB
cana-6180	16	22	,	,	PUNCT
cana-6180	16	23	given	give	VERB
cana-6180	16	24	different	different	ADJ
cana-6180	16	25	possibilities	possibility	NOUN
cana-6180	16	26	,	,	PUNCT
cana-6180	16	27	the	the	DET
cana-6180	16	28	communications	communication	NOUN
cana-6180	16	29	on	on	ADP
cana-6180	16	30	applied	apply	VERB
cana-6180	16	31	nonlinear	nonlinear	ADJ
cana-6180	16	32	analysis	analysis	NOUN
cana-6180	16	33	issn	issn	NOUN
cana-6180	16	34	:	:	PUNCT
cana-6180	16	35	1074	1074	NUM
cana-6180	16	36	-	-	PUNCT
cana-6180	16	37	133x	133x	NUM
cana-6180	16	38	vol	vol	NOUN
cana-6180	16	39	32	32	NUM
cana-6180	16	40	no	no	NOUN
cana-6180	16	41	.	.	NOUN
cana-6180	16	42	3	3	NUM
cana-6180	16	43	(	(	PUNCT
cana-6180	16	44	2025	2025	NUM
cana-6180	16	45	)	)	PUNCT
cana-6180	16	46	1132	1132	NUM
cana-6180	17	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	17	2	optimal	optimal	ADJ
cana-6180	17	3	use	use	NOUN
cana-6180	17	4	of	of	ADP
cana-6180	17	5	the	the	DET
cana-6180	17	6	company	company	NOUN
cana-6180	17	7	’s	’s	PART
cana-6180	17	8	resources	resource	NOUN
cana-6180	17	9	to	to	PART
cana-6180	17	10	achieve	achieve	VERB
cana-6180	17	11	a	a	DET
cana-6180	17	12	specific	specific	ADJ
cana-6180	17	13	objective	objective	NOUN
cana-6180	17	14	,	,	PUNCT
cana-6180	17	15	such	such	ADJ
cana-6180	17	16	as	as	ADP
cana-6180	17	17	maximizing	maximize	VERB
cana-6180	17	18	pro.ts	pro.ts	PROPN
cana-6180	17	19	or	or	CCONJ
cana-6180	17	20	minimizing	minimize	VERB
cana-6180	17	21	costs.[2	costs.[2	NOUN
cana-6180	17	22	]	]	PUNCT
cana-6180	17	23	in	in	ADP
cana-6180	17	24	most	most	ADJ
cana-6180	17	25	cases	case	NOUN
cana-6180	17	26	,	,	PUNCT
cana-6180	17	27	the	the	DET
cana-6180	17	28	company	company	NOUN
cana-6180	17	29	problems	problem	VERB
cana-6180	17	30	that	that	PRON
cana-6180	17	31	can	can	AUX
cana-6180	17	32	be	be	AUX
cana-6180	17	33	treated	treat	VERB
cana-6180	17	34	by	by	ADP
cana-6180	17	35	mathematical	mathematical	ADJ
cana-6180	17	36	programming	programming	NOUN
cana-6180	17	37	involve	involve	VERB
cana-6180	17	38	a	a	DET
cana-6180	17	39	number	number	NOUN
cana-6180	17	40	of	of	ADP
cana-6180	17	41	resources	resource	NOUN
cana-6180	17	42	,	,	PUNCT
cana-6180	17	43	such	such	ADJ
cana-6180	17	44	as	as	ADP
cana-6180	17	45	labor	labor	NOUN
cana-6180	17	46	,	,	PUNCT
cana-6180	17	47	raw	raw	ADJ
cana-6180	17	48	materials	material	NOUN
cana-6180	17	49	,	,	PUNCT
cana-6180	17	50	capital	capital	NOUN
cana-6180	17	51	,	,	PUNCT
cana-6180	17	52	space	space	NOUN
cana-6180	17	53	,	,	PUNCT
cana-6180	17	54	etc	etc	X
cana-6180	17	55	.	.	X
cana-6180	17	56	that	that	PRON
cana-6180	17	57	are	be	AUX
cana-6180	17	58	available	available	ADJ
cana-6180	17	59	in	in	ADP
cana-6180	17	60	limited	limited	ADJ
cana-6180	17	61	quantities	quantity	NOUN
cana-6180	17	62	and	and	CCONJ
cana-6180	17	63	that	that	SCONJ
cana-6180	17	64	we	we	PRON
cana-6180	17	65	want	want	VERB
cana-6180	17	66	to	to	PART
cana-6180	17	67	distribute	distribute	VERB
cana-6180	17	68	in	in	ADP
cana-6180	17	69	an	an	DET
cana-6180	17	70	optimal	optimal	ADJ
cana-6180	17	71	way	way	NOUN
cana-6180	17	72	between	between	ADP
cana-6180	17	73	a	a	DET
cana-6180	17	74	number	number	NOUN
cana-6180	17	75	of	of	ADP
cana-6180	17	76	manufacturing	manufacturing	NOUN
cana-6180	17	77	processes.[3	processes.[3	NOUN
cana-6180	17	78	]	]	PUNCT
cana-6180	17	79	to	to	PART
cana-6180	17	80	solve	solve	VERB
cana-6180	17	81	problems	problem	NOUN
cana-6180	17	82	will	will	AUX
cana-6180	17	83	be	be	AUX
cana-6180	17	84	divided	divide	VERB
cana-6180	17	85	into	into	ADP
cana-6180	17	86	two	two	NUM
cana-6180	17	87	main	main	ADJ
cana-6180	17	88	steps	step	NOUN
cana-6180	17	89	:	:	PUNCT
cana-6180	17	90	1	1	X
cana-6180	17	91	.	.	X
cana-6180	17	92	modeling	model	VERB
cana-6180	17	93	the	the	DET
cana-6180	17	94	problem	problem	NOUN
cana-6180	17	95	in	in	ADP
cana-6180	17	96	the	the	DET
cana-6180	17	97	form	form	NOUN
cana-6180	17	98	of	of	ADP
cana-6180	17	99	equations	equation	NOUN
cana-6180	17	100	or	or	CCONJ
cana-6180	17	101	inequalities	inequality	NOUN
cana-6180	17	102	that	that	PRON
cana-6180	17	103	will	will	AUX
cana-6180	17	104	allow	allow	VERB
cana-6180	17	105	us	we	PRON
cana-6180	17	106	to	to	PART
cana-6180	17	107	properly	properly	ADV
cana-6180	17	108	identify	identify	VERB
cana-6180	17	109	and	and	CCONJ
cana-6180	17	110	structure	structure	VERB
cana-6180	17	111	the	the	DET
cana-6180	17	112	constraints	constraint	NOUN
cana-6180	17	113	that	that	PRON
cana-6180	17	114	the	the	DET
cana-6180	17	115	variables	variable	NOUN
cana-6180	17	116	of	of	ADP
cana-6180	17	117	the	the	DET
cana-6180	17	118	model	model	NOUN
cana-6180	17	119	must	must	AUX
cana-6180	17	120	respect	respect	VERB
cana-6180	17	121	;	;	PUNCT
cana-6180	17	122	in	in	ADP
cana-6180	17	123	addition	addition	NOUN
cana-6180	17	124	,	,	PUNCT
cana-6180	17	125	we	we	PRON
cana-6180	17	126	must	must	AUX
cana-6180	17	127	de.ne	de.ne	VERB
cana-6180	17	128	the	the	DET
cana-6180	17	129	contribution	contribution	NOUN
cana-6180	17	130	of	of	ADP
cana-6180	17	131	each	each	DET
cana-6180	17	132	variable	variable	NOUN
cana-6180	17	133	to	to	ADP
cana-6180	17	134	achieving	achieve	VERB
cana-6180	17	135	the	the	DET
cana-6180	17	136	objective	objective	NOUN
cana-6180	17	137	pursued	pursue	VERB
cana-6180	17	138	by	by	ADP
cana-6180	17	139	the	the	DET
cana-6180	17	140	company	company	NOUN
cana-6180	17	141	,	,	PUNCT
cana-6180	17	142	which	which	PRON
cana-6180	17	143	will	will	AUX
cana-6180	17	144	result	result	VERB
cana-6180	17	145	in	in	ADP
cana-6180	17	146	a	a	DET
cana-6180	17	147	function	function	NOUN
cana-6180	17	148	to	to	PART
cana-6180	17	149	be	be	AUX
cana-6180	17	150	optimized	optimize	VERB
cana-6180	17	151	.	.	PUNCT
cana-6180	18	1	2	2	X
cana-6180	18	2	.	.	X
cana-6180	18	3	determining	determine	VERB
cana-6180	18	4	the	the	DET
cana-6180	18	5	mathematical	mathematical	ADJ
cana-6180	18	6	optimum	optimum	NOUN
cana-6180	18	7	using	use	VERB
cana-6180	18	8	certain	certain	ADJ
cana-6180	18	9	techniques	technique	NOUN
cana-6180	18	10	specific	specific	ADJ
cana-6180	18	11	to	to	ADP
cana-6180	18	12	mathematical	mathematical	ADJ
cana-6180	18	13	programming	programming	NOUN
cana-6180	18	14	.	.	PUNCT
cana-6180	19	1	subsequently	subsequently	ADV
cana-6180	19	2	,	,	PUNCT
cana-6180	19	3	we	we	PRON
cana-6180	19	4	will	will	AUX
cana-6180	19	5	examine	examine	VERB
cana-6180	19	6	the	the	DET
cana-6180	19	7	stability	stability	NOUN
cana-6180	19	8	of	of	ADP
cana-6180	19	9	the	the	DET
cana-6180	19	10	optimal	optimal	ADJ
cana-6180	19	11	solution	solution	NOUN
cana-6180	19	12	in	in	ADP
cana-6180	19	13	the	the	DET
cana-6180	19	14	face	face	NOUN
cana-6180	19	15	of	of	ADP
cana-6180	19	16	certain	certain	ADJ
cana-6180	19	17	variations	variation	NOUN
cana-6180	19	18	in	in	ADP
cana-6180	19	19	the	the	DET
cana-6180	19	20	problem	problem	NOUN
cana-6180	19	21	data	datum	NOUN
cana-6180	19	22	.	.	PUNCT
cana-6180	20	1	manipulating	manipulate	VERB
cana-6180	20	2	the	the	DET
cana-6180	20	3	model	model	NOUN
cana-6180	20	4	using	use	VERB
cana-6180	20	5	mathematical	mathematical	ADJ
cana-6180	20	6	programming	programming	NOUN
cana-6180	20	7	techniques	technique	NOUN
cana-6180	20	8	will	will	AUX
cana-6180	20	9	provide	provide	VERB
cana-6180	20	10	an	an	DET
cana-6180	20	11	objective	objective	ADJ
cana-6180	20	12	and	and	CCONJ
cana-6180	20	13	effective	effective	ADJ
cana-6180	20	14	method	method	NOUN
cana-6180	20	15	for	for	ADP
cana-6180	20	16	arriving	arrive	VERB
cana-6180	20	17	at	at	ADP
cana-6180	20	18	an	an	DET
cana-6180	20	19	optimal	optimal	ADJ
cana-6180	20	20	strategy	strategy	NOUN
cana-6180	20	21	when	when	SCONJ
cana-6180	20	22	several	several	ADJ
cana-6180	20	23	possibilities	possibility	NOUN
cana-6180	20	24	must	must	AUX
cana-6180	20	25	be	be	AUX
cana-6180	20	26	considered	consider	VERB
cana-6180	20	27	.	.	PUNCT
cana-6180	21	1	but	but	CCONJ
cana-6180	21	2	the	the	DET
cana-6180	21	3	fact	fact	NOUN
cana-6180	21	4	remains	remain	VERB
cana-6180	21	5	that	that	SCONJ
cana-6180	21	6	mathematical	mathematical	ADJ
cana-6180	21	7	programming	programming	NOUN
cana-6180	21	8	,	,	PUNCT
cana-6180	21	9	although	although	SCONJ
cana-6180	21	10	it	it	PRON
cana-6180	21	11	allows	allow	VERB
cana-6180	21	12	decisions	decision	NOUN
cana-6180	21	13	to	to	PART
cana-6180	21	14	be	be	AUX
cana-6180	21	15	prepared	prepare	VERB
cana-6180	21	16	,	,	PUNCT
cana-6180	21	17	can	can	AUX
cana-6180	21	18	not	not	PART
cana-6180	21	19	replace	replace	VERB
cana-6180	21	20	the	the	DET
cana-6180	21	21	practical	practical	ADJ
cana-6180	21	22	sense	sense	NOUN
cana-6180	21	23	,	,	PUNCT
cana-6180	21	24	experience	experience	NOUN
cana-6180	21	25	,	,	PUNCT
cana-6180	21	26	leadership	leadership	NOUN
cana-6180	21	27	,	,	PUNCT
cana-6180	21	28	and	and	CCONJ
cana-6180	21	29	risk	risk	NOUN
cana-6180	21	30	appetite	appetite	NOUN
cana-6180	21	31	of	of	ADP
cana-6180	21	32	the	the	DET
cana-6180	21	33	business	business	NOUN
cana-6180	21	34	leader	leader	NOUN
cana-6180	21	35	.	.	PUNCT
cana-6180	22	1	2	2	X
cana-6180	22	2	.	.	X
cana-6180	22	3	objectives	objective	VERB
cana-6180	22	4	the	the	DET
cana-6180	22	5	aim	aim	NOUN
cana-6180	22	6	of	of	ADP
cana-6180	22	7	this	this	DET
cana-6180	22	8	research	research	NOUN
cana-6180	22	9	is	be	AUX
cana-6180	22	10	to	to	PART
cana-6180	22	11	present	present	VERB
cana-6180	22	12	a	a	DET
cana-6180	22	13	new	new	ADJ
cana-6180	22	14	algorithm	algorithm	NOUN
cana-6180	22	15	for	for	ADP
cana-6180	22	16	solving	solve	VERB
cana-6180	22	17	an	an	DET
cana-6180	22	18	integer	integer	NOUN
cana-6180	22	19	linear	linear	NOUN
cana-6180	22	20	programming	programming	NOUN
cana-6180	22	21	problems	problem	NOUN
cana-6180	22	22	,	,	PUNCT
cana-6180	22	23	which	which	PRON
cana-6180	22	24	is	be	AUX
cana-6180	22	25	a	a	DET
cana-6180	22	26	combination	combination	NOUN
cana-6180	22	27	of	of	ADP
cana-6180	22	28	two	two	NUM
cana-6180	22	29	classical	classical	ADJ
cana-6180	22	30	methods	method	NOUN
cana-6180	22	31	,	,	PUNCT
cana-6180	22	32	the	the	DET
cana-6180	22	33	cutting	cut	VERB
cana-6180	22	34	planes	plane	NOUN
cana-6180	22	35	method	method	NOUN
cana-6180	22	36	and	and	CCONJ
cana-6180	22	37	the	the	DET
cana-6180	22	38	branching	branch	VERB
cana-6180	22	39	and	and	CCONJ
cana-6180	22	40	knotting	knotting	NOUN
cana-6180	22	41	method	method	NOUN
cana-6180	22	42	.	.	PUNCT
cana-6180	23	1	this	this	DET
cana-6180	23	2	algorithm	algorithm	NOUN
cana-6180	23	3	is	be	AUX
cana-6180	23	4	added	add	VERB
cana-6180	23	5	to	to	ADP
cana-6180	23	6	the	the	DET
cana-6180	23	7	methods	method	NOUN
cana-6180	23	8	and	and	CCONJ
cana-6180	23	9	algorithms	algorithm	NOUN
cana-6180	23	10	for	for	ADP
cana-6180	23	11	solving	solve	VERB
cana-6180	23	12	an	an	DET
cana-6180	23	13	integer	integer	NOUN
cana-6180	23	14	linear	linear	NOUN
cana-6180	23	15	programming	programming	NOUN
cana-6180	23	16	problems	problem	NOUN
cana-6180	23	17	to	to	PART
cana-6180	23	18	provide	provide	VERB
cana-6180	23	19	new	new	ADJ
cana-6180	23	20	solutions	solution	NOUN
cana-6180	23	21	and	and	CCONJ
cana-6180	23	22	possibilities	possibility	NOUN
cana-6180	23	23	for	for	ADP
cana-6180	23	24	those	those	PRON
cana-6180	23	25	following	follow	VERB
cana-6180	23	26	this	this	DET
cana-6180	23	27	topic	topic	NOUN
cana-6180	23	28	,	,	PUNCT
cana-6180	23	29	showing	show	VERB
cana-6180	23	30	them	they	PRON
cana-6180	23	31	the	the	DET
cana-6180	23	32	importance	importance	NOUN
cana-6180	23	33	of	of	ADP
cana-6180	23	34	working	work	VERB
cana-6180	23	35	and	and	CCONJ
cana-6180	23	36	thinking	think	VERB
cana-6180	23	37	about	about	ADP
cana-6180	23	38	creating	create	VERB
cana-6180	23	39	other	other	ADJ
cana-6180	23	40	new	new	ADJ
cana-6180	23	41	algorithms	algorithm	NOUN
cana-6180	23	42	that	that	PRON
cana-6180	23	43	shorten	shorten	VERB
cana-6180	23	44	the	the	DET
cana-6180	23	45	effort	effort	NOUN
cana-6180	23	46	and	and	CCONJ
cana-6180	23	47	time	time	NOUN
cana-6180	23	48	to	to	PART
cana-6180	23	49	obtain	obtain	VERB
cana-6180	23	50	the	the	DET
cana-6180	23	51	optimal	optimal	ADJ
cana-6180	23	52	solution	solution	NOUN
cana-6180	23	53	to	to	ADP
cana-6180	23	54	integer	integer	NOUN
cana-6180	23	55	linear	linear	ADJ
cana-6180	23	56	programming	programming	NOUN
cana-6180	23	57	problems	problem	NOUN
cana-6180	23	58	.	.	PUNCT
cana-6180	24	1	3	3	X
cana-6180	24	2	.	.	X
cana-6180	24	3	methods	method	NOUN
cana-6180	24	4	3.1	3.1	NUM
cana-6180	24	5	branch	branch	NOUN
cana-6180	24	6	and	and	CCONJ
cana-6180	24	7	bound	bind	VERB
cana-6180	24	8	method	method	NOUN
cana-6180	24	9	-	-	PUNCT
cana-6180	24	10	node	node	NOUN
cana-6180	24	11	algorithm	algorithm	NOUN
cana-6180	24	12	we	we	PRON
cana-6180	24	13	have	have	VERB
cana-6180	24	14	the	the	DET
cana-6180	24	15	following	follow	VERB
cana-6180	24	16	integer	integer	NOUN
cana-6180	24	17	programming	programming	NOUN
cana-6180	24	18	problem	problem	NOUN
cana-6180	24	19	{	{	PUNCT
cana-6180	24	20	max	max	PROPN
cana-6180	25	1	z	z	PROPN
cana-6180	25	2	=	=	PUNCT
cana-6180	25	3	𝑐𝑡𝑥	𝑐𝑡𝑥	NUM
cana-6180	25	4	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	25	5	sc	sc	NOUN
cana-6180	25	6	ax	ax	NOUN
cana-6180	25	7	=	=	SYM
cana-6180	25	8	b	b	PROPN
cana-6180	25	9	;	;	PUNCT
cana-6180	25	10	x	x	X
cana-6180	25	11	≥	≥	NUM
cana-6180	25	12	0	0	NUM
cana-6180	25	13	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	25	14	∈	∈	PROPN
cana-6180	25	15	𝐼	𝐼	PROPN
cana-6180	25	16	;	;	PUNCT
cana-6180	25	17	integer	integer	NOUN
cana-6180	25	18	.	.	PUNCT
cana-6180	26	1	........	........	PUNCT
cana-6180	26	2	1	1	NUM
cana-6180	26	3	a	a	DET
cana-6180	26	4	matrix	matrix	NOUN
cana-6180	26	5	with	with	ADP
cana-6180	26	6	dimension	dimension	NOUN
cana-6180	26	7	m	m	VERB
cana-6180	26	8	×	×	NOUN
cana-6180	26	9	s	s	NOUN
cana-6180	26	10	,	,	PUNCT
cana-6180	26	11	b	b	NOUN
cana-6180	26	12	matrix	matrix	NOUN
cana-6180	26	13	with	with	ADP
cana-6180	26	14	dimension	dimension	NOUN
cana-6180	26	15	m	m	VERB
cana-6180	26	16	×1	×1	NOUN
cana-6180	26	17	;	;	PUNCT
cana-6180	26	18	c	c	NOUN
cana-6180	26	19	matrix	matrix	NOUN
cana-6180	26	20	with	with	ADP
cana-6180	26	21	dimension	dimension	NOUN
cana-6180	26	22	s	s	PART
cana-6180	26	23	×	×	NOUN
cana-6180	26	24	1	1	NUM
cana-6180	26	25	;	;	PUNCT
cana-6180	26	26	x	x	X
cana-6180	26	27	matrix	matrix	NOUN
cana-6180	26	28	with	with	ADP
cana-6180	26	29	dimension	dimension	NOUN
cana-6180	26	30	s	s	PART
cana-6180	26	31	×	×	NOUN
cana-6180	26	32	1	1	NUM
cana-6180	26	33	:	:	PUNCT
cana-6180	26	34	communications	communication	NOUN
cana-6180	26	35	on	on	ADP
cana-6180	26	36	applied	apply	VERB
cana-6180	26	37	nonlinear	nonlinear	ADJ
cana-6180	26	38	analysis	analysis	NOUN
cana-6180	26	39	issn	issn	NOUN
cana-6180	26	40	:	:	PUNCT
cana-6180	26	41	1074	1074	NUM
cana-6180	26	42	-	-	PUNCT
cana-6180	26	43	133x	133x	NUM
cana-6180	26	44	vol	vol	NOUN
cana-6180	26	45	32	32	NUM
cana-6180	26	46	no	no	NOUN
cana-6180	26	47	.	.	NOUN
cana-6180	26	48	3	3	NUM
cana-6180	26	49	(	(	PUNCT
cana-6180	26	50	2025	2025	NUM
cana-6180	26	51	)	)	PUNCT
cana-6180	26	52	1133	1133	NUM
cana-6180	26	53	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	27	1	step	step	NOUN
cana-6180	27	2	1	1	NUM
cana-6180	27	3	:	:	PUNCT
cana-6180	27	4	initial	initial	ADJ
cana-6180	27	5	solution	solution	NOUN
cana-6180	27	6	we	we	PRON
cana-6180	27	7	use	use	VERB
cana-6180	27	8	the	the	DET
cana-6180	27	9	simplex	simplex	NOUN
cana-6180	27	10	method	method	NOUN
cana-6180	27	11	to	to	PART
cana-6180	27	12	solve	solve	VERB
cana-6180	27	13	problem	problem	NOUN
cana-6180	27	14	(	(	PUNCT
cana-6180	27	15	1	1	NUM
cana-6180	27	16	)	)	PUNCT
cana-6180	27	17	then	then	ADV
cana-6180	27	18	we	we	PRON
cana-6180	27	19	neglect	neglect	VERB
cana-6180	27	20	the	the	DET
cana-6180	27	21	restrictions	restriction	NOUN
cana-6180	27	22	related	relate	VERB
cana-6180	27	23	to	to	ADP
cana-6180	27	24	the	the	DET
cana-6180	27	25	integer	integer	NOUN
cana-6180	27	26	variables	variable	NOUN
cana-6180	27	27	,	,	PUNCT
cana-6180	27	28	if	if	SCONJ
cana-6180	27	29	all	all	DET
cana-6180	27	30	values	value	NOUN
cana-6180	27	31	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	27	32	∈	∈	PROPN
cana-6180	27	33	𝐼	𝐼	PROPN
cana-6180	27	34	are	be	AUX
cana-6180	27	35	integer	integer	NOUN
cana-6180	27	36	,	,	PUNCT
cana-6180	27	37	we	we	PRON
cana-6180	27	38	move	move	VERB
cana-6180	27	39	to	to	ADP
cana-6180	27	40	the	the	DET
cana-6180	27	41	step2	step2	PROPN
cana-6180	27	42	step	step	NOUN
cana-6180	27	43	2	2	NUM
cana-6180	27	44	:	:	PUNCT
cana-6180	27	45	we	we	PRON
cana-6180	27	46	choose	choose	VERB
cana-6180	27	47	from	from	ADP
cana-6180	27	48	the	the	DET
cana-6180	27	49	variables	variable	NOUN
cana-6180	27	50	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	27	51	∈	∈	PROPN
cana-6180	27	52	𝐼	𝐼	ADP
cana-6180	27	53	the	the	DET
cana-6180	27	54	variable	variable	NOUN
cana-6180	27	55	whose	whose	DET
cana-6180	27	56	value	value	NOUN
cana-6180	27	57	is	be	AUX
cana-6180	27	58	integer	integer	NOUN
cana-6180	27	59	at	at	ADP
cana-6180	27	60	that	that	DET
cana-6180	27	61	node	node	NOUN
cana-6180	27	62	,	,	PUNCT
cana-6180	27	63	and	and	CCONJ
cana-6180	27	64	this	this	DET
cana-6180	27	65	value	value	NOUN
cana-6180	27	66	has	have	VERB
cana-6180	27	67	the	the	DET
cana-6180	27	68	largest	large	ADJ
cana-6180	27	69	fractional	fractional	ADJ
cana-6180	27	70	part	part	NOUN
cana-6180	27	71	.	.	PUNCT
cana-6180	28	1	the	the	DET
cana-6180	28	2	variables	variable	NOUN
cana-6180	28	3	chosen	choose	VERB
cana-6180	28	4	𝑥𝐽	𝑥𝐽	NOUN
cana-6180	28	5	must	must	AUX
cana-6180	28	6	be	be	AUX
cana-6180	28	7	basic	basic	ADJ
cana-6180	28	8	,	,	PUNCT
cana-6180	28	9	otherwise	otherwise	ADV
cana-6180	28	10	their	their	PRON
cana-6180	28	11	value	value	NOUN
cana-6180	28	12	will	will	AUX
cana-6180	28	13	be	be	AUX
cana-6180	28	14	zero.[6][7	zero.[6][7	NUM
cana-6180	28	15	]	]	PUNCT
cana-6180	28	16	if	if	SCONJ
cana-6180	28	17	the	the	DET
cana-6180	28	18	basic	basic	ADJ
cana-6180	28	19	variable	variable	NOUN
cana-6180	28	20	chosen	choose	VERB
cana-6180	28	21	from	from	ADP
cana-6180	28	22	the	the	DET
cana-6180	28	23	last	last	ADJ
cana-6180	28	24	table	table	NOUN
cana-6180	28	25	in	in	ADP
cana-6180	28	26	solving	solve	VERB
cana-6180	28	27	the	the	DET
cana-6180	28	28	linear	linear	ADJ
cana-6180	28	29	programming	programming	NOUN
cana-6180	28	30	problem	problem	NOUN
cana-6180	28	31	is	be	AUX
cana-6180	28	32	the	the	DET
cana-6180	28	33	variable	variable	NOUN
cana-6180	28	34	whose	whose	DET
cana-6180	28	35	index	index	NOUN
cana-6180	28	36	is	be	AUX
cana-6180	28	37	i;and	i;and	PRON
cana-6180	28	38	its	its	PRON
cana-6180	28	39	incorrect	incorrect	ADJ
cana-6180	28	40	value	value	NOUN
cana-6180	28	41	is	be	AUX
cana-6180	28	42	𝑥𝐵𝑖which	𝑥𝐵𝑖which	PRON
cana-6180	28	43	we	we	PRON
cana-6180	28	44	can	can	AUX
cana-6180	28	45	write	write	VERB
cana-6180	28	46	as	as	SCONJ
cana-6180	28	47	follows	follow	VERB
cana-6180	28	48	:	:	PUNCT
cana-6180	28	49	𝑥𝐵𝑖=[[𝑥𝐵𝑖]]+𝑓𝑖′	𝑥𝐵𝑖=[[𝑥𝐵𝑖]]+𝑓𝑖′	X
cana-6180	29	1	where	where	SCONJ
cana-6180	29	2	:	:	PUNCT
cana-6180	29	3	0	0	NUM
cana-6180	29	4	<	<	X
cana-6180	29	5	𝑓𝑖′	𝑓𝑖′	X
cana-6180	29	6	<	<	X
cana-6180	29	7	1	1	NUM
cana-6180	29	8	since	since	SCONJ
cana-6180	29	9	the	the	DET
cana-6180	29	10	value	value	NOUN
cana-6180	29	11	of	of	ADP
cana-6180	29	12	the	the	DET
cana-6180	29	13	variable	variable	ADJ
cana-6180	29	14	𝑥𝐽	𝑥𝐽	NOUN
cana-6180	29	15	is	be	AUX
cana-6180	29	16	integer	integer	NOUN
cana-6180	29	17	,	,	PUNCT
cana-6180	29	18	it	it	PRON
cana-6180	29	19	satis.es	satis.es	PROPN
cana-6180	29	20	one	one	NUM
cana-6180	29	21	of	of	ADP
cana-6180	29	22	the	the	DET
cana-6180	29	23	inequalities	inequality	NOUN
cana-6180	29	24	𝑥𝐽≤[[𝑥𝐵𝑖]]	𝑥𝐽≤[[𝑥𝐵𝑖]]	ADP
cana-6180	29	25	............	............	PROPN
cana-6180	29	26	2	2	NUM
cana-6180	29	27	𝑥𝐽≥[[𝑥𝐵𝑖]]+1	𝑥𝐽≥[[𝑥𝐵𝑖]]+1	NUM
cana-6180	29	28	.........	.........	PUNCT
cana-6180	29	29	3	3	NUM
cana-6180	29	30	step	step	NOUN
cana-6180	29	31	3	3	NUM
cana-6180	29	32	:	:	PUNCT
cana-6180	29	33	we	we	PRON
cana-6180	29	34	work	work	VERB
cana-6180	29	35	on	on	ADP
cana-6180	29	36	the	the	DET
cana-6180	29	37	two	two	NUM
cana-6180	29	38	problems	problem	NOUN
cana-6180	29	39	identified	identify	VERB
cana-6180	29	40	in	in	ADP
cana-6180	29	41	the	the	DET
cana-6180	29	42	second	second	ADJ
cana-6180	29	43	step	step	NOUN
cana-6180	29	44	.	.	PUNCT
cana-6180	30	1	the	the	PRON
cana-6180	30	2	.	.	PUNCT
cana-6180	31	1	first	first	ADJ
cana-6180	31	2	problem	problem	NOUN
cana-6180	31	3	is	be	AUX
cana-6180	31	4	to	to	PART
cana-6180	31	5	add	add	VERB
cana-6180	31	6	the	the	DET
cana-6180	31	7	second	second	ADJ
cana-6180	31	8	constraint	constraint	NOUN
cana-6180	31	9	,	,	PUNCT
cana-6180	31	10	the	the	DET
cana-6180	31	11	second	second	ADJ
cana-6180	31	12	problem	problem	NOUN
cana-6180	31	13	is	be	AUX
cana-6180	31	14	to	to	PART
cana-6180	31	15	add	add	VERB
cana-6180	31	16	the	the	DET
cana-6180	31	17	third	third	ADJ
cana-6180	31	18	constraint	constraint	NOUN
cana-6180	31	19	,	,	PUNCT
cana-6180	31	20	to	to	PART
cana-6180	31	21	solve	solve	VERB
cana-6180	31	22	them	they	PRON
cana-6180	31	23	,	,	PUNCT
cana-6180	31	24	we	we	PRON
cana-6180	31	25	use	use	VERB
cana-6180	31	26	the	the	DET
cana-6180	31	27	simplex	simplex	NOUN
cana-6180	31	28	method	method	NOUN
cana-6180	31	29	.	.	PUNCT
cana-6180	32	1	step	step	NOUN
cana-6180	32	2	4:(choose	4:(choose	NUM
cana-6180	32	3	the	the	DET
cana-6180	32	4	fi.nal	fi.nal	ADJ
cana-6180	32	5	node	node	NOUN
cana-6180	32	6	)	)	PUNCT
cana-6180	32	7	all	all	DET
cana-6180	32	8	nodes	node	NOUN
cana-6180	32	9	obtained	obtain	VERB
cana-6180	32	10	in	in	ADP
cana-6180	32	11	step	step	NOUN
cana-6180	32	12	3	3	NUM
cana-6180	32	13	may	may	AUX
cana-6180	32	14	be	be	AUX
cana-6180	32	15	.nal	.nal	ADJ
cana-6180	32	16	nodes	node	NOUN
cana-6180	32	17	,	,	PUNCT
cana-6180	32	18	due	due	ADP
cana-6180	32	19	to	to	ADP
cana-6180	32	20	one	one	NUM
cana-6180	32	21	of	of	ADP
cana-6180	32	22	the	the	DET
cana-6180	32	23	following	follow	VERB
cana-6180	32	24	two	two	NUM
cana-6180	32	25	things	thing	NOUN
cana-6180	32	26	:	:	PUNCT
cana-6180	32	27	1	1	NUM
cana-6180	32	28	-	-	PUNCT
cana-6180	32	29	the	the	DET
cana-6180	32	30	problem	problem	NOUN
cana-6180	32	31	at	at	ADP
cana-6180	32	32	that	that	DET
cana-6180	32	33	node	node	NOUN
cana-6180	32	34	has	have	VERB
cana-6180	32	35	no	no	DET
cana-6180	32	36	possible	possible	ADJ
cana-6180	32	37	solution	solution	NOUN
cana-6180	32	38	,	,	PUNCT
cana-6180	32	39	so	so	ADV
cana-6180	32	40	go	go	VERB
cana-6180	32	41	to	to	PART
cana-6180	32	42	step	step	VERB
cana-6180	32	43	5	5	NUM
cana-6180	32	44	2	2	NUM
cana-6180	32	45	-	-	NUM
cana-6180	32	46	the	the	DET
cana-6180	32	47	values	value	NOUN
cana-6180	32	48	of	of	ADP
cana-6180	32	49	the	the	DET
cana-6180	32	50	variables	variable	NOUN
cana-6180	32	51	𝑥𝑗;𝑗	𝑥𝑗;𝑗	PUNCT
cana-6180	32	52	∈	∈	PROPN
cana-6180	33	1	𝐼	𝐼	SCONJ
cana-6180	33	2	iare	iare	VERB
cana-6180	33	3	all	all	DET
cana-6180	33	4	integer	integer	NOUN
cana-6180	33	5	,	,	PUNCT
cana-6180	33	6	so	so	ADV
cana-6180	33	7	of	of	ADP
cana-6180	33	8	the	the	DET
cana-6180	33	9	objective	objective	ADJ
cana-6180	33	10	function	function	NOUN
cana-6180	33	11	at	at	ADP
cana-6180	33	12	that	that	DET
cana-6180	33	13	node	node	NOUN
cana-6180	33	14	with	with	ADP
cana-6180	33	15	the	the	DET
cana-6180	33	16	best	good	ADJ
cana-6180	33	17	value	value	NOUN
cana-6180	33	18	.	.	PUNCT
cana-6180	34	1	i	i	PRON
cana-6180	34	2	arrived	arrive	VERB
cana-6180	34	3	at	at	ADP
cana-6180	34	4	it	it	PRON
cana-6180	34	5	,	,	PUNCT
cana-6180	34	6	if	if	SCONJ
cana-6180	34	7	the	the	DET
cana-6180	34	8	value	value	NOUN
cana-6180	34	9	of	of	ADP
cana-6180	34	10	the	the	DET
cana-6180	34	11	objective	objective	ADJ
cana-6180	34	12	function	function	NOUN
cana-6180	34	13	at	at	ADP
cana-6180	34	14	the	the	DET
cana-6180	34	15	new	new	ADJ
cana-6180	34	16	node	node	NOUN
cana-6180	34	17	is	be	AUX
cana-6180	34	18	better	well	ADJ
cana-6180	34	19	,	,	PUNCT
cana-6180	34	20	communications	communication	NOUN
cana-6180	34	21	on	on	ADP
cana-6180	34	22	applied	apply	VERB
cana-6180	34	23	nonlinear	nonlinear	ADJ
cana-6180	34	24	analysis	analysis	NOUN
cana-6180	34	25	issn	issn	NOUN
cana-6180	34	26	:	:	PUNCT
cana-6180	34	27	1074	1074	NUM
cana-6180	34	28	-	-	PUNCT
cana-6180	34	29	133x	133x	NUM
cana-6180	34	30	vol	vol	NOUN
cana-6180	34	31	32	32	NUM
cana-6180	35	1	no	no	NOUN
cana-6180	35	2	.	.	NOUN
cana-6180	35	3	3	3	NUM
cana-6180	35	4	(	(	PUNCT
cana-6180	35	5	2025	2025	NUM
cana-6180	35	6	)	)	PUNCT
cana-6180	35	7	1134	1134	NUM
cana-6180	35	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	35	9	then	then	ADV
cana-6180	35	10	change	change	VERB
cana-6180	35	11	the	the	DET
cana-6180	35	12	value	value	NOUN
cana-6180	35	13	of	of	ADP
cana-6180	35	14	the	the	DET
cana-6180	35	15	old	old	ADJ
cana-6180	35	16	node	node	NOUN
cana-6180	35	17	to	to	ADP
cana-6180	35	18	this	this	DET
cana-6180	35	19	node	node	NOUN
cana-6180	35	20	and	and	CCONJ
cana-6180	35	21	go	go	VERB
cana-6180	35	22	to	to	ADP
cana-6180	35	23	step5	step5	PROPN
cana-6180	35	24	.	.	PUNCT
cana-6180	36	1	step	step	NOUN
cana-6180	36	2	5	5	NUM
cana-6180	36	3	:	:	PUNCT
cana-6180	36	4	choosing	choose	VERB
cana-6180	36	5	the	the	DET
cana-6180	36	6	node	node	NOUN
cana-6180	36	7	:	:	PUNCT
cana-6180	36	8	1	1	X
cana-6180	36	9	.	.	X
cana-6180	37	1	if	if	SCONJ
cana-6180	37	2	exactly	exactly	ADV
cana-6180	37	3	one	one	NUM
cana-6180	37	4	knot	knot	NOUN
cana-6180	37	5	in	in	ADP
cana-6180	37	6	step	step	NOUN
cana-6180	37	7	4	4	NUM
cana-6180	37	8	is	be	AUX
cana-6180	37	9	.nished	.nishe	VERB
cana-6180	37	10	,	,	PUNCT
cana-6180	37	11	use	use	VERB
cana-6180	37	12	the	the	DET
cana-6180	37	13	non	non	ADJ
cana-6180	37	14	-	-	ADJ
cana-6180	37	15	terminated	terminated	ADJ
cana-6180	37	16	knot	knot	NOUN
cana-6180	37	17	and	and	CCONJ
cana-6180	37	18	go	go	VERB
cana-6180	37	19	to	to	PART
cana-6180	37	20	step	step	VERB
cana-6180	37	21	2	2	NUM
cana-6180	37	22	.	.	PUNCT
cana-6180	37	23	2if	2if	NOUN
cana-6180	37	24	all	all	DET
cana-6180	37	25	the	the	DET
cana-6180	37	26	nodes	node	NOUN
cana-6180	37	27	in	in	ADP
cana-6180	37	28	step	step	NOUN
cana-6180	37	29	4	4	NUM
cana-6180	37	30	are	be	AUX
cana-6180	37	31	in.nite	in.nite	ADJ
cana-6180	37	32	,	,	PUNCT
cana-6180	37	33	choose	choose	VERB
cana-6180	37	34	the	the	DET
cana-6180	37	35	node	node	NOUN
cana-6180	37	36	that	that	PRON
cana-6180	37	37	is	be	AUX
cana-6180	37	38	most	most	ADV
cana-6180	37	39	guar	guar	ADJ
cana-6180	37	40	anteed	anteed	NOUN
cana-6180	37	41	to	to	PART
cana-6180	37	42	reach	reach	VERB
cana-6180	37	43	the	the	DET
cana-6180	37	44	goal	goal	NOUN
cana-6180	37	45	,	,	PUNCT
cana-6180	37	46	which	which	PRON
cana-6180	37	47	is	be	AUX
cana-6180	37	48	the	the	DET
cana-6180	37	49	node	node	NOUN
cana-6180	37	50	at	at	ADP
cana-6180	37	51	which	which	PRON
cana-6180	37	52	the	the	DET
cana-6180	37	53	value	value	NOUN
cana-6180	37	54	of	of	ADP
cana-6180	37	55	the	the	DET
cana-6180	37	56	objective	objective	ADJ
cana-6180	37	57	function	function	NOUN
cana-6180	37	58	is	be	AUX
cana-6180	37	59	the	the	DET
cana-6180	37	60	largest	large	ADJ
cana-6180	37	61	possible	possible	ADJ
cana-6180	37	62	.	.	PUNCT
cana-6180	38	1	go	go	VERB
cana-6180	38	2	to	to	PART
cana-6180	38	3	step	step	VERB
cana-6180	38	4	2	2	NUM
cana-6180	38	5	.	.	PUNCT
cana-6180	39	1	the	the	DET
cana-6180	39	2	main	main	ADJ
cana-6180	39	3	negative	negative	ADJ
cana-6180	39	4	characteristic	characteristic	NOUN
cana-6180	39	5	of	of	ADP
cana-6180	39	6	this	this	DET
cana-6180	39	7	algorithm	algorithm	NOUN
cana-6180	39	8	lies	lie	VERB
cana-6180	39	9	in	in	ADP
cana-6180	39	10	solving	solve	VERB
cana-6180	39	11	a	a	DET
cana-6180	39	12	complete	complete	ADJ
cana-6180	39	13	linear	linear	ADJ
cana-6180	39	14	programming	programming	NOUN
cana-6180	39	15	problem	problem	NOUN
cana-6180	39	16	at	at	ADP
cana-6180	39	17	each	each	DET
cana-6180	39	18	node	node	NOUN
cana-6180	39	19	,	,	PUNCT
cana-6180	39	20	the	the	DET
cana-6180	39	21	procedure	procedure	NOUN
cana-6180	39	22	,	,	PUNCT
cana-6180	39	23	especially	especially	ADV
cana-6180	39	24	for	for	ADP
cana-6180	39	25	large	large	ADJ
cana-6180	39	26	problems	problem	NOUN
cana-6180	39	27	,	,	PUNCT
cana-6180	39	28	will	will	AUX
cana-6180	39	29	take	take	VERB
cana-6180	39	30	a	a	DET
cana-6180	39	31	long	long	ADJ
cana-6180	39	32	time	time	NOUN
cana-6180	39	33	as	as	ADV
cana-6180	39	34	well	well	ADV
cana-6180	39	35	as	as	ADP
cana-6180	39	36	a	a	DET
cana-6180	39	37	greater	great	ADJ
cana-6180	39	38	number	number	NOUN
cana-6180	39	39	of	of	ADP
cana-6180	39	40	iterations.[8][9][10	iterations.[8][9][10	NOUN
cana-6180	39	41	]	]	PUNCT
cana-6180	39	42	3.2	3.2	NUM
cana-6180	39	43	cutting	cut	VERB
cana-6180	39	44	planes	plane	NOUN
cana-6180	39	45	method	method	NOUN
cana-6180	39	46	cutting	cut	VERB
cana-6180	39	47	planes	plane	NOUN
cana-6180	39	48	method	method	NOUN
cana-6180	39	49	or	or	CCONJ
cana-6180	39	50	gomary	gomary	NOUN
cana-6180	39	51	method	method	NOUN
cana-6180	39	52	is	be	AUX
cana-6180	39	53	a	a	DET
cana-6180	39	54	unique	unique	ADJ
cana-6180	39	55	method	method	NOUN
cana-6180	39	56	and	and	CCONJ
cana-6180	39	57	is	be	AUX
cana-6180	39	58	the	the	DET
cana-6180	39	59	second	second	ADJ
cana-6180	39	60	convergent	convergent	NOUN
cana-6180	39	61	method	method	NOUN
cana-6180	39	62	for	for	ADP
cana-6180	39	63	solving	solve	VERB
cana-6180	39	64	integer	integer	NOUN
cana-6180	39	65	programming	programming	NOUN
cana-6180	39	66	problems	problem	NOUN
cana-6180	39	67	,	,	PUNCT
cana-6180	39	68	which	which	PRON
cana-6180	39	69	was	be	AUX
cana-6180	39	70	published	publish	VERB
cana-6180	39	71	in	in	ADP
cana-6180	39	72	1958	1958	NUM
cana-6180	39	73	by	by	ADP
cana-6180	39	74	gomary	gomary	PROPN
cana-6180	39	75	,	,	PUNCT
cana-6180	39	76	the	the	DET
cana-6180	39	77	algorithm	algorithm	NOUN
cana-6180	39	78	was	be	AUX
cana-6180	39	79	named	name	VERB
cana-6180	39	80	after	after	ADP
cana-6180	39	81	him	he	PRON
cana-6180	39	82	ralph.e.gomory	ralph.e.gomory	PROPN
cana-6180	39	83	.	.	PUNCT
cana-6180	40	1	the	the	DET
cana-6180	40	2	basic	basic	ADJ
cana-6180	40	3	idea	idea	NOUN
cana-6180	40	4	of	of	ADP
cana-6180	40	5	this	this	DET
cana-6180	40	6	method	method	NOUN
cana-6180	40	7	is	be	AUX
cana-6180	40	8	to	to	PART
cana-6180	40	9	add	add	VERB
cana-6180	40	10	a	a	DET
cana-6180	40	11	(	(	PUNCT
cana-6180	40	12	conclusive	conclusive	ADJ
cana-6180	40	13	)	)	PUNCT
cana-6180	40	14	constraint	constraint	NOUN
cana-6180	40	15	to	to	ADP
cana-6180	40	16	the	the	DET
cana-6180	40	17	problem	problem	NOUN
cana-6180	40	18	again	again	ADV
cana-6180	40	19	and	and	CCONJ
cana-6180	40	20	again	again	ADV
cana-6180	40	21	until	until	SCONJ
cana-6180	40	22	the	the	DET
cana-6180	40	23	ideal	ideal	ADJ
cana-6180	40	24	solution	solution	NOUN
cana-6180	40	25	is	be	AUX
cana-6180	40	26	reached	reach	VERB
cana-6180	40	27	.	.	PUNCT
cana-6180	41	1	this	this	DET
cana-6180	41	2	restriction	restriction	NOUN
cana-6180	41	3	has	have	VERB
cana-6180	41	4	two	two	NUM
cana-6180	41	5	fundamental	fundamental	ADJ
cana-6180	41	6	characteristics	characteristic	NOUN
cana-6180	41	7	:	:	PUNCT
cana-6180	41	8	first	first	ADV
cana-6180	41	9	,	,	PUNCT
cana-6180	41	10	the	the	DET
cana-6180	41	11	incorrect	incorrect	ADJ
cana-6180	41	12	optimal	optimal	ADJ
cana-6180	41	13	solution	solution	NOUN
cana-6180	41	14	to	to	ADP
cana-6180	41	15	the	the	DET
cana-6180	41	16	linear	linear	ADJ
cana-6180	41	17	programming	programming	NOUN
cana-6180	41	18	problem	problem	NOUN
cana-6180	41	19	does	do	AUX
cana-6180	41	20	not	not	PART
cana-6180	41	21	satisfy	satisfy	VERB
cana-6180	41	22	this	this	DET
cana-6180	41	23	constraint	constraint	NOUN
cana-6180	41	24	.	.	PUNCT
cana-6180	42	1	second	second	ADJ
cana-6180	42	2	,	,	PUNCT
cana-6180	42	3	all	all	DET
cana-6180	42	4	possible	possible	ADJ
cana-6180	42	5	correct	correct	ADJ
cana-6180	42	6	solutions	solution	NOUN
cana-6180	42	7	to	to	ADP
cana-6180	42	8	the	the	DET
cana-6180	42	9	original	original	ADJ
cana-6180	42	10	problem	problem	NOUN
cana-6180	42	11	will	will	AUX
cana-6180	42	12	satisfy	satisfy	VERB
cana-6180	42	13	this	this	DET
cana-6180	42	14	new	new	ADJ
cana-6180	42	15	constraint.[3	constraint.[3	NOUN
cana-6180	42	16	]	]	PUNCT
cana-6180	42	17	cutting	cut	VERB
cana-6180	42	18	planes	plane	NOUN
cana-6180	42	19	method	method	NOUN
cana-6180	42	20	algorithm	algorithm	NOUN
cana-6180	42	21	:	:	PUNCT
cana-6180	42	22	we	we	PRON
cana-6180	42	23	have	have	VERB
cana-6180	42	24	the	the	DET
cana-6180	42	25	following	follow	VERB
cana-6180	42	26	integer	integer	NOUN
cana-6180	42	27	programming	programming	NOUN
cana-6180	42	28	problem	problem	NOUN
cana-6180	42	29	.	.	PUNCT
cana-6180	43	1	{	{	PUNCT
cana-6180	44	1	max	max	PROPN
cana-6180	44	2	z	z	PROPN
cana-6180	44	3	=	=	PUNCT
cana-6180	44	4	𝑐𝑡𝑥	𝑐𝑡𝑥	NUM
cana-6180	44	5	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	44	6	sc	sc	NOUN
cana-6180	44	7	ax	ax	NOUN
cana-6180	44	8	=	=	SYM
cana-6180	44	9	b	b	PROPN
cana-6180	44	10	;	;	PUNCT
cana-6180	44	11	x	x	X
cana-6180	44	12	≥	≥	NUM
cana-6180	44	13	0	0	NUM
cana-6180	44	14	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	44	15	∈	∈	PROPN
cana-6180	44	16	𝐼	𝐼	PROPN
cana-6180	44	17	;	;	PUNCT
cana-6180	44	18	integer	integer	NOUN
cana-6180	44	19	.	.	PUNCT
cana-6180	45	1	........	........	PUNCT
cana-6180	45	2	4	4	NUM
cana-6180	45	3	a	a	DET
cana-6180	45	4	matrix	matrix	NOUN
cana-6180	45	5	with	with	ADP
cana-6180	45	6	dimension	dimension	NOUN
cana-6180	45	7	m	m	VERB
cana-6180	45	8	×	×	NOUN
cana-6180	45	9	s	s	NOUN
cana-6180	45	10	,	,	PUNCT
cana-6180	45	11	b	b	NOUN
cana-6180	45	12	matrix	matrix	NOUN
cana-6180	45	13	with	with	ADP
cana-6180	45	14	dimension	dimension	NOUN
cana-6180	45	15	m	m	VERB
cana-6180	45	16	×1	×1	NOUN
cana-6180	45	17	;	;	PUNCT
cana-6180	45	18	c	c	NOUN
cana-6180	45	19	matrix	matrix	NOUN
cana-6180	45	20	with	with	ADP
cana-6180	45	21	dimension	dimension	NOUN
cana-6180	45	22	s	s	PART
cana-6180	45	23	×	×	NOUN
cana-6180	45	24	1;x	1;x	NUM
cana-6180	45	25	matrix	matrix	NOUN
cana-6180	45	26	with	with	ADP
cana-6180	45	27	dimension	dimension	NOUN
cana-6180	45	28	s	s	PART
cana-6180	45	29	×	×	NOUN
cana-6180	45	30	1	1	NUM
cana-6180	45	31	:	:	PUNCT
cana-6180	45	32	step	step	NOUN
cana-6180	45	33	1	1	NUM
cana-6180	45	34	:	:	PUNCT
cana-6180	45	35	initial	initial	ADJ
cana-6180	45	36	solution	solution	NOUN
cana-6180	45	37	we	we	PRON
cana-6180	45	38	use	use	VERB
cana-6180	45	39	the	the	DET
cana-6180	45	40	simplex	simplex	NOUN
cana-6180	45	41	method	method	NOUN
cana-6180	45	42	to	to	PART
cana-6180	45	43	solve	solve	VERB
cana-6180	45	44	problem	problem	NOUN
cana-6180	45	45	(	(	PUNCT
cana-6180	45	46	2	2	NUM
cana-6180	45	47	)	)	PUNCT
cana-6180	45	48	then	then	ADV
cana-6180	45	49	we	we	PRON
cana-6180	45	50	neglect	neglect	VERB
cana-6180	45	51	the	the	DET
cana-6180	45	52	restrictions	restriction	NOUN
cana-6180	45	53	related	relate	VERB
cana-6180	45	54	to	to	ADP
cana-6180	45	55	the	the	DET
cana-6180	45	56	integer	integer	NOUN
cana-6180	45	57	variables	variable	NOUN
cana-6180	45	58	,	,	PUNCT
cana-6180	45	59	if	if	SCONJ
cana-6180	45	60	all	all	DET
cana-6180	45	61	values	value	NOUN
cana-6180	45	62	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	45	63	∈	∈	PROPN
cana-6180	45	64	𝐼	𝐼	PROPN
cana-6180	45	65	are	be	AUX
cana-6180	45	66	integer	integer	NOUN
cana-6180	45	67	,	,	PUNCT
cana-6180	45	68	we	we	PRON
cana-6180	45	69	move	move	VERB
cana-6180	45	70	to	to	ADP
cana-6180	45	71	the	the	DET
cana-6180	45	72	step2	step2	PROPN
cana-6180	45	73	communications	communication	NOUN
cana-6180	45	74	on	on	ADP
cana-6180	45	75	applied	apply	VERB
cana-6180	45	76	nonlinear	nonlinear	ADJ
cana-6180	45	77	analysis	analysis	NOUN
cana-6180	45	78	issn	issn	NOUN
cana-6180	45	79	:	:	PUNCT
cana-6180	45	80	1074	1074	NUM
cana-6180	45	81	-	-	PUNCT
cana-6180	45	82	133x	133x	NUM
cana-6180	45	83	vol	vol	NOUN
cana-6180	45	84	32	32	NUM
cana-6180	45	85	no	no	NOUN
cana-6180	45	86	.	.	NOUN
cana-6180	45	87	3	3	NUM
cana-6180	45	88	(	(	PUNCT
cana-6180	45	89	2025	2025	NUM
cana-6180	45	90	)	)	PUNCT
cana-6180	45	91	1135	1135	NUM
cana-6180	45	92	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	45	93	step	step	NOUN
cana-6180	45	94	2	2	NUM
cana-6180	45	95	:	:	PUNCT
cana-6180	45	96	choose	choose	VERB
cana-6180	45	97	the	the	DET
cana-6180	45	98	line	line	NOUN
cana-6180	45	99	from	from	ADP
cana-6180	45	100	the	the	DET
cana-6180	45	101	last	last	ADJ
cana-6180	45	102	table	table	NOUN
cana-6180	45	103	in	in	ADP
cana-6180	45	104	the	the	DET
cana-6180	45	105	solution	solution	NOUN
cana-6180	45	106	to	to	ADP
cana-6180	45	107	the	the	DET
cana-6180	45	108	linear	linear	ADJ
cana-6180	45	109	programming	programming	NOUN
cana-6180	45	110	problem	problem	NOUN
cana-6180	45	111	in	in	ADP
cana-6180	45	112	which	which	PRON
cana-6180	45	113	the	the	DET
cana-6180	45	114	basic	basic	ADJ
cana-6180	45	115	variable	variable	ADJ
cana-6180	45	116	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	45	117	is	be	AUX
cana-6180	45	118	not	not	PART
cana-6180	45	119	an	an	DET
cana-6180	45	120	integer	integer	NOUN
cana-6180	45	121	value	value	NOUN
cana-6180	45	122	(	(	PUNCT
cana-6180	45	123	bi	bi	NOUN
cana-6180	45	124	use	use	VERB
cana-6180	45	125	the	the	DET
cana-6180	45	126	line	line	NOUN
cana-6180	45	127	in	in	ADP
cana-6180	45	128	which	which	PRON
cana-6180	45	129	the	the	DET
cana-6180	45	130	value	value	NOUN
cana-6180	45	131	of	of	ADP
cana-6180	45	132	that	that	DET
cana-6180	45	133	variable	variable	NOUN
cana-6180	45	134	has	have	VERB
cana-6180	45	135	the	the	DET
cana-6180	45	136	largest	large	ADJ
cana-6180	45	137	fractional	fractional	ADJ
cana-6180	45	138	part	part	NOUN
cana-6180	45	139	,	,	PUNCT
cana-6180	45	140	because	because	SCONJ
cana-6180	45	141	this	this	PRON
cana-6180	45	142	may	may	AUX
cana-6180	45	143	help	help	VERB
cana-6180	45	144	reduce	reduce	VERB
cana-6180	45	145	the	the	DET
cana-6180	45	146	number	number	NOUN
cana-6180	45	147	of	of	ADP
cana-6180	45	148	iterations	iteration	NOUN
cana-6180	45	149	and	and	CCONJ
cana-6180	45	150	the	the	DET
cana-6180	45	151	time	time	NOUN
cana-6180	45	152	it	it	PRON
cana-6180	45	153	takes	take	VERB
cana-6180	45	154	to	to	PART
cana-6180	45	155	converge	converge	VERB
cana-6180	45	156	)	)	PUNCT
cana-6180	45	157	and	and	CCONJ
cana-6180	45	158	from	from	ADP
cana-6180	45	159	it	it	PRON
cana-6180	45	160	generate	generate	VERB
cana-6180	45	161	or	or	CCONJ
cana-6180	45	162	create	create	VERB
cana-6180	45	163	a	a	DET
cana-6180	45	164	cutting	cut	VERB
cana-6180	45	165	planes	plane	NOUN
cana-6180	45	166	constraint	constraint	NOUN
cana-6180	45	167	.	.	PUNCT
cana-6180	46	1	step	step	NOUN
cana-6180	46	2	3	3	NUM
cana-6180	46	3	let	let	VERB
cana-6180	46	4	the	the	DET
cana-6180	46	5	chosen	choose	VERB
cana-6180	46	6	line	line	NOUN
cana-6180	46	7	be	be	AUX
cana-6180	46	8	the	the	DET
cana-6180	46	9	line	line	NOUN
cana-6180	46	10	with	with	ADP
cana-6180	46	11	index	index	NOUN
cana-6180	46	12	i	i	PRON
cana-6180	46	13	and	and	CCONJ
cana-6180	46	14	its	its	PRON
cana-6180	46	15	equation	equation	NOUN
cana-6180	46	16	is	be	AUX
cana-6180	46	17	:	:	PUNCT
cana-6180	46	18	𝑥𝐵𝑖	𝑥𝐵𝑖	NUM
cana-6180	46	19	+	+	NOUN
cana-6180	46	20	∑	∑	NOUN
cana-6180	46	21	𝑎𝑖𝑗.	𝑎𝑖𝑗.	X
cana-6180	46	22	𝑛	𝑛	PROPN
cana-6180	46	23	𝐽=1	𝐽=1	PROPN
cana-6180	46	24	𝑥𝑗	𝑥𝑗	NOUN
cana-6180	46	25	=	=	PUNCT
cana-6180	46	26	𝑏𝑖𝑗	𝑏𝑖𝑗	NOUN
cana-6180	46	27	;	;	PUNCT
cana-6180	46	28	𝑗	𝑗	PRON
cana-6180	46	29	∈	∈	NOUN
cana-6180	46	30	𝐼	𝐼	ADP
cana-6180	46	31	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	46	32	+	+	NOUN
cana-6180	46	33	∑	∑	PROPN
cana-6180	46	34	(	(	PUNCT
cana-6180	46	35	𝑛	𝑛	PROPN
cana-6180	46	36	𝐽=1	𝐽=1	PROPN
cana-6180	47	1	[	[	X
cana-6180	47	2	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-6180	47	3	]	]	X
cana-6180	47	4	+	+	CCONJ
cana-6180	47	5	𝑓𝑖𝑗.)𝑥𝑖	𝑓𝑖𝑗.)𝑥𝑖	NUM
cana-6180	47	6	=	=	PUNCT
cana-6180	48	1	[	[	X
cana-6180	48	2	𝑏𝑖	𝑏𝑖	X
cana-6180	48	3	]	]	X
cana-6180	48	4	+	+	CCONJ
cana-6180	48	5	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	48	6	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	48	7	+	+	NOUN
cana-6180	48	8	∑	∑	PROPN
cana-6180	48	9	(	(	PUNCT
cana-6180	48	10	𝑛	𝑛	PROPN
cana-6180	48	11	𝐽=1	𝐽=1	PROPN
cana-6180	49	1	[	[	X
cana-6180	49	2	𝑎𝑖𝑗]𝑥𝑖	𝑎𝑖𝑗]𝑥𝑖	NUM
cana-6180	49	3	−	−	PROPN
cana-6180	50	1	[	[	X
cana-6180	50	2	𝑏𝑖])𝑥𝑖	𝑏𝑖])𝑥𝑖	PROPN
cana-6180	50	3	=	=	SYM
cana-6180	50	4	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	50	5	−∑	−∑	PROPN
cana-6180	50	6	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	50	7	𝑛	𝑛	PROPN
cana-6180	50	8	𝐽=1	𝐽=1	PROPN
cana-6180	50	9	𝑥𝑖	𝑥𝑖	CCONJ
cana-6180	50	10	≤0	≤0	NOUN
cana-6180	50	11	new	new	ADJ
cana-6180	50	12	condition	condition	NOUN
cana-6180	50	13	is	be	AUX
cana-6180	50	14	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	50	15	−∑	−∑	PROPN
cana-6180	50	16	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	50	17	𝑛	𝑛	PROPN
cana-6180	50	18	𝐽=1	𝐽=1	PROPN
cana-6180	50	19	𝑥𝑖	𝑥𝑖	PRON
cana-6180	50	20	+	+	CCONJ
cana-6180	50	21	µ	µ	X
cana-6180	50	22	=	=	SYM
cana-6180	50	23	0	0	NUM
cana-6180	50	24	…	…	SYM
cana-6180	50	25	5	5	NUM
cana-6180	50	26	such	such	ADJ
cana-6180	50	27	as	as	ADP
cana-6180	50	28	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	50	29	=	=	SYM
cana-6180	50	30	𝑎𝑖𝑗.	𝑎𝑖𝑗.	NOUN
cana-6180	50	31	−	−	PROPN
cana-6180	51	1	[	[	X
cana-6180	51	2	𝑎𝑖𝑗]is	𝑎𝑖𝑗]is	VERB
cana-6180	51	3	the	the	DET
cana-6180	51	4	fractional	fractional	ADJ
cana-6180	51	5	part	part	NOUN
cana-6180	51	6	of	of	ADP
cana-6180	51	7	𝑎𝑖𝑗.0	𝑎𝑖𝑗.0	NOUN
cana-6180	51	8	≤	≤	NUM
cana-6180	51	9	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	51	10	≤	≤	NOUN
cana-6180	51	11	1	1	NUM
cana-6180	51	12	𝑓𝑖	𝑓𝑖	NOUN
cana-6180	51	13	=	=	PUNCT
cana-6180	51	14	𝑏𝑖	𝑏𝑖	ADP
cana-6180	51	15	−	−	PROPN
cana-6180	52	1	[	[	X
cana-6180	52	2	𝑏𝑖	𝑏𝑖	X
cana-6180	52	3	]	]	X
cana-6180	52	4	is	be	AUX
cana-6180	52	5	the	the	DET
cana-6180	52	6	fractional	fractional	ADJ
cana-6180	52	7	part	part	NOUN
cana-6180	52	8	of	of	ADP
cana-6180	52	9	𝑏𝑖0	𝑏𝑖0	PROPN
cana-6180	52	10	≤	≤	X
cana-6180	52	11	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	52	12	≤	≤	NUM
cana-6180	52	13	1	1	NUM
cana-6180	52	14	µ	µ	PRON
cana-6180	52	15	new	new	ADJ
cana-6180	52	16	auxiliary	auxiliary	ADJ
cana-6180	52	17	variable	variable	NOUN
cana-6180	52	18	is	be	AUX
cana-6180	52	19	integer	integer	ADJ
cana-6180	52	20	step	step	NOUN
cana-6180	52	21	4	4	NUM
cana-6180	52	22	add	add	VERB
cana-6180	52	23	constraint	constraint	NOUN
cana-6180	52	24	add	add	VERB
cana-6180	52	25	the	the	DET
cana-6180	52	26	constraint	constraint	NOUN
cana-6180	52	27	5	5	NUM
cana-6180	52	28	to	to	ADP
cana-6180	52	29	the	the	DET
cana-6180	52	30	last	last	ADJ
cana-6180	52	31	table	table	NOUN
cana-6180	52	32	of	of	ADP
cana-6180	52	33	the	the	DET
cana-6180	52	34	solution	solution	NOUN
cana-6180	52	35	to	to	ADP
cana-6180	52	36	the	the	DET
cana-6180	52	37	simplex	simplex	NOUN
cana-6180	52	38	algorithm	algorithm	NOUN
cana-6180	52	39	and	and	CCONJ
cana-6180	52	40	solve	solve	VERB
cana-6180	52	41	the	the	DET
cana-6180	52	42	solution	solution	NOUN
cana-6180	52	43	as	as	ADP
cana-6180	52	44	a	a	DET
cana-6180	52	45	linear	linear	ADJ
cana-6180	52	46	programming	programming	NOUN
cana-6180	52	47	problem	problem	NOUN
cana-6180	52	48	.	.	PUNCT
cana-6180	53	1	[	[	X
cana-6180	53	2	11	11	NUM
cana-6180	53	3	]	]	PUNCT
cana-6180	53	4	here	here	ADV
cana-6180	53	5	we	we	PRON
cana-6180	53	6	discuss	discuss	VERB
cana-6180	53	7	the	the	DET
cana-6180	53	8	following	follow	VERB
cana-6180	53	9	cases	case	NOUN
cana-6180	53	10	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	NOUN
cana-6180	53	11	∈	∈	NOUN
cana-6180	53	12	𝐼	𝐼	ADP
cana-6180	53	13	if	if	SCONJ
cana-6180	53	14	the	the	DET
cana-6180	53	15	values	value	NOUN
cana-6180	53	16	are	be	AUX
cana-6180	53	17	integer	integer	NOUN
cana-6180	53	18	and	and	CCONJ
cana-6180	53	19	possible	possible	ADJ
cana-6180	53	20	,	,	PUNCT
cana-6180	53	21	the	the	DET
cana-6180	53	22	problem	problem	NOUN
cana-6180	53	23	is	be	AUX
cana-6180	53	24	end	end	NOUN
cana-6180	53	25	.	.	PUNCT
cana-6180	54	1	otherwise	otherwise	ADV
cana-6180	54	2	,	,	PUNCT
cana-6180	54	3	go	go	VERB
cana-6180	54	4	to	to	ADP
cana-6180	54	5	the	the	DET
cana-6180	54	6	next	next	ADJ
cana-6180	54	7	step2	step2	PROPN
cana-6180	54	8	,	,	PUNCT
cana-6180	54	9	3.3	3.3	NUM
cana-6180	54	10	new	new	ADJ
cana-6180	54	11	algorithm	algorithm	NOUN
cana-6180	54	12	for	for	ADP
cana-6180	54	13	solving	solve	VERB
cana-6180	54	14	integer	integer	NOUN
cana-6180	54	15	linear	linear	NOUN
cana-6180	54	16	programming	programming	NOUN
cana-6180	54	17	problems	problem	NOUN
cana-6180	54	18	the	the	DET
cana-6180	54	19	proposed	propose	VERB
cana-6180	54	20	method	method	NOUN
cana-6180	54	21	is	be	AUX
cana-6180	54	22	a	a	DET
cana-6180	54	23	new	new	ADJ
cana-6180	54	24	technique	technique	NOUN
cana-6180	54	25	that	that	PRON
cana-6180	54	26	is	be	AUX
cana-6180	54	27	very	very	ADV
cana-6180	54	28	successful	successful	ADJ
cana-6180	54	29	in	in	ADP
cana-6180	54	30	solving	solve	VERB
cana-6180	54	31	a	a	DET
cana-6180	54	32	wide	wide	ADJ
cana-6180	54	33	range	range	NOUN
cana-6180	54	34	of	of	ADP
cana-6180	54	35	integer	integer	NOUN
cana-6180	54	36	programming	programming	NOUN
cana-6180	54	37	problems	problem	NOUN
cana-6180	54	38	guarantee	guarantee	VERB
cana-6180	54	39	of	of	ADP
cana-6180	54	40	reaching	reach	VERB
cana-6180	54	41	the	the	DET
cana-6180	54	42	integer	integer	NOUN
cana-6180	54	43	ideal	ideal	ADJ
cana-6180	54	44	solution	solution	NOUN
cana-6180	54	45	.	.	PUNCT
cana-6180	55	1	we	we	PRON
cana-6180	55	2	will	will	AUX
cana-6180	55	3	explain	explain	VERB
cana-6180	55	4	below	below	ADP
cana-6180	55	5	how	how	SCONJ
cana-6180	55	6	this	this	DET
cana-6180	55	7	technique	technique	NOUN
cana-6180	55	8	is	be	AUX
cana-6180	55	9	performed	perform	VERB
cana-6180	55	10	,	,	PUNCT
cana-6180	55	11	noting	note	VERB
cana-6180	55	12	that	that	SCONJ
cana-6180	55	13	the	the	DET
cana-6180	55	14	new	new	ADJ
cana-6180	55	15	cutting	cutting	NOUN
cana-6180	55	16	and	and	CCONJ
cana-6180	55	17	branching	branch	VERB
cana-6180	55	18	algorithm	algorithm	NOUN
cana-6180	55	19	is	be	AUX
cana-6180	55	20	used	use	VERB
cana-6180	55	21	it	it	PRON
cana-6180	55	22	can	can	AUX
cana-6180	55	23	be	be	AUX
cana-6180	55	24	developed	develop	VERB
cana-6180	55	25	and	and	CCONJ
cana-6180	55	26	expanded	expand	VERB
cana-6180	55	27	,	,	PUNCT
cana-6180	55	28	and	and	CCONJ
cana-6180	55	29	it	it	PRON
cana-6180	55	30	is	be	AUX
cana-6180	55	31	a	a	DET
cana-6180	55	32	promising	promising	ADJ
cana-6180	55	33	algorithm	algorithm	NOUN
cana-6180	55	34	that	that	PRON
cana-6180	55	35	can	can	AUX
cana-6180	55	36	be	be	AUX
cana-6180	55	37	computer	computer	NOUN
cana-6180	55	38	programmed	program	VERB
cana-6180	55	39	,	,	PUNCT
cana-6180	55	40	and	and	CCONJ
cana-6180	55	41	it	it	PRON
cana-6180	55	42	will	will	AUX
cana-6180	55	43	be	be	AUX
cana-6180	55	44	of	of	ADP
cana-6180	55	45	greater	great	ADJ
cana-6180	55	46	importance	importance	NOUN
cana-6180	55	47	with	with	ADP
cana-6180	55	48	the	the	DET
cana-6180	55	49	exploitation	exploitation	NOUN
cana-6180	55	50	of	of	ADP
cana-6180	55	51	speed	speed	NOUN
cana-6180	55	52	current	current	ADJ
cana-6180	55	53	computers	computer	NOUN
cana-6180	55	54	.	.	PUNCT
cana-6180	56	1	communications	communication	NOUN
cana-6180	56	2	on	on	ADP
cana-6180	56	3	applied	apply	VERB
cana-6180	56	4	nonlinear	nonlinear	ADJ
cana-6180	56	5	analysis	analysis	NOUN
cana-6180	56	6	issn	issn	NOUN
cana-6180	56	7	:	:	PUNCT
cana-6180	56	8	1074	1074	NUM
cana-6180	56	9	-	-	PUNCT
cana-6180	56	10	133x	133x	NUM
cana-6180	56	11	vol	vol	NOUN
cana-6180	56	12	32	32	NUM
cana-6180	56	13	no	no	NOUN
cana-6180	56	14	.	.	NOUN
cana-6180	56	15	3	3	NUM
cana-6180	56	16	(	(	PUNCT
cana-6180	56	17	2025	2025	NUM
cana-6180	56	18	)	)	PUNCT
cana-6180	56	19	1136	1136	NUM
cana-6180	56	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	56	21	the	the	DET
cana-6180	56	22	new	new	ADJ
cana-6180	56	23	technique	technique	NOUN
cana-6180	56	24	and	and	CCONJ
cana-6180	56	25	branching	branch	VERB
cana-6180	56	26	algorithm	algorithm	NOUN
cana-6180	56	27	is	be	AUX
cana-6180	56	28	a	a	DET
cana-6180	56	29	combination	combination	NOUN
cana-6180	56	30	of	of	ADP
cana-6180	56	31	the	the	DET
cana-6180	56	32	cutting	cut	VERB
cana-6180	56	33	planes	plane	NOUN
cana-6180	56	34	method	method	NOUN
cana-6180	56	35	and	and	CCONJ
cana-6180	56	36	the	the	DET
cana-6180	56	37	branching	branch	VERB
cana-6180	56	38	and	and	CCONJ
cana-6180	56	39	knotting	knotting	NOUN
cana-6180	56	40	method	method	NOUN
cana-6180	56	41	,	,	PUNCT
cana-6180	56	42	and	and	CCONJ
cana-6180	56	43	it	it	PRON
cana-6180	56	44	works	work	VERB
cana-6180	56	45	like	like	ADP
cana-6180	56	46	its	its	PRON
cana-6180	56	47	predecessors	predecessor	NOUN
cana-6180	56	48	,	,	PUNCT
cana-6180	56	49	it	it	PRON
cana-6180	56	50	involves	involve	VERB
cana-6180	56	51	solving	solve	VERB
cana-6180	56	52	a	a	DET
cana-6180	56	53	successive	successive	ADJ
cana-6180	56	54	series	series	NOUN
cana-6180	56	55	of	of	ADP
cana-6180	56	56	linear	linear	PROPN
cana-6180	56	57	programming	programming	NOUN
cana-6180	56	58	problems	problem	NOUN
cana-6180	56	59	to	to	PART
cana-6180	56	60	obtain	obtain	VERB
cana-6180	56	61	the	the	DET
cana-6180	56	62	solution	solution	NOUN
cana-6180	56	63	to	to	ADP
cana-6180	56	64	the	the	DET
cana-6180	56	65	integert	integert	ADJ
cana-6180	56	66	programming	programming	NOUN
cana-6180	56	67	problem	problem	NOUN
cana-6180	56	68	.	.	PUNCT
cana-6180	57	1	the	the	DET
cana-6180	57	2	method	method	NOUN
cana-6180	57	3	of	of	ADP
cana-6180	57	4	cutting	cut	VERB
cana-6180	57	5	planes	plane	NOUN
cana-6180	57	6	that	that	PRON
cana-6180	57	7	was	be	AUX
cana-6180	57	8	explained	explain	VERB
cana-6180	57	9	in	in	ADP
cana-6180	57	10	the	the	DET
cana-6180	57	11	previous	previous	ADJ
cana-6180	57	12	paragraph	paragraph	NOUN
cana-6180	57	13	5	5	NUM
cana-6180	57	14	does	do	AUX
cana-6180	57	15	not	not	PART
cana-6180	57	16	seem	seem	VERB
cana-6180	57	17	to	to	PART
cana-6180	57	18	be	be	AUX
cana-6180	57	19	a	a	DET
cana-6180	57	20	strong	strong	ADJ
cana-6180	57	21	method	method	NOUN
cana-6180	57	22	,	,	PUNCT
cana-6180	57	23	as	as	SCONJ
cana-6180	57	24	it	it	PRON
cana-6180	57	25	seeks	seek	VERB
cana-6180	57	26	to	to	ADP
cana-6180	57	27	obtaining	obtain	VERB
cana-6180	57	28	the	the	DET
cana-6180	57	29	integer	integer	NOUN
cana-6180	57	30	ideal	ideal	ADJ
cana-6180	57	31	solution	solution	NOUN
cana-6180	57	32	has	have	VERB
cana-6180	57	33	a	a	DET
cana-6180	57	34	slow	slow	ADJ
cana-6180	57	35	convergence	convergence	NOUN
cana-6180	57	36	,	,	PUNCT
cana-6180	57	37	and	and	CCONJ
cana-6180	57	38	may	may	AUX
cana-6180	57	39	not	not	PART
cana-6180	57	40	give	give	VERB
cana-6180	57	41	the	the	DET
cana-6180	57	42	optimal	optimal	ADJ
cana-6180	57	43	solution	solution	NOUN
cana-6180	57	44	or	or	CCONJ
cana-6180	57	45	guarantee	guarantee	NOUN
cana-6180	57	46	obtaining	obtain	VERB
cana-6180	57	47	it	it	PRON
cana-6180	57	48	,	,	PUNCT
cana-6180	57	49	as	as	ADP
cana-6180	57	50	in	in	ADP
cana-6180	57	51	the	the	DET
cana-6180	57	52	branching	branch	VERB
cana-6180	57	53	method	method	NOUN
cana-6180	57	54	and	and	CCONJ
cana-6180	57	55	the	the	DET
cana-6180	57	56	nodes	node	NOUN
cana-6180	57	57	that	that	PRON
cana-6180	57	58	are	be	AUX
cana-6180	57	59	faster	fast	ADJ
cana-6180	57	60	and	and	CCONJ
cana-6180	57	61	more	more	ADV
cana-6180	57	62	guaranteed	guarantee	VERB
cana-6180	57	63	to	to	PART
cana-6180	57	64	reach	reach	VERB
cana-6180	57	65	the	the	DET
cana-6180	57	66	optimal	optimal	ADJ
cana-6180	57	67	solution	solution	NOUN
cana-6180	57	68	,	,	PUNCT
cana-6180	57	69	so	so	ADV
cana-6180	57	70	we	we	PRON
cana-6180	57	71	tried	try	VERB
cana-6180	57	72	to	to	PART
cana-6180	57	73	make	make	VERB
cana-6180	57	74	the	the	DET
cana-6180	57	75	level	level	NOUN
cana-6180	57	76	cutting	cutting	NOUN
cana-6180	57	77	method	method	NOUN
cana-6180	57	78	better	well	ADV
cana-6180	57	79	from	from	ADP
cana-6180	57	80	the	the	DET
cana-6180	57	81	previous	previous	ADJ
cana-6180	57	82	,	,	PUNCT
cana-6180	57	83	this	this	PRON
cana-6180	57	84	was	be	AUX
cana-6180	57	85	done	do	VERB
cana-6180	57	86	by	by	ADP
cana-6180	57	87	making	make	VERB
cana-6180	57	88	a	a	DET
cana-6180	57	89	synthesis	synthesis	NOUN
cana-6180	57	90	and	and	CCONJ
cana-6180	57	91	linking	link	VERB
cana-6180	57	92	it	it	PRON
cana-6180	57	93	with	with	ADP
cana-6180	57	94	the	the	DET
cana-6180	57	95	method	method	NOUN
cana-6180	57	96	of	of	ADP
cana-6180	57	97	branch	branch	NOUN
cana-6180	57	98	ing	ing	NOUN
cana-6180	57	99	and	and	CCONJ
cana-6180	57	100	contracting	contracting	NOUN
cana-6180	57	101	,	,	PUNCT
cana-6180	57	102	and	and	CCONJ
cana-6180	57	103	we	we	PRON
cana-6180	57	104	called	call	VERB
cana-6180	57	105	this	this	DET
cana-6180	57	106	new	new	ADJ
cana-6180	57	107	synthesis	synthesis	NOUN
cana-6180	57	108	the	the	DET
cana-6180	57	109	method	method	NOUN
cana-6180	57	110	of	of	ADP
cana-6180	57	111	cutting	cut	VERB
cana-6180	57	112	and	and	CCONJ
cana-6180	57	113	branching	branch	VERB
cana-6180	57	114	,	,	PUNCT
cana-6180	57	115	noting	note	VERB
cana-6180	57	116	here	here	ADV
cana-6180	57	117	that	that	SCONJ
cana-6180	57	118	this	this	DET
cana-6180	57	119	new	new	ADJ
cana-6180	57	120	structure	structure	NOUN
cana-6180	57	121	was	be	AUX
cana-6180	57	122	built	build	VERB
cana-6180	57	123	through	through	ADP
cana-6180	57	124	the	the	DET
cana-6180	57	125	two	two	NUM
cana-6180	57	126	algorithms	algorithm	NOUN
cana-6180	57	127	described	describe	VERB
cana-6180	57	128	in	in	ADP
cana-6180	57	129	paragraphs	paragraph	NOUN
cana-6180	57	130	1.6	1.6	NUM
cana-6180	57	131	.	.	PUNCT
cana-6180	58	1	and	and	CCONJ
cana-6180	58	2	the	the	DET
cana-6180	58	3	following	follow	VERB
cana-6180	58	4	two.6	two.6	PRON
cana-6180	58	5	we	we	PRON
cana-6180	58	6	have	have	VERB
cana-6180	58	7	the	the	DET
cana-6180	58	8	following	follow	VERB
cana-6180	58	9	integer	integer	NOUN
cana-6180	58	10	programming	programming	NOUN
cana-6180	58	11	problem	problem	NOUN
cana-6180	58	12	.	.	PUNCT
cana-6180	59	1	{	{	PUNCT
cana-6180	60	1	max	max	PROPN
cana-6180	60	2	z	z	PROPN
cana-6180	60	3	=	=	PUNCT
cana-6180	60	4	𝑐𝑡𝑥	𝑐𝑡𝑥	NUM
cana-6180	60	5	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	60	6	sc	sc	NOUN
cana-6180	60	7	ax	ax	NOUN
cana-6180	60	8	=	=	SYM
cana-6180	60	9	b	b	PROPN
cana-6180	60	10	;	;	PUNCT
cana-6180	60	11	x	x	X
cana-6180	60	12	≥	≥	NUM
cana-6180	60	13	0	0	NUM
cana-6180	60	14	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	60	15	∈	∈	PROPN
cana-6180	60	16	𝐼	𝐼	PROPN
cana-6180	60	17	;	;	PUNCT
cana-6180	60	18	integer	integer	NOUN
cana-6180	60	19	.	.	PUNCT
cana-6180	61	1	........	........	PUNCT
cana-6180	61	2	6	6	NUM
cana-6180	61	3	a	a	DET
cana-6180	61	4	matrix	matrix	NOUN
cana-6180	61	5	with	with	ADP
cana-6180	61	6	dimension	dimension	NOUN
cana-6180	61	7	m	m	VERB
cana-6180	61	8	×	×	NOUN
cana-6180	61	9	s	s	NOUN
cana-6180	61	10	,	,	PUNCT
cana-6180	61	11	b	b	NOUN
cana-6180	61	12	matrix	matrix	NOUN
cana-6180	61	13	with	with	ADP
cana-6180	61	14	dimension	dimension	NOUN
cana-6180	61	15	m	m	VERB
cana-6180	61	16	×1	×1	NOUN
cana-6180	61	17	;	;	PUNCT
cana-6180	61	18	c	c	NOUN
cana-6180	61	19	matrix	matrix	NOUN
cana-6180	61	20	with	with	ADP
cana-6180	61	21	dimension	dimension	NOUN
cana-6180	61	22	s	s	PART
cana-6180	61	23	×	×	NOUN
cana-6180	61	24	1;x	1;x	NUM
cana-6180	61	25	matrix	matrix	NOUN
cana-6180	61	26	with	with	ADP
cana-6180	61	27	dimension	dimension	NOUN
cana-6180	61	28	s	s	PART
cana-6180	61	29	×	×	NOUN
cana-6180	61	30	1	1	NUM
cana-6180	61	31	:	:	PUNCT
cana-6180	61	32	step	step	NOUN
cana-6180	61	33	1	1	NUM
cana-6180	61	34	:	:	PUNCT
cana-6180	61	35	initial	initial	ADJ
cana-6180	61	36	solution	solution	NOUN
cana-6180	61	37	start	start	VERB
cana-6180	61	38	by	by	ADP
cana-6180	61	39	solving	solve	VERB
cana-6180	61	40	the	the	DET
cana-6180	61	41	problem	problem	NOUN
cana-6180	61	42	given	give	VERB
cana-6180	61	43	in	in	ADP
cana-6180	61	44	6	6	NUM
cana-6180	61	45	as	as	ADP
cana-6180	61	46	a	a	DET
cana-6180	61	47	linear	linear	ADJ
cana-6180	61	48	programming	programming	NOUN
cana-6180	61	49	problem	problem	NOUN
cana-6180	61	50	using	use	VERB
cana-6180	61	51	the	the	DET
cana-6180	61	52	simplex	simplex	NOUN
cana-6180	61	53	algorithm	algorithm	NOUN
cana-6180	61	54	,	,	PUNCT
cana-6180	61	55	ignoring	ignore	VERB
cana-6180	61	56	the	the	DET
cana-6180	61	57	constraints	constraint	NOUN
cana-6180	61	58	.	.	PUNCT
cana-6180	62	1	intrgera	intrgera	NOUN
cana-6180	62	2	on	on	ADP
cana-6180	62	3	the	the	DET
cana-6180	62	4	decision	decision	NOUN
cana-6180	62	5	variables	variable	NOUN
cana-6180	62	6	𝑥𝑗;𝑗	𝑥𝑗;𝑗	PUNCT
cana-6180	62	7	∈	∈	VERB
cana-6180	62	8	𝐼	𝐼	SCONJ
cana-6180	62	9	if	if	SCONJ
cana-6180	62	10	all	all	DET
cana-6180	62	11	variables	variable	NOUN
cana-6180	62	12	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	62	13	∈	∈	PROPN
cana-6180	62	14	𝐼	𝐼	PROPN
cana-6180	62	15	are	be	AUX
cana-6180	62	16	integer	integer	NOUN
cana-6180	62	17	values	value	NOUN
cana-6180	62	18	,	,	PUNCT
cana-6180	62	19	stop	stop	VERB
cana-6180	62	20	,	,	PUNCT
cana-6180	62	21	otherwise	otherwise	ADV
cana-6180	62	22	go	go	VERB
cana-6180	62	23	to	to	ADP
cana-6180	62	24	step2	step2	PROPN
cana-6180	62	25	.	.	PUNCT
cana-6180	63	1	step	step	NOUN
cana-6180	63	2	2	2	NUM
cana-6180	63	3	:	:	PUNCT
cana-6180	63	4	we	we	PRON
cana-6180	63	5	choose	choose	VERB
cana-6180	63	6	the	the	DET
cana-6180	63	7	aconstraint	aconstraint	NOUN
cana-6180	63	8	we	we	PRON
cana-6180	63	9	use	use	VERB
cana-6180	63	10	the	the	DET
cana-6180	63	11	simplex	simplex	NOUN
cana-6180	63	12	method	method	NOUN
cana-6180	63	13	to	to	PART
cana-6180	63	14	solve	solve	VERB
cana-6180	63	15	problem	problem	NOUN
cana-6180	63	16	(	(	PUNCT
cana-6180	63	17	6	6	NUM
cana-6180	63	18	)	)	PUNCT
cana-6180	63	19	then	then	ADV
cana-6180	63	20	we	we	PRON
cana-6180	63	21	neglect	neglect	VERB
cana-6180	63	22	the	the	DET
cana-6180	63	23	restrictions	restriction	NOUN
cana-6180	63	24	related	relate	VERB
cana-6180	63	25	to	to	ADP
cana-6180	63	26	the	the	DET
cana-6180	63	27	integer	integer	NOUN
cana-6180	63	28	variables	variable	NOUN
cana-6180	63	29	,	,	PUNCT
cana-6180	63	30	if	if	SCONJ
cana-6180	63	31	all	all	DET
cana-6180	63	32	values	value	NOUN
cana-6180	63	33	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	63	34	∈	∈	PROPN
cana-6180	63	35	𝐼	𝐼	PROPN
cana-6180	63	36	are	be	AUX
cana-6180	63	37	integer	integer	NOUN
cana-6180	63	38	,	,	PUNCT
cana-6180	63	39	we	we	PRON
cana-6180	63	40	move	move	VERB
cana-6180	63	41	to	to	ADP
cana-6180	63	42	the	the	DET
cana-6180	63	43	step	step	NOUN
cana-6180	63	44	6	6	NUM
cana-6180	63	45	.	.	PUNCT
cana-6180	64	1	choose	choose	VERB
cana-6180	64	2	the	the	DET
cana-6180	64	3	line	line	NOUN
cana-6180	64	4	from	from	ADP
cana-6180	64	5	the	the	DET
cana-6180	64	6	last	last	ADJ
cana-6180	64	7	table	table	NOUN
cana-6180	64	8	in	in	ADP
cana-6180	64	9	the	the	DET
cana-6180	64	10	solution	solution	NOUN
cana-6180	64	11	to	to	ADP
cana-6180	64	12	the	the	DET
cana-6180	64	13	linear	linear	ADJ
cana-6180	64	14	programming	programming	NOUN
cana-6180	64	15	problem	problem	NOUN
cana-6180	64	16	in	in	ADP
cana-6180	64	17	which	which	PRON
cana-6180	64	18	the	the	DET
cana-6180	64	19	basic	basic	ADJ
cana-6180	64	20	variable	variable	ADJ
cana-6180	64	21	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	64	22	is	be	AUX
cana-6180	64	23	not	not	PART
cana-6180	64	24	integer	integer	NOUN
cana-6180	64	25	value	value	NOUN
cana-6180	64	26	(	(	PUNCT
cana-6180	64	27	𝑏𝑖	𝑏𝑖	AUX
cana-6180	64	28	use	use	VERB
cana-6180	64	29	the	the	DET
cana-6180	64	30	line	line	NOUN
cana-6180	64	31	in	in	ADP
cana-6180	64	32	which	which	PRON
cana-6180	64	33	the	the	DET
cana-6180	64	34	value	value	NOUN
cana-6180	64	35	of	of	ADP
cana-6180	64	36	that	that	DET
cana-6180	64	37	variable	variable	NOUN
cana-6180	64	38	has	have	VERB
cana-6180	64	39	the	the	DET
cana-6180	64	40	largest	large	ADJ
cana-6180	64	41	fractional	fractional	ADJ
cana-6180	64	42	part	part	NOUN
cana-6180	64	43	,	,	PUNCT
cana-6180	64	44	because	because	SCONJ
cana-6180	64	45	this	this	PRON
cana-6180	64	46	may	may	AUX
cana-6180	64	47	help	help	VERB
cana-6180	64	48	reduce	reduce	VERB
cana-6180	64	49	the	the	DET
cana-6180	64	50	number	number	NOUN
cana-6180	64	51	of	of	ADP
cana-6180	64	52	iterations	iteration	NOUN
cana-6180	64	53	and	and	CCONJ
cana-6180	64	54	the	the	DET
cana-6180	64	55	time	time	NOUN
cana-6180	64	56	it	it	PRON
cana-6180	64	57	takes	take	VERB
cana-6180	64	58	to	to	PART
cana-6180	64	59	converge	converge	VERB
cana-6180	64	60	)	)	PUNCT
cana-6180	64	61	and	and	CCONJ
cana-6180	64	62	from	from	ADP
cana-6180	64	63	it	it	PRON
cana-6180	64	64	generate	generate	VERB
cana-6180	64	65	or	or	CCONJ
cana-6180	64	66	create	create	VERB
cana-6180	64	67	a	a	DET
cana-6180	64	68	cutting	cut	VERB
cana-6180	64	69	planes	plane	NOUN
cana-6180	64	70	constraint	constraint	NOUN
cana-6180	64	71	.	.	PUNCT
cana-6180	65	1	step	step	NOUN
cana-6180	65	2	3	3	NUM
cana-6180	65	3	:	:	PUNCT
cana-6180	65	4	generate	generate	VERB
cana-6180	65	5	the	the	DET
cana-6180	65	6	cutting	cut	VERB
cana-6180	65	7	planes	plane	NOUN
cana-6180	65	8	constraint	constraint	NOUN
cana-6180	65	9	:	:	PUNCT
cana-6180	65	10	𝑥𝐵𝑖	𝑥𝐵𝑖	NUM
cana-6180	65	11	+	+	NOUN
cana-6180	65	12	∑	∑	NOUN
cana-6180	65	13	𝑎𝑖𝑗.	𝑎𝑖𝑗.	X
cana-6180	65	14	𝑛	𝑛	PROPN
cana-6180	65	15	𝐽=1	𝐽=1	PROPN
cana-6180	65	16	𝑥𝑗	𝑥𝑗	NOUN
cana-6180	65	17	=	=	PUNCT
cana-6180	65	18	𝑏𝑖𝑗	𝑏𝑖𝑗	NOUN
cana-6180	65	19	;	;	PUNCT
cana-6180	65	20	𝑗	𝑗	PRON
cana-6180	65	21	∈	∈	NOUN
cana-6180	65	22	𝐼	𝐼	ADP
cana-6180	65	23	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	65	24	+	+	NOUN
cana-6180	65	25	∑	∑	PROPN
cana-6180	65	26	(	(	PUNCT
cana-6180	65	27	𝑛	𝑛	PROPN
cana-6180	65	28	𝐽=1	𝐽=1	PROPN
cana-6180	66	1	[	[	X
cana-6180	66	2	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-6180	66	3	]	]	X
cana-6180	66	4	+	+	CCONJ
cana-6180	66	5	𝑓𝑖𝑗.)𝑥𝑖	𝑓𝑖𝑗.)𝑥𝑖	NUM
cana-6180	66	6	=	=	PUNCT
cana-6180	67	1	[	[	X
cana-6180	67	2	𝑏𝑖	𝑏𝑖	X
cana-6180	67	3	]	]	X
cana-6180	67	4	+	+	CCONJ
cana-6180	67	5	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	67	6	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	67	7	+	+	NOUN
cana-6180	67	8	∑	∑	PROPN
cana-6180	67	9	(	(	PUNCT
cana-6180	67	10	𝑛	𝑛	PROPN
cana-6180	67	11	𝐽=1	𝐽=1	PROPN
cana-6180	68	1	[	[	X
cana-6180	68	2	𝑎𝑖𝑗]𝑥𝑖	𝑎𝑖𝑗]𝑥𝑖	NUM
cana-6180	68	3	−	−	PROPN
cana-6180	69	1	[	[	X
cana-6180	69	2	𝑏𝑖])𝑥𝑖	𝑏𝑖])𝑥𝑖	PROPN
cana-6180	69	3	=	=	SYM
cana-6180	69	4	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	69	5	−∑	−∑	PROPN
cana-6180	69	6	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	69	7	𝑛	𝑛	PROPN
cana-6180	69	8	𝐽=1	𝐽=1	PROPN
cana-6180	69	9	𝑥𝑖	𝑥𝑖	ADP
cana-6180	69	10	≤0	≤0	NOUN
cana-6180	69	11	communications	communication	NOUN
cana-6180	69	12	on	on	ADP
cana-6180	69	13	applied	apply	VERB
cana-6180	69	14	nonlinear	nonlinear	ADJ
cana-6180	69	15	analysis	analysis	NOUN
cana-6180	69	16	issn	issn	NOUN
cana-6180	69	17	:	:	PUNCT
cana-6180	69	18	1074	1074	NUM
cana-6180	69	19	-	-	PUNCT
cana-6180	69	20	133x	133x	NUM
cana-6180	69	21	vol	vol	NOUN
cana-6180	69	22	32	32	NUM
cana-6180	69	23	no	no	NOUN
cana-6180	69	24	.	.	NOUN
cana-6180	69	25	3	3	NUM
cana-6180	69	26	(	(	PUNCT
cana-6180	69	27	2025	2025	NUM
cana-6180	69	28	)	)	PUNCT
cana-6180	69	29	1137	1137	NUM
cana-6180	69	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	70	1	new	new	ADJ
cana-6180	70	2	condition	condition	NOUN
cana-6180	70	3	is	be	AUX
cana-6180	70	4	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	70	5	−∑	−∑	PROPN
cana-6180	70	6	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	70	7	𝑛	𝑛	PROPN
cana-6180	70	8	𝐽=1	𝐽=1	PROPN
cana-6180	70	9	𝑥𝑖	𝑥𝑖	PRON
cana-6180	70	10	+	+	CCONJ
cana-6180	70	11	µ	µ	X
cana-6180	70	12	=	=	SYM
cana-6180	70	13	0	0	NUM
cana-6180	70	14	…	…	SYM
cana-6180	70	15	7	7	NUM
cana-6180	70	16	such	such	ADJ
cana-6180	70	17	as	as	ADP
cana-6180	70	18	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	70	19	=	=	SYM
cana-6180	70	20	𝑎𝑖𝑗.	𝑎𝑖𝑗.	NOUN
cana-6180	70	21	−	−	PROPN
cana-6180	71	1	[	[	X
cana-6180	71	2	𝑎𝑖𝑗]is	𝑎𝑖𝑗]is	VERB
cana-6180	71	3	the	the	DET
cana-6180	71	4	fractional	fractional	ADJ
cana-6180	71	5	part	part	NOUN
cana-6180	71	6	of	of	ADP
cana-6180	71	7	𝑎𝑖𝑗.0	𝑎𝑖𝑗.0	NOUN
cana-6180	71	8	≤	≤	NUM
cana-6180	71	9	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
cana-6180	71	10	≤	≤	NOUN
cana-6180	71	11	1	1	NUM
cana-6180	71	12	𝑓𝑖	𝑓𝑖	NOUN
cana-6180	71	13	=	=	PUNCT
cana-6180	71	14	𝑏𝑖	𝑏𝑖	ADP
cana-6180	71	15	−	−	PROPN
cana-6180	72	1	[	[	X
cana-6180	72	2	𝑏𝑖	𝑏𝑖	X
cana-6180	72	3	]	]	X
cana-6180	72	4	is	be	AUX
cana-6180	72	5	the	the	DET
cana-6180	72	6	fractional	fractional	ADJ
cana-6180	72	7	part	part	NOUN
cana-6180	72	8	of	of	ADP
cana-6180	72	9	𝑏𝑖0	𝑏𝑖0	PROPN
cana-6180	72	10	≤	≤	X
cana-6180	72	11	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	72	12	≤	≤	NUM
cana-6180	72	13	1	1	NUM
cana-6180	72	14	µ	µ	PRON
cana-6180	72	15	new	new	ADJ
cana-6180	72	16	auxiliary	auxiliary	ADJ
cana-6180	72	17	variable	variable	NOUN
cana-6180	72	18	is	be	AUX
cana-6180	72	19	integer	integer	ADJ
cana-6180	72	20	step	step	NOUN
cana-6180	72	21	4	4	NUM
cana-6180	72	22	add	add	VERB
cana-6180	72	23	constraint	constraint	NOUN
cana-6180	72	24	add	add	VERB
cana-6180	72	25	the	the	DET
cana-6180	72	26	constraint	constraint	NOUN
cana-6180	72	27	7	7	NUM
cana-6180	72	28	to	to	ADP
cana-6180	72	29	the	the	DET
cana-6180	72	30	last	last	ADJ
cana-6180	72	31	table	table	NOUN
cana-6180	72	32	of	of	ADP
cana-6180	72	33	the	the	DET
cana-6180	72	34	solution	solution	NOUN
cana-6180	72	35	to	to	ADP
cana-6180	72	36	the	the	DET
cana-6180	72	37	simplex	simplex	NOUN
cana-6180	72	38	algorithm	algorithm	NOUN
cana-6180	72	39	and	and	CCONJ
cana-6180	72	40	solve	solve	VERB
cana-6180	72	41	the	the	DET
cana-6180	72	42	solution	solution	NOUN
cana-6180	72	43	as	as	ADP
cana-6180	72	44	a	a	DET
cana-6180	72	45	linear	linear	ADJ
cana-6180	72	46	programming	programming	NOUN
cana-6180	72	47	problem	problem	NOUN
cana-6180	72	48	.	.	PUNCT
cana-6180	73	1	here	here	ADV
cana-6180	73	2	we	we	PRON
cana-6180	73	3	discuss	discuss	VERB
cana-6180	73	4	the	the	DET
cana-6180	73	5	following	follow	VERB
cana-6180	73	6	cases	case	NOUN
cana-6180	73	7	1	1	NUM
cana-6180	73	8	-	-	PUNCT
cana-6180	73	9	variables∀𝑥𝑗;𝑗	variables∀𝑥𝑗;𝑗	NOUN
cana-6180	73	10	∈	∈	NOUN
cana-6180	73	11	𝐼	𝐼	ADP
cana-6180	73	12	if	if	SCONJ
cana-6180	73	13	the	the	DET
cana-6180	73	14	values	value	NOUN
cana-6180	73	15	are	be	AUX
cana-6180	73	16	integer	integer	NOUN
cana-6180	73	17	and	and	CCONJ
cana-6180	73	18	possible	possible	ADJ
cana-6180	73	19	,	,	PUNCT
cana-6180	73	20	the	the	DET
cana-6180	73	21	problem	problem	NOUN
cana-6180	73	22	is	be	AUX
cana-6180	73	23	end	end	NOUN
cana-6180	73	24	.	.	PUNCT
cana-6180	74	1	otherwise	otherwise	ADV
cana-6180	74	2	,	,	PUNCT
cana-6180	74	3	go	go	VERB
cana-6180	74	4	to	to	ADP
cana-6180	74	5	the	the	DET
cana-6180	74	6	next	next	ADJ
cana-6180	74	7	step2	step2	PROPN
cana-6180	74	8	.	.	PUNCT
cana-6180	75	1	2	2	NUM
cana-6180	75	2	-	-	PUNCT
cana-6180	75	3	some	some	DET
cana-6180	75	4	variables	variable	NOUN
cana-6180	75	5	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	75	6	∈	∈	PROPN
cana-6180	75	7	𝐼	𝐼	ADP
cana-6180	75	8	if	if	SCONJ
cana-6180	75	9	the	the	DET
cana-6180	75	10	values	value	NOUN
cana-6180	75	11	are	be	AUX
cana-6180	75	12	not	not	PART
cana-6180	75	13	integer	integer	ADJ
cana-6180	75	14	,	,	PUNCT
cana-6180	75	15	go	go	VERB
cana-6180	75	16	to	to	PART
cana-6180	75	17	step	step	VERB
cana-6180	75	18	2	2	NUM
cana-6180	75	19	.	.	PUNCT
cana-6180	76	1	otherwise	otherwise	ADV
cana-6180	76	2	,	,	PUNCT
cana-6180	76	3	go	go	VERB
cana-6180	76	4	to	to	ADP
cana-6180	76	5	the	the	DET
cana-6180	76	6	next	next	ADJ
cana-6180	76	7	step	step	NOUN
cana-6180	76	8	3	3	NUM
cana-6180	76	9	.	.	NOUN
cana-6180	76	10	3	3	NUM
cana-6180	76	11	-	-	SYM
cana-6180	76	12	one	one	NUM
cana-6180	76	13	of	of	ADP
cana-6180	76	14	the	the	DET
cana-6180	76	15	variables	variable	NOUN
cana-6180	77	1	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	77	2	∈	∈	PROPN
cana-6180	78	1	𝐼	𝐼	SCONJ
cana-6180	78	2	i	i	PRON
cana-6180	78	3	has	have	VERB
cana-6180	78	4	an	an	DET
cana-6180	78	5	integer	integer	NOUN
cana-6180	78	6	value	value	NOUN
cana-6180	78	7	,	,	PUNCT
cana-6180	78	8	then	then	ADV
cana-6180	78	9	start	start	VERB
cana-6180	78	10	using	use	VERB
cana-6180	78	11	the	the	DET
cana-6180	78	12	branch	branch	NOUN
cana-6180	78	13	and	and	CCONJ
cana-6180	78	14	node	node	ADJ
cana-6180	78	15	method	method	NOUN
cana-6180	78	16	to	to	ADP
cana-6180	78	17	branch	branch	NOUN
cana-6180	78	18	,	,	PUNCT
cana-6180	78	19	the	the	DET
cana-6180	78	20	values	value	NOUN
cana-6180	78	21	are	be	AUX
cana-6180	78	22	not	not	PART
cana-6180	78	23	integer	integer	ADJ
cana-6180	78	24	variable	variable	NOUN
cana-6180	78	25	,	,	PUNCT
cana-6180	78	26	go	go	VERB
cana-6180	78	27	to	to	ADP
cana-6180	78	28	step5	step5	PROPN
cana-6180	78	29	.	.	PUNCT
cana-6180	79	1	step	step	NOUN
cana-6180	79	2	5	5	NUM
cana-6180	79	3	:	:	PUNCT
cana-6180	79	4	choose	choose	VERB
cana-6180	79	5	the	the	DET
cana-6180	79	6	branching	branch	VERB
cana-6180	79	7	variable	variable	NOUN
cana-6180	79	8	choose	choose	VERB
cana-6180	79	9	the	the	DET
cana-6180	79	10	variable	variable	NOUN
cana-6180	79	11	with	with	ADP
cana-6180	79	12	the	the	DET
cana-6180	79	13	not	not	PART
cana-6180	79	14	integer	integer	NOUN
cana-6180	79	15	value	value	NOUN
cana-6180	79	16	from	from	ADP
cana-6180	79	17	the	the	DET
cana-6180	79	18	variables	variable	NOUN
cana-6180	79	19	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	79	20	∈	∈	PROPN
cana-6180	79	21	𝐼	𝐼	PROPN
cana-6180	79	22	,	,	PUNCT
cana-6180	79	23	which	which	PRON
cana-6180	79	24	will	will	AUX
cana-6180	79	25	be	be	AUX
cana-6180	79	26	used	use	VERB
cana-6180	79	27	to	to	PART
cana-6180	79	28	form	form	VERB
cana-6180	79	29	the	the	DET
cana-6180	79	30	branching	branch	VERB
cana-6180	79	31	constraints	constraint	NOUN
cana-6180	79	32	,	,	PUNCT
cana-6180	79	33	which	which	PRON
cana-6180	79	34	it	it	PRON
cana-6180	79	35	has	have	VERB
cana-6180	79	36	the	the	DET
cana-6180	79	37	largest	large	ADJ
cana-6180	79	38	fractional	fractional	ADJ
cana-6180	79	39	part.he	part.he	ADJ
cana-6180	79	40	variable	variable	NOUN
cana-6180	79	41	𝑥𝑖	𝑥𝑖	X
cana-6180	79	42	that	that	PRON
cana-6180	79	43	is	be	AUX
cana-6180	79	44	chosen	choose	VERB
cana-6180	79	45	must	must	AUX
cana-6180	79	46	be	be	AUX
cana-6180	79	47	a	a	DET
cana-6180	79	48	basic	basic	ADJ
cana-6180	79	49	variable	variable	NOUN
cana-6180	79	50	,	,	PUNCT
cana-6180	79	51	otherwise	otherwise	ADV
cana-6180	79	52	its	its	PRON
cana-6180	79	53	value	value	NOUN
cana-6180	79	54	will	will	AUX
cana-6180	79	55	be	be	AUX
cana-6180	79	56	zero	zero	NUM
cana-6180	79	57	.	.	PUNCT
cana-6180	80	1	assume	assume	VERB
cana-6180	80	2	that	that	SCONJ
cana-6180	80	3	the	the	DET
cana-6180	80	4	variable	variable	NOUN
cana-6180	80	5	is	be	AUX
cana-6180	80	6	let	let	VERB
cana-6180	80	7	the	the	DET
cana-6180	80	8	basic	basic	ADJ
cana-6180	80	9	variable	variable	NOUN
cana-6180	80	10	i	i	PROPN
cana-6180	80	11	from	from	ADP
cana-6180	80	12	the	the	DET
cana-6180	80	13	last	last	ADJ
cana-6180	80	14	table	table	NOUN
cana-6180	80	15	to	to	PART
cana-6180	80	16	solve	solve	VERB
cana-6180	80	17	the	the	DET
cana-6180	80	18	simplex	simplex	NOUN
cana-6180	80	19	algorithm	algorithm	NOUN
cana-6180	80	20	be	be	VERB
cana-6180	80	21	its	its	PRON
cana-6180	80	22	value	value	NOUN
cana-6180	80	23	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	80	24	we	we	PRON
cana-6180	80	25	will	will	AUX
cana-6180	80	26	write	write	VERB
cana-6180	80	27	𝑥𝐵𝑖	𝑥𝐵𝑖	NOUN
cana-6180	80	28	=	=	PUNCT
cana-6180	81	1	[	[	X
cana-6180	81	2	𝑥𝐵𝑖	𝑥𝐵𝑖	X
cana-6180	81	3	]	]	X
cana-6180	82	1	+	+	CCONJ
cana-6180	82	2	𝑓𝑖	𝑓𝑖	VERB
cana-6180	82	3	where	where	SCONJ
cana-6180	82	4	0	0	X
cana-6180	82	5	<	<	X
cana-6180	82	6	𝑓𝑖	𝑓𝑖	PROPN
cana-6180	82	7	<	<	X
cana-6180	82	8	1	1	NUM
cana-6180	82	9	𝑥𝐽satisfies	𝑥𝐽satisfies	PROPN
cana-6180	82	10	one	one	NUM
cana-6180	82	11	of	of	ADP
cana-6180	82	12	the	the	DET
cana-6180	82	13	8	8	NUM
cana-6180	82	14	and	and	CCONJ
cana-6180	82	15	9	9	NUM
cana-6180	82	16	inequalities	inequality	NOUN
cana-6180	82	17	.	.	PUNCT
cana-6180	83	1	𝑥𝐽≤[[𝑥𝐵𝑖]]	𝑥𝐽≤[[𝑥𝐵𝑖]]	NOUN
cana-6180	83	2	............	............	PROPN
cana-6180	83	3	8	8	NUM
cana-6180	83	4	𝑥𝐽≥[[𝑥𝐵𝑖]]+1	𝑥𝐽≥[[𝑥𝐵𝑖]]+1	NUM
cana-6180	83	5	.........	.........	PUNCT
cana-6180	83	6	9	9	NUM
cana-6180	83	7	step	step	NOUN
cana-6180	83	8	6	6	NUM
cana-6180	83	9	:	:	PUNCT
cana-6180	83	10	new	new	ADJ
cana-6180	83	11	nodes	node	NOUN
cana-6180	83	12	create	create	VERB
cana-6180	83	13	two	two	NUM
cana-6180	83	14	new	new	ADJ
cana-6180	83	15	integer	integer	NOUN
cana-6180	83	16	programming	programming	NOUN
cana-6180	83	17	problems	problem	NOUN
cana-6180	83	18	with	with	ADP
cana-6180	83	19	the	the	DET
cana-6180	83	20	constraints	constraint	NOUN
cana-6180	83	21	in	in	ADP
cana-6180	83	22	step	step	NOUN
cana-6180	83	23	5	5	NUM
cana-6180	83	24	the	the	DET
cana-6180	83	25	first	first	ADJ
cana-6180	83	26	problem	problem	NOUN
cana-6180	83	27	consists	consist	VERB
cana-6180	83	28	of	of	ADP
cana-6180	83	29	adding	add	VERB
cana-6180	83	30	the	the	DET
cana-6180	83	31	constraint	constraint	NOUN
cana-6180	83	32	,	,	PUNCT
cana-6180	83	33	8	8	NUM
cana-6180	83	34	,	,	PUNCT
cana-6180	83	35	and	and	CCONJ
cana-6180	83	36	the	the	DET
cana-6180	83	37	second	second	ADJ
cana-6180	83	38	problem	problem	NOUN
cana-6180	83	39	consists	consist	VERB
cana-6180	83	40	of	of	ADP
cana-6180	83	41	adding	add	VERB
cana-6180	83	42	the	the	DET
cana-6180	83	43	constraint,9	constraint,9	NOUN
cana-6180	83	44	.	.	PUNCT
cana-6180	84	1	solve	solve	VERB
cana-6180	84	2	each	each	PRON
cana-6180	84	3	of	of	ADP
cana-6180	84	4	the	the	DET
cana-6180	84	5	following	following	NOUN
cana-6180	84	6	:	:	PUNCT
cana-6180	84	7	,	,	PUNCT
cana-6180	84	8	these	these	DET
cana-6180	84	9	two	two	NUM
cana-6180	84	10	problems	problem	NOUN
cana-6180	84	11	are	be	AUX
cana-6180	84	12	linear	linear	ADJ
cana-6180	84	13	programming	programming	NOUN
cana-6180	84	14	problems	problem	NOUN
cana-6180	84	15	using	use	VERB
cana-6180	84	16	the	the	DET
cana-6180	84	17	simplex	simplex	NOUN
cana-6180	84	18	algorithm	algorithm	NOUN
cana-6180	84	19	step	step	NOUN
cana-6180	84	20	7	7	NUM
cana-6180	84	21	:	:	PUNCT
cana-6180	84	22	node	node	ADJ
cana-6180	84	23	test	test	NOUN
cana-6180	84	24	each	each	PRON
cana-6180	84	25	of	of	ADP
cana-6180	84	26	the	the	DET
cana-6180	84	27	nodes	node	NOUN
cana-6180	84	28	obtained	obtain	VERB
cana-6180	84	29	in	in	ADP
cana-6180	84	30	step	step	NOUN
cana-6180	84	31	6	6	NUM
cana-6180	84	32	is	be	AUX
cana-6180	84	33	a	a	DET
cana-6180	84	34	finished	finished	ADJ
cana-6180	84	35	node	node	NOUN
cana-6180	84	36	in	in	ADP
cana-6180	84	37	one	one	NUM
cana-6180	84	38	of	of	ADP
cana-6180	84	39	the	the	DET
cana-6180	84	40	following	follow	VERB
cana-6180	84	41	two	two	NUM
cana-6180	84	42	cases	case	NOUN
cana-6180	84	43	:	:	PUNCT
cana-6180	84	44	communications	communication	NOUN
cana-6180	84	45	on	on	ADP
cana-6180	84	46	applied	apply	VERB
cana-6180	84	47	nonlinear	nonlinear	ADJ
cana-6180	84	48	analysis	analysis	NOUN
cana-6180	84	49	issn	issn	NOUN
cana-6180	84	50	:	:	PUNCT
cana-6180	84	51	1074	1074	NUM
cana-6180	84	52	-	-	PUNCT
cana-6180	84	53	133x	133x	NUM
cana-6180	84	54	vol	vol	NOUN
cana-6180	84	55	32	32	NUM
cana-6180	84	56	no	no	NOUN
cana-6180	84	57	.	.	NOUN
cana-6180	84	58	3	3	NUM
cana-6180	84	59	(	(	PUNCT
cana-6180	84	60	2025	2025	NUM
cana-6180	84	61	)	)	PUNCT
cana-6180	84	62	1138	1138	NUM
cana-6180	84	63	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	85	1	the	the	DET
cana-6180	85	2	first	first	ADJ
cana-6180	85	3	case	case	NOUN
cana-6180	85	4	:	:	PUNCT
cana-6180	85	5	the	the	DET
cana-6180	85	6	problem	problem	NOUN
cana-6180	85	7	represented	represent	VERB
cana-6180	85	8	by	by	ADP
cana-6180	85	9	this	this	DET
cana-6180	85	10	node	node	NOUN
cana-6180	85	11	has	have	VERB
cana-6180	85	12	no	no	DET
cana-6180	85	13	possible	possible	ADJ
cana-6180	85	14	solution	solution	NOUN
cana-6180	85	15	.	.	PUNCT
cana-6180	86	1	the	the	DET
cana-6180	86	2	second	second	ADJ
cana-6180	86	3	case	case	NOUN
cana-6180	86	4	:	:	PUNCT
cana-6180	86	5	all	all	DET
cana-6180	86	6	the	the	DET
cana-6180	86	7	variables	variable	NOUN
cana-6180	86	8	∀𝑥𝑗;𝑗	∀𝑥𝑗;𝑗	PROPN
cana-6180	86	9	∈	∈	PROPN
cana-6180	86	10	𝐼	𝐼	PROPN
cana-6180	86	11	are	be	AUX
cana-6180	86	12	integer	integer	NOUN
cana-6180	86	13	and	and	CCONJ
cana-6180	86	14	this	this	PRON
cana-6180	86	15	is	be	AUX
cana-6180	86	16	the	the	DET
cana-6180	86	17	optimal	optimal	ADJ
cana-6180	86	18	solution	solution	NOUN
cana-6180	86	19	to	to	ADP
cana-6180	86	20	the	the	DET
cana-6180	86	21	problem	problem	NOUN
cana-6180	86	22	6	6	NUM
cana-6180	86	23	.	.	PUNCT
cana-6180	87	1	but	but	CCONJ
cana-6180	87	2	if	if	SCONJ
cana-6180	87	3	those	those	PRON
cana-6180	87	4	,	,	PUNCT
cana-6180	87	5	the	the	DET
cana-6180	87	6	knot	knot	NOUN
cana-6180	87	7	is	be	AUX
cana-6180	87	8	not	not	PART
cana-6180	87	9	finished	finish	VERB
cana-6180	87	10	,	,	PUNCT
cana-6180	87	11	so	so	ADV
cana-6180	87	12	go	go	VERB
cana-6180	87	13	to	to	ADP
cana-6180	87	14	the	the	DET
cana-6180	87	15	next	next	ADJ
cana-6180	87	16	step5	step5	PROPN
cana-6180	87	17	.	.	PUNCT
cana-6180	88	1	4.results	4.result	NOUN
cana-6180	88	2	the	the	DET
cana-6180	88	3	general	general	ADJ
cana-6180	88	4	problem	problem	NOUN
cana-6180	88	5	of	of	ADP
cana-6180	88	6	linear	linear	PROPN
cana-6180	88	7	programming	programming	NOUN
cana-6180	88	8	is	be	AUX
cana-6180	88	9	to	to	PART
cana-6180	88	10	.nd	.nd	PUNCT
cana-6180	89	1	the	the	DET
cana-6180	89	2	values	value	NOUN
cana-6180	89	3	of	of	ADP
cana-6180	89	4	variables	variable	NOUN
cana-6180	89	5	that	that	PRON
cana-6180	89	6	maximize	maximize	VERB
cana-6180	89	7	or	or	CCONJ
cana-6180	89	8	minimize	minimize	VERB
cana-6180	89	9	the	the	DET
cana-6180	89	10	value	value	NOUN
cana-6180	89	11	of	of	ADP
cana-6180	89	12	the	the	DET
cana-6180	89	13	objective	objective	ADJ
cana-6180	89	14	function	function	NOUN
cana-6180	89	15	according	accord	VERB
cana-6180	89	16	to	to	ADP
cana-6180	89	17	constraints	constraint	NOUN
cana-6180	89	18	representing	represent	VERB
cana-6180	89	19	the	the	DET
cana-6180	89	20	amount	amount	NOUN
cana-6180	89	21	of	of	ADP
cana-6180	89	22	available	available	ADJ
cana-6180	89	23	resources	resource	NOUN
cana-6180	89	24	.	.	PUNCT
cana-6180	90	1	we	we	PRON
cana-6180	90	2	solve	solve	VERB
cana-6180	90	3	the	the	DET
cana-6180	90	4	integer	integer	NOUN
cana-6180	90	5	linear	linear	PROPN
cana-6180	90	6	programming	programming	NOUN
cana-6180	90	7	problem	problem	NOUN
cana-6180	90	8	first	first	ADV
cana-6180	90	9	,	,	PUNCT
cana-6180	90	10	ignoring	ignore	VERB
cana-6180	90	11	the	the	DET
cana-6180	90	12	conditions	condition	NOUN
cana-6180	90	13	for	for	ADP
cana-6180	90	14	the	the	DET
cana-6180	90	15	variables	variable	NOUN
cana-6180	90	16	to	to	PART
cana-6180	90	17	take	take	VERB
cana-6180	90	18	integer	integer	NOUN
cana-6180	90	19	values	value	NOUN
cana-6180	90	20	,	,	PUNCT
cana-6180	90	21	that	that	ADV
cana-6180	90	22	is	is	ADV
cana-6180	90	23	,	,	PUNCT
cana-6180	90	24	we	we	PRON
cana-6180	90	25	solve	solve	VERB
cana-6180	90	26	the	the	DET
cana-6180	90	27	problem	problem	NOUN
cana-6180	90	28	as	as	ADP
cana-6180	90	29	a	a	DET
cana-6180	90	30	linear	linear	ADJ
cana-6180	90	31	programming	programming	NOUN
cana-6180	90	32	problem	problem	NOUN
cana-6180	90	33	in	in	ADP
cana-6180	90	34	which	which	PRON
cana-6180	90	35	we	we	PRON
cana-6180	90	36	are	be	AUX
cana-6180	90	37	asked	ask	VERB
cana-6180	90	38	to	to	PART
cana-6180	90	39	find	find	VERB
cana-6180	90	40	the	the	DET
cana-6180	90	41	optimal	optimal	ADJ
cana-6180	90	42	true	true	ADJ
cana-6180	90	43	solution	solution	NOUN
cana-6180	90	44	.	.	PUNCT
cana-6180	91	1	after	after	ADP
cana-6180	91	2	that	that	PRON
cana-6180	91	3	,	,	PUNCT
cana-6180	91	4	we	we	PRON
cana-6180	91	5	use	use	VERB
cana-6180	91	6	the	the	DET
cana-6180	91	7	algorithms	algorithm	NOUN
cana-6180	91	8	of	of	ADP
cana-6180	91	9	the	the	DET
cana-6180	91	10	integer	integer	NOUN
cana-6180	91	11	linear	linear	PROPN
cana-6180	91	12	programming	programming	NOUN
cana-6180	91	13	problem	problem	NOUN
cana-6180	91	14	to	to	PART
cana-6180	91	15	move	move	VERB
cana-6180	91	16	from	from	ADP
cana-6180	91	17	noi	noi	PROPN
cana-6180	91	18	number	number	NOUN
cana-6180	91	19	of	of	ADP
cana-6180	91	20	reiteration	reiteration	NOUN
cana-6180	91	21	;	;	PUNCT
cana-6180	91	22	cpu	cpu	NOUN
cana-6180	91	23	time	time	NOUN
cana-6180	91	24	problems	problem	NOUN
cana-6180	91	25	cutting	cut	VERB
cana-6180	91	26	planes	plane	NOUN
cana-6180	91	27	noi	noi	PROPN
cana-6180	91	28	cpu	cpu	NOUN
cana-6180	91	29	branch	branch	NOUN
cana-6180	91	30	and	and	CCONJ
cana-6180	91	31	bound	bind	VERB
cana-6180	91	32	noi	noi	PROPN
cana-6180	91	33	cpu	cpu	VERB
cana-6180	91	34	new	new	ADJ
cana-6180	91	35	algorithm	algorithm	NOUN
cana-6180	91	36	noi	noi	PROPN
cana-6180	91	37	cpu	cpu	NOUN
cana-6180	91	38	{	{	PUNCT
cana-6180	91	39	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	91	40	𝑧	𝑧	NOUN
cana-6180	91	41	=	=	X
cana-6180	91	42	6𝑥1	6𝑥1	NUM
cana-6180	91	43	+	+	CCONJ
cana-6180	91	44	7𝑥2	7𝑥2	NUM
cana-6180	91	45	𝑠𝑡	𝑠𝑡	NUM
cana-6180	91	46	𝑥1	𝑥1	NOUN
cana-6180	91	47	+	+	CCONJ
cana-6180	91	48	2𝑥2	2𝑥2	NUM
cana-6180	91	49	≤	≤	NUM
cana-6180	91	50	8	8	NUM
cana-6180	91	51	𝑥1	𝑥1	NOUN
cana-6180	91	52	−	−	NOUN
cana-6180	91	53	𝑥2	𝑥2	PROPN
cana-6180	91	54	≤	≤	NUM
cana-6180	91	55	4	4	NUM
cana-6180	91	56	𝑥1	𝑥1	NOUN
cana-6180	91	57	;	;	PUNCT
cana-6180	91	58	𝑥2	𝑥2	NOUN
cana-6180	91	59	≥	≥	NUM
cana-6180	91	60	0	0	NUM
cana-6180	91	61	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	NOUN
cana-6180	91	62	2	2	NUM
cana-6180	91	63	.	.	NUM
cana-6180	91	64	1.07	1.07	NUM
cana-6180	91	65	9.00	9.00	NUM
cana-6180	91	66	0.72	0.72	NUM
cana-6180	91	67	3	3	NUM
cana-6180	91	68	0.82	0.82	NUM
cana-6180	91	69	{	{	PUNCT
cana-6180	91	70	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	91	71	𝑧	𝑧	NOUN
cana-6180	92	1	=	=	SYM
cana-6180	93	1	2𝑥1	2𝑥1	NUM
cana-6180	94	1	+	+	CCONJ
cana-6180	94	2	1𝑥2	1𝑥2	NUM
cana-6180	94	3	−	−	PROPN
cana-6180	94	4	𝑥3	𝑥3	PROPN
cana-6180	94	5	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	94	6	1𝑥1	1𝑥1	NUM
cana-6180	95	1	+	+	CCONJ
cana-6180	95	2	2𝑥2	2𝑥2	NUM
cana-6180	95	3	−	−	PROPN
cana-6180	95	4	𝑥3	𝑥3	NOUN
cana-6180	95	5	≤	≤	NOUN
cana-6180	95	6	5	5	NUM
cana-6180	95	7	−𝑥1	−𝑥1	NOUN
cana-6180	95	8	+	+	CCONJ
cana-6180	95	9	2𝑥2	2𝑥2	NUM
cana-6180	96	1	+	+	CCONJ
cana-6180	96	2	3𝑥3	3𝑥3	NUM
cana-6180	96	3	≤	≤	PROPN
cana-6180	96	4	−2	−2	PROPN
cana-6180	96	5	𝑥1	𝑥1	NOUN
cana-6180	96	6	;	;	PUNCT
cana-6180	96	7	𝑥2	𝑥2	NOUN
cana-6180	96	8	;	;	PUNCT
cana-6180	96	9	𝑥3	𝑥3	NOUN
cana-6180	96	10	≥	≥	NOUN
cana-6180	96	11	0	0	NUM
cana-6180	96	12	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	ADJ
cana-6180	96	13	1	1	NUM
cana-6180	96	14	0.66	0.66	NUM
cana-6180	96	15	2	2	NUM
cana-6180	96	16	0.32	0.32	NUM
cana-6180	96	17	1	1	NUM
cana-6180	96	18	0.48	0.48	NUM
cana-6180	96	19	{	{	PUNCT
cana-6180	96	20	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	96	21	𝑧	𝑧	NOUN
cana-6180	96	22	=	=	PROPN
cana-6180	96	23	𝑥1	𝑥1	PROPN
cana-6180	96	24	+	+	CCONJ
cana-6180	96	25	1𝑥2	1𝑥2	NUM
cana-6180	96	26	−	−	PROPN
cana-6180	96	27	𝑥3	𝑥3	PROPN
cana-6180	96	28	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	96	29	𝑥1	𝑥1	PROPN
cana-6180	96	30	+	+	CCONJ
cana-6180	96	31	2𝑥2	2𝑥2	NUM
cana-6180	96	32	−	−	PROPN
cana-6180	96	33	𝑥3	𝑥3	NOUN
cana-6180	96	34	≤	≤	NOUN
cana-6180	96	35	3	3	NUM
cana-6180	96	36	−𝑥1	−𝑥1	PROPN
cana-6180	96	37	+	+	CCONJ
cana-6180	96	38	2𝑥2	2𝑥2	NUM
cana-6180	96	39	+	+	CCONJ
cana-6180	96	40	3𝑥3	3𝑥3	NUM
cana-6180	96	41	≤	≤	ADV
cana-6180	96	42	2	2	NUM
cana-6180	96	43	𝑥1	𝑥1	NOUN
cana-6180	96	44	;	;	PUNCT
cana-6180	96	45	𝑥2	𝑥2	NOUN
cana-6180	96	46	;	;	PUNCT
cana-6180	96	47	𝑥3	𝑥3	NOUN
cana-6180	96	48	≥	≥	NOUN
cana-6180	96	49	0	0	NUM
cana-6180	96	50	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	ADJ
cana-6180	96	51	2	2	NUM
cana-6180	96	52	0/86	0/86	NUM
cana-6180	96	53	9	9	NUM
cana-6180	96	54	0.72	0.72	NUM
cana-6180	96	55	1	1	NUM
cana-6180	96	56	0.48	0.48	NUM
cana-6180	96	57	{	{	PUNCT
cana-6180	96	58	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	96	59	𝑧	𝑧	NOUN
cana-6180	96	60	=	=	SYM
cana-6180	96	61	4𝑥1	4𝑥1	NUM
cana-6180	96	62	+	+	SYM
cana-6180	96	63	3𝑥2	3𝑥2	NUM
cana-6180	96	64	𝑠𝑡	𝑠𝑡	NUM
cana-6180	96	65	2𝑥1	2𝑥1	NUM
cana-6180	96	66	+	+	CCONJ
cana-6180	96	67	𝑥2	𝑥2	NOUN
cana-6180	96	68	≤	≤	NUM
cana-6180	96	69	11	11	NUM
cana-6180	96	70	−𝑥1	−𝑥1	PROPN
cana-6180	96	71	+	+	CCONJ
cana-6180	96	72	𝑥2	𝑥2	NOUN
cana-6180	96	73	≤	≤	NUM
cana-6180	96	74	6	6	NUM
cana-6180	96	75	𝑥1	𝑥1	NOUN
cana-6180	96	76	;	;	PUNCT
cana-6180	96	77	𝑥2	𝑥2	NOUN
cana-6180	96	78	≥	≥	NUM
cana-6180	96	79	0	0	NUM
cana-6180	96	80	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	NOUN
cana-6180	96	81	4	4	NUM
cana-6180	96	82	1.04	1.04	NUM
cana-6180	96	83	5	5	NUM
cana-6180	96	84	0.39	0.39	NUM
cana-6180	96	85	1	1	NUM
cana-6180	96	86	0.48	0.48	NUM
cana-6180	96	87	{	{	PUNCT
cana-6180	96	88	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	96	89	𝑧	𝑧	NOUN
cana-6180	96	90	=	=	SYM
cana-6180	96	91	3𝑥1	3𝑥1	NUM
cana-6180	96	92	+	+	NUM
cana-6180	96	93	𝑥2	𝑥2	PROPN
cana-6180	96	94	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	96	95	𝑥1	𝑥1	PROPN
cana-6180	96	96	+	+	CCONJ
cana-6180	96	97	2𝑥2	2𝑥2	NUM
cana-6180	96	98	≤	≤	NUM
cana-6180	96	99	8	8	NUM
cana-6180	96	100	3𝑥1	3𝑥1	NUM
cana-6180	96	101	−	−	NOUN
cana-6180	96	102	4𝑥2	4𝑥2	NUM
cana-6180	96	103	≤	≤	NUM
cana-6180	96	104	12	12	NUM
cana-6180	96	105	𝑥1	𝑥1	NOUN
cana-6180	96	106	;	;	PUNCT
cana-6180	96	107	𝑥2	𝑥2	NOUN
cana-6180	96	108	≥	≥	NUM
cana-6180	96	109	0	0	NUM
cana-6180	96	110	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	96	111	5	5	NUM
cana-6180	96	112	1.6	1.6	NUM
cana-6180	96	113	7	7	NUM
cana-6180	96	114	0.32	0.32	NUM
cana-6180	96	115	3	3	NUM
cana-6180	96	116	0.54	0.54	NUM
cana-6180	96	117	communications	communication	NOUN
cana-6180	96	118	on	on	ADP
cana-6180	96	119	applied	apply	VERB
cana-6180	96	120	nonlinear	nonlinear	ADJ
cana-6180	96	121	analysis	analysis	NOUN
cana-6180	96	122	issn	issn	NOUN
cana-6180	96	123	:	:	PUNCT
cana-6180	96	124	1074	1074	NUM
cana-6180	96	125	-	-	PUNCT
cana-6180	96	126	133x	133x	NUM
cana-6180	96	127	vol	vol	NOUN
cana-6180	96	128	32	32	NUM
cana-6180	96	129	no	no	NOUN
cana-6180	96	130	.	.	NOUN
cana-6180	96	131	3	3	NUM
cana-6180	96	132	(	(	PUNCT
cana-6180	96	133	2025	2025	NUM
cana-6180	96	134	)	)	PUNCT
cana-6180	96	135	1139	1139	NUM
cana-6180	96	136	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	96	137	{	{	PUNCT
cana-6180	96	138	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	96	139	𝑧	𝑧	NOUN
cana-6180	97	1	=	=	SYM
cana-6180	97	2	5𝑥1	5𝑥1	NUM
cana-6180	97	3	+	+	SYM
cana-6180	97	4	8𝑥2	8𝑥2	NUM
cana-6180	97	5	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	97	6	𝑥1	𝑥1	PROPN
cana-6180	97	7	+	+	CCONJ
cana-6180	97	8	𝑥2	𝑥2	PROPN
cana-6180	97	9	≤	≤	NUM
cana-6180	97	10	6	6	NUM
cana-6180	97	11	5𝑥1	5𝑥1	NUM
cana-6180	97	12	+	+	CCONJ
cana-6180	97	13	94𝑥2	94𝑥2	NUM
cana-6180	97	14	≤	≤	NUM
cana-6180	97	15	49	49	NUM
cana-6180	97	16	𝑥1	𝑥1	NOUN
cana-6180	97	17	;	;	PUNCT
cana-6180	97	18	𝑥2	𝑥2	NOUN
cana-6180	97	19	≥	≥	NUM
cana-6180	97	20	0	0	NUM
cana-6180	97	21	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	97	22	3	3	NUM
cana-6180	97	23	0.88	0.88	NUM
cana-6180	97	24	8	8	NUM
cana-6180	97	25	0.32	0.32	NUM
cana-6180	97	26	6	6	NUM
cana-6180	97	27	0.76	0.76	NUM
cana-6180	97	28	{	{	PUNCT
cana-6180	98	1	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	98	2	𝑧	𝑧	NOUN
cana-6180	98	3	=	=	SYM
cana-6180	98	4	120𝑥1	120𝑥1	NUM
cana-6180	98	5	+	+	SYM
cana-6180	98	6	80𝑥2	80𝑥2	NUM
cana-6180	98	7	𝑠𝑡	𝑠𝑡	NUM
cana-6180	98	8	2𝑥1	2𝑥1	NUM
cana-6180	98	9	+	+	CCONJ
cana-6180	98	10	𝑥2	𝑥2	NOUN
cana-6180	98	11	≤	≤	NUM
cana-6180	98	12	6	6	NUM
cana-6180	98	13	7𝑥1	7𝑥1	NUM
cana-6180	98	14	+	+	NUM
cana-6180	98	15	8𝑥2	8𝑥2	NUM
cana-6180	98	16	≤	≤	NUM
cana-6180	98	17	28	28	NUM
cana-6180	98	18	𝑥1	𝑥1	NOUN
cana-6180	98	19	;	;	PUNCT
cana-6180	98	20	𝑥2	𝑥2	NOUN
cana-6180	98	21	≥	≥	NUM
cana-6180	98	22	0	0	NUM
cana-6180	98	23	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	99	1	4	4	NUM
cana-6180	99	2	0.91	0.91	NUM
cana-6180	99	3	7	7	NUM
cana-6180	99	4	0.34	0.34	NUM
cana-6180	99	5	3	3	NUM
cana-6180	99	6	0.63	0.63	NUM
cana-6180	99	7	{	{	PUNCT
cana-6180	99	8	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	99	9	𝑧	𝑧	NOUN
cana-6180	99	10	=	=	SYM
cana-6180	99	11	3𝑥1	3𝑥1	NUM
cana-6180	99	12	+	+	NUM
cana-6180	99	13	𝑥2	𝑥2	NOUN
cana-6180	99	14	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	99	15	4𝑥1	4𝑥1	NUM
cana-6180	99	16	+	+	CCONJ
cana-6180	99	17	3𝑥2	3𝑥2	NUM
cana-6180	99	18	≤	≤	NUM
cana-6180	99	19	18	18	NUM
cana-6180	99	20	3𝑥1	3𝑥1	NUM
cana-6180	99	21	−	−	NOUN
cana-6180	99	22	4𝑥2	4𝑥2	NUM
cana-6180	99	23	≤	≤	NUM
cana-6180	99	24	6	6	NUM
cana-6180	99	25	𝑥1	𝑥1	NOUN
cana-6180	99	26	;	;	PUNCT
cana-6180	99	27	𝑥2	𝑥2	NOUN
cana-6180	99	28	≥	≥	NUM
cana-6180	99	29	0	0	NUM
cana-6180	99	30	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	ADJ
cana-6180	99	31	1	1	NUM
cana-6180	99	32	0.33	0.33	NUM
cana-6180	99	33	2	2	NUM
cana-6180	99	34	0.12	0.12	NUM
cana-6180	99	35	5	5	NUM
cana-6180	99	36	0.67	0.67	NUM
cana-6180	99	37	{	{	PUNCT
cana-6180	99	38	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	99	39	𝑧	𝑧	NOUN
cana-6180	99	40	=	=	SYM
cana-6180	99	41	3𝑥1	3𝑥1	NUM
cana-6180	99	42	+	+	NUM
cana-6180	99	43	𝑥2	𝑥2	NOUN
cana-6180	99	44	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	99	45	2𝑥1	2𝑥1	NUM
cana-6180	99	46	+	+	CCONJ
cana-6180	99	47	3𝑥2	3𝑥2	NUM
cana-6180	99	48	≤	≤	NUM
cana-6180	99	49	8	8	NUM
cana-6180	99	50	2𝑥1	2𝑥1	NUM
cana-6180	99	51	−	−	NOUN
cana-6180	99	52	4𝑥2	4𝑥2	NUM
cana-6180	99	53	≤	≤	NUM
cana-6180	99	54	3	3	NUM
cana-6180	99	55	𝑥1	𝑥1	NOUN
cana-6180	99	56	;	;	PUNCT
cana-6180	99	57	𝑥2	𝑥2	NOUN
cana-6180	99	58	≥	≥	NUM
cana-6180	99	59	0	0	NUM
cana-6180	99	60	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	99	61	3	3	NUM
cana-6180	99	62	0.64	0.64	NUM
cana-6180	99	63	4	4	NUM
cana-6180	99	64	0.25	0.25	NUM
cana-6180	99	65	1	1	NUM
cana-6180	99	66	0.18	0.18	NUM
cana-6180	99	67	{	{	PUNCT
cana-6180	99	68	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	99	69	𝑧	𝑧	NOUN
cana-6180	99	70	=	=	PUNCT
cana-6180	99	71	−2𝑥1	−2𝑥1	PROPN
cana-6180	100	1	+	+	NUM
cana-6180	100	2	1𝑥2	1𝑥2	NUM
cana-6180	100	3	−	−	PROPN
cana-6180	100	4	𝑥3	𝑥3	PROPN
cana-6180	100	5	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	100	6	1𝑥1	1𝑥1	NUM
cana-6180	100	7	+	+	CCONJ
cana-6180	100	8	𝑥2	𝑥2	NOUN
cana-6180	100	9	−	−	NOUN
cana-6180	100	10	2𝑥3	2𝑥3	NUM
cana-6180	100	11	≤	≤	NUM
cana-6180	100	12	5	5	NUM
cana-6180	100	13	−2𝑥1	−2𝑥1	NUM
cana-6180	100	14	−	−	NUM
cana-6180	100	15	2𝑥2	2𝑥2	NUM
cana-6180	100	16	+	+	CCONJ
cana-6180	100	17	𝑥3	𝑥3	ADJ
cana-6180	100	18	≤	≤	ADJ
cana-6180	100	19	2	2	NUM
cana-6180	100	20	𝑥1	𝑥1	NOUN
cana-6180	100	21	;	;	PUNCT
cana-6180	100	22	𝑥2	𝑥2	NOUN
cana-6180	100	23	;	;	PUNCT
cana-6180	100	24	𝑥3	𝑥3	NOUN
cana-6180	100	25	≥	≥	NOUN
cana-6180	100	26	0	0	NUM
cana-6180	100	27	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	100	28	3	3	NUM
cana-6180	100	29	0.63	0.63	NUM
cana-6180	100	30	4	4	NUM
cana-6180	100	31	0.23	0.23	NUM
cana-6180	100	32	3	3	NUM
cana-6180	100	33	0.42	0.42	NUM
cana-6180	100	34	{	{	PUNCT
cana-6180	100	35	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
cana-6180	100	36	𝑧	𝑧	NOUN
cana-6180	100	37	=	=	SYM
cana-6180	100	38	2𝑥1	2𝑥1	NUM
cana-6180	100	39	−	−	NOUN
cana-6180	100	40	1𝑥2	1𝑥2	NUM
cana-6180	101	1	+	+	CCONJ
cana-6180	101	2	𝑥3	𝑥3	PROPN
cana-6180	101	3	𝑠𝑡	𝑠𝑡	PROPN
cana-6180	101	4	1𝑥1	1𝑥1	NUM
cana-6180	101	5	+	+	CCONJ
cana-6180	101	6	2𝑥2	2𝑥2	NUM
cana-6180	101	7	−	−	PROPN
cana-6180	101	8	𝑥3	𝑥3	NOUN
cana-6180	101	9	≤	≤	ADV
cana-6180	101	10	5	5	NUM
cana-6180	101	11	−2𝑥1	−2𝑥1	NUM
cana-6180	101	12	−	−	NUM
cana-6180	101	13	2𝑥2	2𝑥2	NUM
cana-6180	102	1	+	+	CCONJ
cana-6180	102	2	3𝑥3	3𝑥3	NUM
cana-6180	102	3	≤	≤	PROPN
cana-6180	102	4	−2	−2	PROPN
cana-6180	102	5	𝑥1	𝑥1	NOUN
cana-6180	102	6	;	;	PUNCT
cana-6180	102	7	𝑥2	𝑥2	NOUN
cana-6180	102	8	;	;	PUNCT
cana-6180	102	9	𝑥3	𝑥3	NOUN
cana-6180	102	10	≥	≥	NOUN
cana-6180	102	11	0	0	NUM
cana-6180	102	12	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	𝑖𝑛𝑡𝑒𝑔𝑒𝑟	PROPN
cana-6180	102	13	3	3	NUM
cana-6180	102	14	0.62	0.62	NUM
cana-6180	102	15	4	4	NUM
cana-6180	102	16	0.24	0.24	NUM
cana-6180	102	17	3	3	NUM
cana-6180	102	18	0.62	0.62	NUM
cana-6180	102	19	total	total	NOUN
cana-6180	102	20	30	30	NUM
cana-6180	102	21	6.78	6.78	NUM
cana-6180	102	22	53	53	NUM
cana-6180	102	23	3.81	3.81	NUM
cana-6180	102	24	36	36	NUM
cana-6180	102	25	6.47	6.47	NUM
cana-6180	102	26	4.1.interpretation	4.1.interpretation	NUM
cana-6180	102	27	of	of	ADP
cana-6180	102	28	results	result	NOUN
cana-6180	102	29	we	we	PRON
cana-6180	102	30	show	show	VERB
cana-6180	102	31	the	the	DET
cana-6180	102	32	percentage	percentage	NOUN
cana-6180	102	33	of	of	ADP
cana-6180	102	34	performance	performance	NOUN
cana-6180	102	35	improvement	improvement	NOUN
cana-6180	102	36	in	in	ADP
cana-6180	102	37	the	the	DET
cana-6180	102	38	new	new	ADJ
cana-6180	102	39	algorithm	algorithm	NOUN
cana-6180	102	40	compared	compare	VERB
cana-6180	102	41	to	to	ADP
cana-6180	102	42	the	the	DET
cana-6180	102	43	classical	classical	ADJ
cana-6180	102	44	methods	method	NOUN
cana-6180	102	45	.	.	PUNCT
cana-6180	103	1	classic	classic	ADJ
cana-6180	103	2	cutting	cut	VERB
cana-6180	103	3	planes	plane	NOUN
cana-6180	103	4	,	,	PUNCT
cana-6180	103	5	branching	branch	VERB
cana-6180	103	6	and	and	CCONJ
cana-6180	103	7	nodes	nod	VERB
cana-6180	103	8	total	total	ADJ
cana-6180	103	9	branch	branch	NOUN
cana-6180	103	10	and	and	CCONJ
cana-6180	103	11	bound	bind	VERB
cana-6180	103	12	number	number	NOUN
cana-6180	103	13	of	of	ADP
cana-6180	103	14	iterations	iteration	NOUN
cana-6180	103	15	58.88	58.88	NUM
cana-6180	103	16	%	%	NOUN
cana-6180	103	17	solution	solution	NOUN
cana-6180	103	18	time	time	NOUN
cana-6180	103	19	147%number	147%number	NUM
cana-6180	103	20	of	of	ADP
cana-6180	103	21	iterations	iteration	NOUN
cana-6180	103	22	cutting	cut	VERB
cana-6180	103	23	planes	plane	NOUN
cana-6180	103	24	number	number	NOUN
cana-6180	103	25	of	of	ADP
cana-6180	103	26	iterations	iteration	NOUN
cana-6180	103	27	101.19	101.19	NUM
cana-6180	103	28	%	%	NOUN
cana-6180	103	29	communications	communication	NOUN
cana-6180	103	30	on	on	ADP
cana-6180	103	31	applied	apply	VERB
cana-6180	103	32	nonlinear	nonlinear	ADJ
cana-6180	103	33	analysis	analysis	NOUN
cana-6180	103	34	issn	issn	NOUN
cana-6180	103	35	:	:	PUNCT
cana-6180	103	36	1074	1074	NUM
cana-6180	103	37	-	-	PUNCT
cana-6180	103	38	133x	133x	NUM
cana-6180	103	39	vol	vol	NOUN
cana-6180	103	40	32	32	NUM
cana-6180	103	41	no	no	NOUN
cana-6180	103	42	.	.	NOUN
cana-6180	103	43	3	3	NUM
cana-6180	103	44	(	(	PUNCT
cana-6180	103	45	2025	2025	NUM
cana-6180	103	46	)	)	PUNCT
cana-6180	103	47	1140	1140	NUM
cana-6180	103	48	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	103	49	solution	solution	NOUN
cana-6180	103	50	time	time	NOUN
cana-6180	103	51	83.33%number	83.33%number	PROPN
cana-6180	103	52	of	of	ADP
cana-6180	103	53	iterations	iteration	NOUN
cana-6180	103	54	new	new	ADJ
cana-6180	103	55	algorithm	algorithm	NOUN
cana-6180	103	56	number	number	NOUN
cana-6180	103	57	of	of	ADP
cana-6180	103	58	iterations	iteration	NOUN
cana-6180	103	59	99.99	99.99	NUM
cana-6180	103	60	%	%	NOUN
cana-6180	103	61	solution	solution	NOUN
cana-6180	103	62	time	time	NOUN
cana-6180	103	63	99.98%number	99.98%number	NUM
cana-6180	103	64	of	of	ADP
cana-6180	103	65	iterations	iteration	NOUN
cana-6180	103	66	the	the	DET
cana-6180	103	67	efficiency	efficiency	NOUN
cana-6180	103	68	of	of	ADP
cana-6180	103	69	the	the	DET
cana-6180	103	70	calculation	calculation	NOUN
cana-6180	103	71	and	and	CCONJ
cana-6180	103	72	the	the	DET
cana-6180	103	73	precision	precision	NOUN
cana-6180	103	74	of	of	ADP
cana-6180	103	75	the	the	DET
cana-6180	103	76	results	result	NOUN
cana-6180	103	77	.	.	PUNCT
cana-6180	104	1	we	we	PRON
cana-6180	104	2	show	show	VERB
cana-6180	104	3	the	the	DET
cana-6180	104	4	percentage	percentage	NOUN
cana-6180	104	5	of	of	ADP
cana-6180	104	6	performance	performance	NOUN
cana-6180	104	7	improvement	improvement	NOUN
cana-6180	104	8	in	in	ADP
cana-6180	104	9	the	the	DET
cana-6180	104	10	new	new	ADJ
cana-6180	104	11	algorithm	algorithm	NOUN
cana-6180	104	12	compared	compare	VERB
cana-6180	104	13	to	to	ADP
cana-6180	104	14	the	the	DET
cana-6180	104	15	classical	classical	ADJ
cana-6180	104	16	methods	method	NOUN
cana-6180	104	17	.	.	PUNCT
cana-6180	105	1	classic	classic	ADJ
cana-6180	105	2	cutting	cut	VERB
cana-6180	105	3	planes	plane	NOUN
cana-6180	105	4	,	,	PUNCT
cana-6180	105	5	branching	branch	VERB
cana-6180	105	6	and	and	CCONJ
cana-6180	105	7	nodes	nod	VERB
cana-6180	105	8	efficiency	efficiency	NOUN
cana-6180	105	9	ratio	ratio	NOUN
cana-6180	105	10	branch	branch	NOUN
cana-6180	105	11	and	and	CCONJ
cana-6180	105	12	bound	bind	VERB
cana-6180	105	13	07.18	07.18	NUM
cana-6180	105	14	%	%	NOUN
cana-6180	105	15	cutting	cut	VERB
cana-6180	105	16	planes	plane	NOUN
cana-6180	105	17	22.6	22.6	NUM
cana-6180	105	18	%	%	NOUN
cana-6180	105	19	new	new	ADJ
cana-6180	105	20	algorithm	algorithm	NOUN
cana-6180	105	21	17.99	17.99	NUM
cana-6180	105	22	%	%	NOUN
cana-6180	105	23	we	we	PRON
cana-6180	105	24	notice	notice	VERB
cana-6180	105	25	that	that	SCONJ
cana-6180	105	26	the	the	DET
cana-6180	105	27	first	first	ADJ
cana-6180	105	28	and	and	CCONJ
cana-6180	105	29	second	second	ADJ
cana-6180	105	30	features	feature	NOUN
cana-6180	105	31	of	of	ADP
cana-6180	105	32	the	the	DET
cana-6180	105	33	new	new	ADJ
cana-6180	105	34	algorithm	algorithm	NOUN
cana-6180	105	35	are	be	AUX
cana-6180	105	36	achieved	achieve	VERB
cana-6180	105	37	from	from	ADP
cana-6180	105	38	the	the	DET
cana-6180	105	39	characteristics	characteristic	NOUN
cana-6180	105	40	of	of	ADP
cana-6180	105	41	the	the	DET
cana-6180	105	42	new	new	ADJ
cana-6180	105	43	cut	cut	NOUN
cana-6180	105	44	and	and	CCONJ
cana-6180	105	45	branch	branch	NOUN
cana-6180	105	46	method	method	NOUN
cana-6180	105	47	.	.	PUNCT
cana-6180	106	1	4	4	X
cana-6180	106	2	.	.	X
cana-6180	106	3	discussion	discussion	NOUN
cana-6180	106	4	we	we	PRON
cana-6180	106	5	conclude	conclude	VERB
cana-6180	106	6	from	from	ADP
cana-6180	106	7	this	this	DET
cana-6180	106	8	research	research	NOUN
cana-6180	106	9	that	that	SCONJ
cana-6180	106	10	two	two	NUM
cana-6180	106	11	methods	method	NOUN
cana-6180	106	12	can	can	AUX
cana-6180	106	13	be	be	AUX
cana-6180	106	14	combined	combine	VERB
cana-6180	106	15	to	to	PART
cana-6180	106	16	obtain	obtain	VERB
cana-6180	106	17	a	a	DET
cana-6180	106	18	third	third	ADJ
cana-6180	106	19	method	method	NOUN
cana-6180	106	20	with	with	ADP
cana-6180	106	21	better	well	ADJ
cana-6180	106	22	results	result	NOUN
cana-6180	106	23	or	or	CCONJ
cana-6180	106	24	similar	similar	ADJ
cana-6180	106	25	to	to	ADP
cana-6180	106	26	the	the	DET
cana-6180	106	27	results	result	NOUN
cana-6180	106	28	of	of	ADP
cana-6180	106	29	other	other	ADJ
cana-6180	106	30	algorithms	algorithm	NOUN
cana-6180	106	31	.	.	PUNCT
cana-6180	107	1	the	the	DET
cana-6180	107	2	cutting	cut	VERB
cana-6180	107	3	planes	plane	NOUN
cana-6180	107	4	method	method	NOUN
cana-6180	107	5	and	and	CCONJ
cana-6180	107	6	the	the	DET
cana-6180	107	7	branch	branch	NOUN
cana-6180	107	8	-	-	PUNCT
cana-6180	107	9	and	and	CCONJ
cana-6180	107	10	-	-	PUNCT
cana-6180	107	11	bound	bind	VERB
cana-6180	107	12	method	method	NOUN
cana-6180	107	13	can	can	AUX
cana-6180	107	14	be	be	AUX
cana-6180	107	15	combined	combine	VERB
cana-6180	107	16	more	more	ADV
cana-6180	107	17	than	than	ADP
cana-6180	107	18	once	once	ADV
cana-6180	107	19	.	.	PUNCT
cana-6180	108	1	we	we	PRON
cana-6180	108	2	also	also	ADV
cana-6180	108	3	note	note	VERB
cana-6180	108	4	that	that	SCONJ
cana-6180	108	5	the	the	DET
cana-6180	108	6	cutting	cut	VERB
cana-6180	108	7	planes	plane	NOUN
cana-6180	108	8	method	method	NOUN
cana-6180	108	9	was	be	AUX
cana-6180	108	10	reconnected	reconnecte	VERB
cana-6180	108	11	,	,	PUNCT
cana-6180	108	12	meaning	mean	VERB
cana-6180	108	13	we	we	PRON
cana-6180	108	14	obtained	obtain	VERB
cana-6180	108	15	a	a	DET
cana-6180	108	16	branch	branch	NOUN
cana-6180	108	17	a	a	DET
cana-6180	108	18	branching	branching	NOUN
cana-6180	108	19	,	,	PUNCT
cana-6180	108	20	resulting	result	VERB
cana-6180	108	21	in	in	ADP
cana-6180	108	22	two	two	NUM
cana-6180	108	23	solutions	solution	NOUN
cana-6180	108	24	:	:	PUNCT
cana-6180	108	25	a	a	DET
cana-6180	108	26	solution	solution	NOUN
cana-6180	108	27	outside	outside	ADP
cana-6180	108	28	the	the	DET
cana-6180	108	29	solution	solution	NOUN
cana-6180	108	30	region	region	NOUN
cana-6180	108	31	and	and	CCONJ
cana-6180	108	32	an	an	DET
cana-6180	108	33	integer	integer	NOUN
cana-6180	108	34	optimal	optimal	ADJ
cana-6180	108	35	solution	solution	NOUN
cana-6180	108	36	to	to	ADP
cana-6180	108	37	the	the	DET
cana-6180	108	38	problem	problem	NOUN
cana-6180	108	39	.	.	PUNCT
cana-6180	109	1	this	this	DET
cana-6180	109	2	new	new	ADJ
cana-6180	109	3	triple	triple	ADJ
cana-6180	109	4	combination	combination	NOUN
cana-6180	109	5	is	be	AUX
cana-6180	109	6	an	an	DET
cana-6180	109	7	excellent	excellent	ADJ
cana-6180	109	8	combination	combination	NOUN
cana-6180	109	9	,	,	PUNCT
cana-6180	109	10	as	as	SCONJ
cana-6180	109	11	it	it	PRON
cana-6180	109	12	takes	take	VERB
cana-6180	109	13	on	on	ADP
cana-6180	109	14	the	the	DET
cana-6180	109	15	good	good	ADJ
cana-6180	109	16	qualities	quality	NOUN
cana-6180	109	17	of	of	ADP
cana-6180	109	18	the	the	DET
cana-6180	109	19	new	new	ADJ
cana-6180	109	20	method	method	NOUN
cana-6180	109	21	and	and	CCONJ
cana-6180	109	22	the	the	DET
cana-6180	109	23	cutting	cut	VERB
cana-6180	109	24	planes	plane	NOUN
cana-6180	109	25	method	method	NOUN
cana-6180	109	26	.	.	PUNCT
cana-6180	110	1	this	this	PRON
cana-6180	110	2	opens	open	VERB
cana-6180	110	3	up	up	ADP
cana-6180	110	4	a	a	DET
cana-6180	110	5	broad	broad	ADJ
cana-6180	110	6	and	and	CCONJ
cana-6180	110	7	new	new	ADJ
cana-6180	110	8	field	field	NOUN
cana-6180	110	9	in	in	ADP
cana-6180	110	10	integer	integer	PROPN
cana-6180	110	11	linear	linear	PROPN
cana-6180	110	12	programming	programming	NOUN
cana-6180	110	13	problems	problem	NOUN
cana-6180	110	14	.	.	PUNCT
cana-6180	111	1	from	from	ADP
cana-6180	111	2	the	the	DET
cana-6180	111	3	three	three	NUM
cana-6180	111	4	previous	previous	ADJ
cana-6180	111	5	properties	property	NOUN
cana-6180	111	6	,	,	PUNCT
cana-6180	111	7	the	the	DET
cana-6180	111	8	new	new	ADJ
cana-6180	111	9	cut	cut	NOUN
cana-6180	111	10	-	-	PUNCT
cana-6180	111	11	and	and	CCONJ
cana-6180	111	12	-	-	PUNCT
cana-6180	111	13	knot	knot	NOUN
cana-6180	111	14	method	method	NOUN
cana-6180	111	15	is	be	AUX
cana-6180	111	16	guaranteed	guarantee	VERB
cana-6180	111	17	to	to	PART
cana-6180	111	18	reach	reach	VERB
cana-6180	111	19	the	the	DET
cana-6180	111	20	optimal	optimal	ADJ
cana-6180	111	21	solution	solution	NOUN
cana-6180	111	22	because	because	SCONJ
cana-6180	111	23	it	it	PRON
cana-6180	111	24	ends	end	VERB
cana-6180	111	25	with	with	ADP
cana-6180	111	26	the	the	DET
cana-6180	111	27	branching	branch	VERB
cana-6180	111	28	-	-	PUNCT
cana-6180	111	29	andknotting	andknotte	VERB
cana-6180	111	30	method	method	NOUN
cana-6180	111	31	.	.	PUNCT
cana-6180	112	1	from	from	ADP
cana-6180	112	2	the	the	DET
cana-6180	112	3	three	three	NUM
cana-6180	112	4	properties	property	NOUN
cana-6180	112	5	mentioned	mention	VERB
cana-6180	112	6	in	in	ADP
cana-6180	112	7	the	the	DET
cana-6180	112	8	paragraph	paragraph	NOUN
cana-6180	112	9	above	above	ADV
cana-6180	112	10	,	,	PUNCT
cana-6180	112	11	the	the	DET
cana-6180	112	12	efficiency	efficiency	NOUN
cana-6180	112	13	of	of	ADP
cana-6180	112	14	the	the	DET
cana-6180	112	15	calculation	calculation	NOUN
cana-6180	112	16	and	and	CCONJ
cana-6180	112	17	the	the	DET
cana-6180	112	18	precision	precision	NOUN
cana-6180	112	19	of	of	ADP
cana-6180	112	20	the	the	DET
cana-6180	112	21	results	result	NOUN
cana-6180	112	22	,	,	PUNCT
cana-6180	112	23	which	which	PRON
cana-6180	112	24	indicate	indicate	VERB
cana-6180	112	25	that	that	SCONJ
cana-6180	112	26	the	the	DET
cana-6180	112	27	new	new	ADJ
cana-6180	112	28	cut	cut	NOUN
cana-6180	112	29	-	-	PUNCT
cana-6180	112	30	and	and	CCONJ
cana-6180	112	31	-	-	PUNCT
cana-6180	112	32	knot	knot	NOUN
cana-6180	112	33	method	method	NOUN
cana-6180	112	34	is	be	AUX
cana-6180	112	35	guaranteed	guarantee	VERB
cana-6180	112	36	to	to	PART
cana-6180	112	37	reach	reach	VERB
cana-6180	112	38	the	the	DET
cana-6180	112	39	optimal	optimal	ADJ
cana-6180	112	40	solution	solution	NOUN
cana-6180	112	41	because	because	SCONJ
cana-6180	112	42	it	it	PRON
cana-6180	112	43	ends	end	VERB
cana-6180	112	44	with	with	ADP
cana-6180	112	45	the	the	DET
cana-6180	112	46	branching	branch	VERB
cana-6180	112	47	-	-	PUNCT
cana-6180	112	48	and	and	CCONJ
cana-6180	112	49	-	-	PUNCT
cana-6180	112	50	knotting	knotting	NOUN
cana-6180	112	51	method	method	NOUN
cana-6180	112	52	,	,	PUNCT
cana-6180	112	53	it	it	PRON
cana-6180	112	54	is	be	AUX
cana-6180	112	55	guaranteed	guarantee	VERB
cana-6180	112	56	to	to	PART
cana-6180	112	57	reach	reach	VERB
cana-6180	112	58	the	the	DET
cana-6180	112	59	optimal	optimal	ADJ
cana-6180	112	60	solution	solution	NOUN
cana-6180	112	61	.	.	PUNCT
cana-6180	113	1	therefore	therefore	ADV
cana-6180	113	2	,	,	PUNCT
cana-6180	113	3	we	we	PRON
cana-6180	113	4	recommend	recommend	VERB
cana-6180	113	5	using	use	VERB
cana-6180	113	6	this	this	DET
cana-6180	113	7	method	method	NOUN
cana-6180	113	8	and	and	CCONJ
cana-6180	113	9	exploring	explore	VERB
cana-6180	113	10	other	other	ADJ
cana-6180	113	11	combinations	combination	NOUN
cana-6180	113	12	of	of	ADP
cana-6180	113	13	known	know	VERB
cana-6180	113	14	algorithms	algorithm	NOUN
cana-6180	113	15	in	in	ADP
cana-6180	113	16	integer	integer	PROPN
cana-6180	113	17	linear	linear	PROPN
cana-6180	113	18	programming	programming	NOUN
cana-6180	113	19	to	to	PART
cana-6180	113	20	develop	develop	VERB
cana-6180	113	21	new	new	ADJ
cana-6180	113	22	methods	method	NOUN
cana-6180	113	23	,	,	PUNCT
cana-6180	113	24	taking	take	VERB
cana-6180	113	25	advantage	advantage	NOUN
cana-6180	113	26	of	of	ADP
cana-6180	113	27	the	the	DET
cana-6180	113	28	high	high	ADJ
cana-6180	113	29	speeds	speed	NOUN
cana-6180	113	30	of	of	ADP
cana-6180	113	31	current	current	ADJ
cana-6180	113	32	computers	computer	NOUN
cana-6180	113	33	.	.	PUNCT
cana-6180	114	1	we	we	PRON
cana-6180	114	2	also	also	ADV
cana-6180	114	3	recommend	recommend	VERB
cana-6180	114	4	using	use	VERB
cana-6180	114	5	the	the	DET
cana-6180	114	6	new	new	ADJ
cana-6180	114	7	algorithm	algorithm	NOUN
cana-6180	114	8	to	to	PART
cana-6180	114	9	solve	solve	VERB
cana-6180	114	10	the	the	DET
cana-6180	114	11	integer	integer	NOUN
cana-6180	114	12	linear	linear	PROPN
cana-6180	114	13	programming	programming	NOUN
cana-6180	114	14	problem	problem	NOUN
cana-6180	114	15	,	,	PUNCT
cana-6180	114	16	as	as	SCONJ
cana-6180	114	17	it	it	PRON
cana-6180	114	18	is	be	AUX
cana-6180	114	19	a	a	DET
cana-6180	114	20	very	very	ADV
cana-6180	114	21	successful	successful	ADJ
cana-6180	114	22	technique	technique	NOUN
cana-6180	114	23	in	in	ADP
cana-6180	114	24	solving	solve	VERB
cana-6180	114	25	a	a	DET
cana-6180	114	26	wide	wide	ADJ
cana-6180	114	27	range	range	NOUN
cana-6180	114	28	of	of	ADP
cana-6180	114	29	integer	integer	NOUN
cana-6180	114	30	programming	programming	NOUN
cana-6180	114	31	problems	problem	NOUN
cana-6180	114	32	and	and	CCONJ
cana-6180	114	33	it	it	PRON
cana-6180	114	34	provides	provide	VERB
cana-6180	114	35	a	a	DET
cana-6180	114	36	guarantee	guarantee	NOUN
cana-6180	114	37	of	of	ADP
cana-6180	114	38	reaching	reach	VERB
cana-6180	114	39	the	the	DET
cana-6180	114	40	optimal	optimal	ADJ
cana-6180	114	41	solution	solution	NOUN
cana-6180	114	42	.	.	PUNCT
cana-6180	115	1	communications	communication	NOUN
cana-6180	115	2	on	on	ADP
cana-6180	115	3	applied	apply	VERB
cana-6180	115	4	nonlinear	nonlinear	ADJ
cana-6180	115	5	analysis	analysis	NOUN
cana-6180	115	6	issn	issn	NOUN
cana-6180	115	7	:	:	PUNCT
cana-6180	115	8	1074	1074	NUM
cana-6180	115	9	-	-	PUNCT
cana-6180	115	10	133x	133x	NUM
cana-6180	115	11	vol	vol	NOUN
cana-6180	115	12	32	32	NUM
cana-6180	115	13	no	no	NOUN
cana-6180	115	14	.	.	NOUN
cana-6180	115	15	3	3	NUM
cana-6180	115	16	(	(	PUNCT
cana-6180	115	17	2025	2025	NUM
cana-6180	115	18	)	)	PUNCT
cana-6180	115	19	1141	1141	NUM
cana-6180	115	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6180	115	21	since	since	SCONJ
cana-6180	115	22	the	the	DET
cana-6180	115	23	steps	step	NOUN
cana-6180	115	24	are	be	AUX
cana-6180	115	25	precise	precise	ADJ
cana-6180	115	26	enough	enough	ADV
cana-6180	115	27	to	to	PART
cana-6180	115	28	specify	specify	VERB
cana-6180	115	29	exactly	exactly	ADV
cana-6180	115	30	what	what	PRON
cana-6180	115	31	to	to	PART
cana-6180	115	32	do	do	VERB
cana-6180	115	33	at	at	ADP
cana-6180	115	34	each	each	DET
cana-6180	115	35	step	step	NOUN
cana-6180	115	36	,	,	PUNCT
cana-6180	115	37	the	the	DET
cana-6180	115	38	precise	precise	ADJ
cana-6180	115	39	order	order	NOUN
cana-6180	115	40	of	of	ADP
cana-6180	115	41	operations	operation	NOUN
cana-6180	115	42	in	in	ADP
cana-6180	115	43	the	the	DET
cana-6180	115	44	algorithm	algorithm	NOUN
cana-6180	115	45	is	be	AUX
cana-6180	115	46	well	well	ADV
cana-6180	115	47	organized	organized	ADJ
cana-6180	115	48	and	and	CCONJ
cana-6180	115	49	concrete	concrete	ADJ
cana-6180	115	50	.	.	PUNCT
cana-6180	116	1	all	all	DET
cana-6180	116	2	steps	step	NOUN
cana-6180	116	3	in	in	ADP
cana-6180	116	4	the	the	DET
cana-6180	116	5	algorithm	algorithm	NOUN
cana-6180	116	6	are	be	AUX
cana-6180	116	7	feasible	feasible	ADJ
cana-6180	116	8	(	(	PUNCT
cana-6180	116	9	also	also	ADV
cana-6180	116	10	known	know	VERB
cana-6180	116	11	as	as	ADP
cana-6180	116	12	efficiently	efficiently	ADV
cana-6180	116	13	computable	computable	ADJ
cana-6180	116	14	)	)	PUNCT
cana-6180	116	15	.	.	PUNCT
cana-6180	117	1	i	i	PRON
cana-6180	117	2	recommend	recommend	VERB
cana-6180	117	3	using	use	VERB
cana-6180	117	4	the	the	DET
cana-6180	117	5	algorithm	algorithm	NOUN
cana-6180	117	6	.	.	PUNCT
cana-6180	118	1	references	reference	NOUN
cana-6180	118	2	[	[	X
cana-6180	118	3	1	1	NUM
cana-6180	118	4	]	]	PUNCT
cana-6180	118	5	cornuéjols	cornuéjol	NOUN
cana-6180	118	6	,	,	PUNCT
cana-6180	118	7	gérard	gérard	PROPN
cana-6180	118	8	(	(	PUNCT
cana-6180	118	9	2007	2007	NUM
cana-6180	118	10	)	)	PUNCT
cana-6180	118	11	.	.	PUNCT
cana-6180	119	1	revival	revival	NOUN
cana-6180	119	2	of	of	ADP
cana-6180	119	3	the	the	DET
cana-6180	119	4	gomory	gomory	NOUN
cana-6180	119	5	cuts	cut	NOUN
cana-6180	119	6	in	in	ADP
cana-6180	119	7	the	the	DET
cana-6180	119	8	1990s	1990s	NUM
cana-6180	119	9	.	.	PUNCT
cana-6180	120	1	annals	annal	NOUN
cana-6180	120	2	of	of	ADP
cana-6180	120	3	operations	operation	NOUN
cana-6180	120	4	research	research	NOUN
cana-6180	120	5	,	,	PUNCT
cana-6180	120	6	vol	vol	NOUN
cana-6180	120	7	.	.	PROPN
cana-6180	120	8	149	149	NUM
cana-6180	120	9	(	(	PUNCT
cana-6180	120	10	2007	2007	NUM
cana-6180	120	11	)	)	PUNCT
cana-6180	120	12	,	,	PUNCT
cana-6180	120	13	pp	pp	ADP
cana-6180	120	14	.	.	PUNCT
cana-6180	121	1	63.66	63.66	NUM
cana-6180	121	2	.	.	PUNCT
cana-6180	122	1	[	[	X
cana-6180	122	2	2	2	NUM
cana-6180	122	3	]	]	X
cana-6180	122	4	gilmore	gilmore	PROPN
cana-6180	122	5	,	,	PUNCT
cana-6180	122	6	paul	paul	PROPN
cana-6180	122	7	c	c	PROPN
cana-6180	122	8	;	;	PUNCT
cana-6180	122	9	gomory	gomory	NOUN
cana-6180	122	10	,	,	PUNCT
cana-6180	122	11	ralph	ralph	PROPN
cana-6180	122	12	e	e	PROPN
cana-6180	122	13	(	(	PUNCT
cana-6180	122	14	1963	1963	NUM
cana-6180	122	15	)	)	PUNCT
cana-6180	122	16	.	.	PUNCT
cana-6180	123	1	"	"	PUNCT
cana-6180	123	2	a	a	DET
cana-6180	123	3	linear	linear	ADJ
cana-6180	123	4	programming	programming	NOUN
cana-6180	123	5	approach	approach	NOUN
cana-6180	123	6	to	to	ADP
cana-6180	123	7	the	the	DET
cana-6180	123	8	cutting	cut	VERB
cana-6180	123	9	stock	stock	NOUN
cana-6180	123	10	problem	problem	NOUN
cana-6180	123	11	-	-	PUNCT
cana-6180	123	12	part	part	NOUN
cana-6180	123	13	ii	ii	NOUN
cana-6180	123	14	"	"	PUNCT
cana-6180	123	15	.	.	PUNCT
cana-6180	124	1	operations	operation	NOUN
cana-6180	124	2	research	research	NOUN
cana-6180	124	3	.	.	PUNCT
cana-6180	125	1	11	11	NUM
cana-6180	125	2	(	(	PUNCT
cana-6180	125	3	6):863.888	6):863.888	NUM
cana-6180	125	4	[	[	X
cana-6180	125	5	3	3	NUM
cana-6180	125	6	]	]	PUNCT
cana-6180	125	7	cornuéjols	cornuéjol	NOUN
cana-6180	125	8	,	,	PUNCT
cana-6180	125	9	gérard	gérard	PROPN
cana-6180	125	10	,	,	PUNCT
cana-6180	125	11	"	"	PUNCT
cana-6180	125	12	revival	revival	NOUN
cana-6180	125	13	of	of	ADP
cana-6180	125	14	the	the	DET
cana-6180	125	15	gomory	gomory	NOUN
cana-6180	125	16	cuts	cut	NOUN
cana-6180	125	17	in	in	ADP
cana-6180	125	18	the	the	DET
cana-6180	125	19	1990	1990	NUM
cana-6180	125	20	’s	’s	NOUN
cana-6180	125	21	"	"	PUNCT
cana-6180	125	22	(	(	PUNCT
cana-6180	125	23	2005	2005	NUM
cana-6180	125	24	)	)	PUNCT
cana-6180	125	25	.	.	PUNCT
cana-6180	126	1	tepper	tepper	PROPN
cana-6180	126	2	school	school	PROPN
cana-6180	126	3	of	of	ADP
cana-6180	126	4	business	business	NOUN
cana-6180	126	5	.	.	PUNCT
cana-6180	127	1	paper71	paper71	NOUN
cana-6180	128	1	http://repository.cmu.edu/tepper/71	http://repository.cmu.edu/tepper/71	PROPN
cana-6180	128	2	.	.	PUNCT
cana-6180	129	1	[	[	X
cana-6180	129	2	4	4	NUM
cana-6180	129	3	]	]	PUNCT
cana-6180	129	4	cornuéjols	cornuéjol	NOUN
cana-6180	129	5	,	,	PUNCT
cana-6180	129	6	gérard	gérard	PROPN
cana-6180	129	7	(	(	PUNCT
cana-6180	129	8	2008	2008	NUM
cana-6180	129	9	)	)	PUNCT
cana-6180	129	10	.	.	PUNCT
cana-6180	130	1	valid	valid	ADJ
cana-6180	130	2	inequalities	inequality	NOUN
cana-6180	130	3	for	for	ADP
cana-6180	130	4	mixed	mixed	ADJ
cana-6180	130	5	integer	integer	NOUN
cana-6180	130	6	linear	linear	NOUN
cana-6180	130	7	programs	program	NOUN
cana-6180	130	8	.	.	PUNCT
cana-6180	131	1	mathematical	mathematical	ADJ
cana-6180	131	2	programming	programming	NOUN
cana-6180	131	3	ser	ser	NOUN
cana-6180	131	4	.	.	PUNCT
cana-6180	132	1	b	b	NUM
cana-6180	132	2	,	,	PUNCT
cana-6180	132	3	(	(	PUNCT
cana-6180	132	4	2008	2008	NUM
cana-6180	132	5	)	)	PUNCT
cana-6180	132	6	112:3.44	112:3.44	NUM
cana-6180	132	7	.	.	PUNCT
cana-6180	133	1	[	[	X
cana-6180	133	2	5	5	NUM
cana-6180	133	3	]	]	PUNCT
cana-6180	133	4	dantzig	dantzig	NOUN
cana-6180	133	5	,	,	PUNCT
cana-6180	133	6	g.	g.	PROPN
cana-6180	133	7	b.	b.	PROPN
cana-6180	133	8	1963	1963	NUM
cana-6180	133	9	,	,	PUNCT
cana-6180	133	10	linear	linear	NOUN
cana-6180	133	11	programming	programming	NOUN
cana-6180	133	12	and	and	CCONJ
cana-6180	133	13	extensions	extension	NOUN
cana-6180	133	14	,	,	PUNCT
cana-6180	133	15	princeton	princeton	PROPN
cana-6180	133	16	university	university	PROPN
cana-6180	133	17	press	press	PROPN
cana-6180	133	18	,	,	PUNCT
cana-6180	133	19	princeton	princeton	PROPN
cana-6180	133	20	,	,	PUNCT
cana-6180	133	21	nj	nj	PROPN
cana-6180	133	22	.	.	PUNCT
cana-6180	134	1	[	[	X
cana-6180	134	2	6	6	NUM
cana-6180	134	3	]	]	PUNCT
cana-6180	134	4	a	a	DET
cana-6180	134	5	h.	h.	PROPN
cana-6180	134	6	land	land	NOUN
cana-6180	134	7	and	and	CCONJ
cana-6180	134	8	a.	a.	NOUN
cana-6180	134	9	g.	g.	PROPN
cana-6180	134	10	doig	doig	PROPN
cana-6180	134	11	(	(	PUNCT
cana-6180	134	12	1960	1960	NUM
cana-6180	134	13	)	)	PUNCT
cana-6180	134	14	.	.	PUNCT
cana-6180	135	1	"	"	PUNCT
cana-6180	135	2	an	an	DET
cana-6180	135	3	automatic	automatic	ADJ
cana-6180	135	4	method	method	NOUN
cana-6180	135	5	of	of	ADP
cana-6180	135	6	solving	solve	VERB
cana-6180	135	7	discrete	discrete	ADJ
cana-6180	135	8	programming	programming	NOUN
cana-6180	135	9	problems	problem	NOUN
cana-6180	135	10	"	"	PUNCT
cana-6180	135	11	.	.	PUNCT
cana-6180	136	1	econometrica	econometrica	PROPN
cana-6180	136	2	.	.	PUNCT
cana-6180	137	1	28	28	NUM
cana-6180	137	2	(	(	PUNCT
cana-6180	137	3	3	3	NUM
cana-6180	137	4	):	):	PUNCT
cana-6180	137	5	497.520	497.520	NUM
cana-6180	137	6	.	.	PUNCT
cana-6180	138	1	[	[	X
cana-6180	138	2	7	7	NUM
cana-6180	138	3	]	]	X
cana-6180	138	4	narendra	narendra	PROPN
cana-6180	138	5	,	,	PUNCT
cana-6180	138	6	patrenahalli	patrenahalli	NOUN
cana-6180	138	7	m.	m.	NOUN
cana-6180	138	8	;	;	PUNCT
cana-6180	138	9	fukunaga	fukunaga	PROPN
cana-6180	138	10	,	,	PUNCT
cana-6180	138	11	k.	k.	PROPN
cana-6180	138	12	(	(	PUNCT
cana-6180	138	13	1977	1977	NUM
cana-6180	138	14	)	)	PUNCT
cana-6180	138	15	.	.	PUNCT
cana-6180	139	1	"	"	PUNCT
cana-6180	139	2	a	a	DET
cana-6180	139	3	branch	branch	NOUN
cana-6180	139	4	and	and	CCONJ
cana-6180	139	5	bound	bind	VERB
cana-6180	139	6	algorithm	algorithm	NOUN
cana-6180	139	7	for	for	ADP
cana-6180	139	8	feature	feature	NOUN
cana-6180	139	9	subset	subset	NOUN
cana-6180	139	10	selection	selection	NOUN
cana-6180	139	11	"	"	PUNCT
cana-6180	139	12	(	(	PUNCT
cana-6180	139	13	pdf	pdf	NOUN
cana-6180	139	14	)	)	PUNCT
cana-6180	139	15	.	.	PUNCT
cana-6180	140	1	ieee	ieee	NOUN
cana-6180	140	2	transactions	transaction	NOUN
cana-6180	140	3	on	on	ADP
cana-6180	140	4	computers	computer	NOUN
cana-6180	140	5	.	.	PUNCT
cana-6180	141	1	c-26	c-26	PROPN
cana-6180	141	2	(	(	PUNCT
cana-6180	141	3	9	9	NUM
cana-6180	141	4	):	):	PUNCT
cana-6180	141	5	917.922	917.922	NUM
cana-6180	141	6	.	.	PUNCT
cana-6180	142	1	[	[	X
cana-6180	142	2	8	8	NUM
cana-6180	142	3	]	]	X
cana-6180	142	4	nowozin	nowozin	PROPN
cana-6180	142	5	,	,	PUNCT
cana-6180	142	6	sebastian	sebastian	PROPN
cana-6180	142	7	;	;	PUNCT
cana-6180	142	8	lampert	lampert	PROPN
cana-6180	142	9	,	,	PUNCT
cana-6180	142	10	christoph	christoph	PROPN
cana-6180	142	11	h.	h.	PROPN
cana-6180	142	12	(	(	PUNCT
cana-6180	142	13	2011	2011	NUM
cana-6180	142	14	)	)	PUNCT
cana-6180	142	15	.	.	PUNCT
cana-6180	143	1	"	"	PUNCT
cana-6180	143	2	structured	structured	ADJ
cana-6180	143	3	learning	learning	NOUN
cana-6180	143	4	and	and	CCONJ
cana-6180	143	5	prediction	prediction	NOUN
cana-6180	143	6	in	in	ADP
cana-6180	143	7	computer	computer	NOUN
cana-6180	143	8	vision	vision	NOUN
cana-6180	143	9	"	"	PUNCT
cana-6180	143	10	.	.	PUNCT
cana-6180	144	1	foundations	foundation	NOUN
cana-6180	144	2	and	and	CCONJ
cana-6180	144	3	trends	trend	NOUN
cana-6180	144	4	in	in	ADP
cana-6180	144	5	computer	computer	NOUN
cana-6180	144	6	graphics	graphic	NOUN
cana-6180	144	7	and	and	CCONJ
cana-6180	144	8	vision	vision	NOUN
cana-6180	144	9	.	.	PUNCT
cana-6180	145	1	6	6	NUM
cana-6180	145	2	(	(	PUNCT
cana-6180	145	3	3.4	3.4	NUM
cana-6180	145	4	):	):	PUNCT
cana-6180	145	5	185.365	185.365	NUM
cana-6180	145	6	.	.	PUNCT
cana-6180	146	1	[	[	X
cana-6180	146	2	9	9	NUM
cana-6180	146	3	]	]	X
cana-6180	146	4	d.r	d.r	PROPN
cana-6180	146	5	.	.	PROPN
cana-6180	146	6	morrison	morrison	PROPN
cana-6180	146	7	,	,	PUNCT
cana-6180	146	8	e.c	e.c	PROPN
cana-6180	146	9	.	.	PROPN
cana-6180	146	10	sewell	sewell	PROPN
cana-6180	146	11	,	,	PUNCT
cana-6180	146	12	s.h	s.h	PROPN
cana-6180	146	13	.	.	PROPN
cana-6180	146	14	jacobson	jacobson	PROPN
cana-6180	146	15	,	,	PUNCT
cana-6180	146	16	an	an	DET
cana-6180	146	17	application	application	NOUN
cana-6180	146	18	of	of	ADP
cana-6180	146	19	the	the	DET
cana-6180	146	20	branch	branch	NOUN
cana-6180	146	21	,	,	PUNCT
cana-6180	146	22	bound	bind	VERB
cana-6180	146	23	,	,	PUNCT
cana-6180	146	24	and	and	CCONJ
cana-6180	146	25	remember	remember	VERB
cana-6180	146	26	algorithm	algorithm	NOUN
cana-6180	146	27	to	to	ADP
cana-6180	146	28	a	a	DET
cana-6180	146	29	newsimple	newsimple	NOUN
cana-6180	146	30	assembly	assembly	NOUN
cana-6180	146	31	line	line	NOUN
cana-6180	146	32	balancing	balance	VERB
cana-6180	146	33	dataset	dataset	NOUN
cana-6180	146	34	,	,	PUNCT
cana-6180	146	35	european	european	PROPN
cana-6180	146	36	j.	j.	PROPN
cana-6180	146	37	oper	oper	PROPN
cana-6180	146	38	.	.	PUNCT
cana-6180	147	1	res	res	PROPN
cana-6180	147	2	.	.	PUNCT
cana-6180	148	1	(	(	PUNCT
cana-6180	148	2	2013	2013	NUM
cana-6180	148	3	)	)	PUNCT
cana-6180	148	4	in	in	ADP
cana-6180	148	5	press	press	NOUN
cana-6180	148	6	.	.	PUNCT
cana-6180	149	1	[	[	X
cana-6180	149	2	10	10	NUM
cana-6180	149	3	]	]	PUNCT
cana-6180	149	4	t.	t.	PROPN
cana-6180	149	5	koch	koch	PROPN
cana-6180	149	6	,	,	PUNCT
cana-6180	149	7	t.	t.	PROPN
cana-6180	149	8	achterberg	achterberg	PROPN
cana-6180	149	9	,	,	PUNCT
cana-6180	149	10	e.	e.	PROPN
cana-6180	149	11	andersen	andersen	PROPN
cana-6180	149	12	,	,	PUNCT
cana-6180	149	13	o.	o.	PROPN
cana-6180	149	14	bastert	bastert	NOUN
cana-6180	149	15	,	,	PUNCT
cana-6180	149	16	t.	t.	PROPN
cana-6180	149	17	berthold	berthold	PROPN
cana-6180	149	18	,	,	PUNCT
cana-6180	149	19	r.	r.	PROPN
cana-6180	149	20	bixby	bixby	PROPN
cana-6180	149	21	,	,	PUNCT
cana-6180	149	22	e.	e.	PROPN
cana-6180	149	23	danna	danna	PROPN
cana-6180	149	24	,	,	PUNCT
cana-6180	149	25	g.	g.	PROPN
cana-6180	149	26	gamrath	gamrath	PROPN
cana-6180	149	27	,	,	PUNCT
cana-6180	149	28	a.	a.	NOUN
cana-6180	149	29	gleixner	gleixner	PROPN
cana-6180	149	30	,	,	PUNCT
cana-6180	149	31	s.	s.	PROPN
cana-6180	149	32	heinz	heinz	PROPN
cana-6180	149	33	,	,	PUNCT
cana-6180	149	34	a.	a.	NOUN
cana-6180	149	35	lodi	lodi	PROPN
cana-6180	149	36	,	,	PUNCT
cana-6180	149	37	h.	h.	PROPN
cana-6180	149	38	mittelmann	mittelmann	PROPN
cana-6180	149	39	,	,	PUNCT
cana-6180	149	40	t.	t.	PROPN
cana-6180	149	41	ralphs	ralphs	PROPN
cana-6180	149	42	,	,	PUNCT
cana-6180	149	43	d.	d.	PROPN
cana-6180	149	44	salvagnin	salvagnin	PROPN
cana-6180	149	45	,	,	PUNCT
cana-6180	149	46	d.	d.	PROPN
cana-6180	149	47	ste¤y	ste¤y	PROPN
cana-6180	149	48	,	,	PUNCT
cana-6180	149	49	k.	k.	PROPN
cana-6180	149	50	wolter	wolter	PROPN
cana-6180	149	51	,	,	PUNCT
cana-6180	149	52	miplib	miplib	PROPN
cana-6180	149	53	2010	2010	NUM
cana-6180	149	54	:	:	PUNCT
cana-6180	149	55	mixed	mixed	ADJ
cana-6180	149	56	integer	integer	NOUN
cana-6180	149	57	programming	programming	NOUN
cana-6180	149	58	library	library	NOUN
cana-6180	149	59	version	version	NOUN
cana-6180	149	60	5	5	NUM
cana-6180	149	61	,	,	PUNCT
cana-6180	149	62	math	math	NOUN
cana-6180	149	63	.	.	PUNCT
cana-6180	149	64	program	program	NOUN
cana-6180	149	65	.	.	PUNCT
cana-6180	150	1	comput	comput	NOUN
cana-6180	150	2	.	.	PUNCT
cana-6180	151	1	3	3	NUM
cana-6180	151	2	(	(	PUNCT
cana-6180	151	3	2011	2011	NUM
cana-6180	151	4	)	)	PUNCT
cana-6180	151	5	103.163	103.163	NUM
cana-6180	152	1	[	[	PUNCT
cana-6180	152	2	11	11	NUM
cana-6180	152	3	]	]	X
cana-6180	152	4	e.c	e.c	PROPN
cana-6180	152	5	.	.	PROPN
cana-6180	152	6	sewell	sewell	PROPN
cana-6180	152	7	,	,	PUNCT
cana-6180	152	8	s.h	s.h	PROPN
cana-6180	152	9	.	.	PROPN
cana-6180	152	10	jacobson	jacobson	PROPN
cana-6180	152	11	,	,	PUNCT
cana-6180	152	12	a	a	DET
cana-6180	152	13	branch	branch	NOUN
cana-6180	152	14	,	,	PUNCT
cana-6180	152	15	bound	bind	VERB
cana-6180	152	16	,	,	PUNCT
cana-6180	152	17	and	and	CCONJ
cana-6180	152	18	remember	remember	VERB
cana-6180	152	19	algorithm	algorithm	NOUN
cana-6180	152	20	for	for	ADP
cana-6180	152	21	the	the	DET
cana-6180	152	22	simple	simple	ADJ
cana-6180	152	23	assembly	assembly	NOUN
cana-6180	152	24	line	line	NOUN
cana-6180	152	25	balancing	balancing	NOUN
cana-6180	152	26	problem	problem	NOUN
cana-6180	152	27	,	,	PUNCT
cana-6180	152	28	informs	inform	VERB
cana-6180	152	29	j.	j.	PROPN
cana-6180	152	30	comput	comput	PROPN
cana-6180	152	31	.	.	PUNCT
cana-6180	153	1	24(2012	24(2012	NUM
cana-6180	153	2	)	)	PUNCT
cana-6180	153	3	433.442	433.442	NUM
cana-6180	153	4	http://repository.cmu.edu/tepper/71	http://repository.cmu.edu/tepper/71	NOUN