id	sid	tid	token	lemma	pos
cusj-5634	1	1	microsoft	microsoft	PROPN
cusj-5634	1	2	word	word	PROPN
cusj-5634	1	3	cusj_spring_2015_journal.docx	cusj_spring_2015_journal.docx	NOUN
cusj-5634	1	4	!	!	PUNCT
cusj-5634	2	1	cusj%|%volume%9%|%spring%2015	cusj%|%volume%9%|%spring%2015	NOUN
cusj-5634	2	2	%	%	NOUN
cusj-5634	2	3	27	27	NUM
cusj-5634	2	4	%	%	NOUN
cusj-5634	2	5	polynomial	polynomial	ADJ
cusj-5634	2	6	-	-	PUNCT
cusj-5634	2	7	time	time	NOUN
cusj-5634	2	8	matrix	matrix	NOUN
cusj-5634	2	9	-	-	PUNCT
cusj-5634	2	10	based	base	VERB
cusj-5634	2	11	method	method	NOUN
cusj-5634	2	12	of	of	ADP
cusj-5634	2	13	determining	determine	VERB
cusj-5634	2	14	subset	subset	ADJ
cusj-5634	2	15	sum	sum	NOUN
cusj-5634	2	16	solutions	solution	NOUN
cusj-5634	2	17	aubrey	aubrey	PROPN
cusj-5634	2	18	alston1	alston1	PROPN
cusj-5634	3	1	1department	1department	NUM
cusj-5634	3	2	of	of	ADP
cusj-5634	3	3	computer	computer	NOUN
cusj-5634	3	4	science	science	NOUN
cusj-5634	3	5	,	,	PUNCT
cusj-5634	3	6	columbia	columbia	PROPN
cusj-5634	3	7	university	university	PROPN
cusj-5634	3	8	,	,	PUNCT
cusj-5634	3	9	new	new	PROPN
cusj-5634	3	10	york	york	PROPN
cusj-5634	3	11	,	,	PUNCT
cusj-5634	3	12	ny	ny	PROPN
cusj-5634	3	13	,	,	PUNCT
cusj-5634	3	14	usa	usa	PROPN
cusj-5634	3	15	1	1	NUM
cusj-5634	3	16	introduction	introduction	NOUN
cusj-5634	3	17	:	:	PUNCT
cusj-5634	3	18	the	the	DET
cusj-5634	3	19	subset	subset	NOUN
cusj-5634	3	20	sum	sum	NOUN
cusj-5634	3	21	problem	problem	NOUN
cusj-5634	3	22	is	be	AUX
cusj-5634	3	23	a	a	DET
cusj-5634	3	24	well	well	ADV
cusj-5634	3	25	-	-	PUNCT
cusj-5634	3	26	known	know	VERB
cusj-5634	3	27	member	member	NOUN
cusj-5634	3	28	of	of	ADP
cusj-5634	3	29	the	the	DET
cusj-5634	3	30	npcomplete	npcomplete	ADJ
cusj-5634	3	31	complexity	complexity	NOUN
cusj-5634	3	32	class	class	NOUN
cusj-5634	3	33	:	:	PUNCT
cusj-5634	3	34	given	give	VERB
cusj-5634	3	35	a	a	DET
cusj-5634	3	36	set	set	NOUN
cusj-5634	3	37	of	of	ADP
cusj-5634	3	38	integers	integer	NOUN
cusj-5634	3	39	a	a	PRON
cusj-5634	3	40	and	and	CCONJ
cusj-5634	3	41	some	some	DET
cusj-5634	3	42	constant	constant	ADJ
cusj-5634	3	43	c	c	NOUN
cusj-5634	3	44	,	,	PUNCT
cusj-5634	3	45	is	be	AUX
cusj-5634	3	46	there	there	PRON
cusj-5634	3	47	some	some	DET
cusj-5634	3	48	subset	subset	NOUN
cusj-5634	3	49	of	of	ADP
cusj-5634	3	50	a	a	PRON
cusj-5634	3	51	which	which	PRON
cusj-5634	3	52	sums	sum	VERB
cusj-5634	3	53	to	to	ADP
cusj-5634	3	54	c	c	NOUN
cusj-5634	3	55	?	?	PUNCT
cusj-5634	4	1	there	there	PRON
cusj-5634	4	2	have	have	AUX
cusj-5634	4	3	been	be	AUX
cusj-5634	4	4	no	no	DET
cusj-5634	4	5	known	know	VERB
cusj-5634	4	6	algorithms	algorithm	NOUN
cusj-5634	4	7	or	or	CCONJ
cusj-5634	4	8	methods	method	NOUN
cusj-5634	4	9	to	to	PART
cusj-5634	4	10	solve	solve	VERB
cusj-5634	4	11	the	the	DET
cusj-5634	4	12	value	value	NOUN
cusj-5634	4	13	-	-	PUNCT
cusj-5634	4	14	unbounded	unbounded	ADJ
cusj-5634	4	15	,	,	PUNCT
cusj-5634	4	16	general	general	ADJ
cusj-5634	4	17	-	-	PUNCT
cusj-5634	4	18	case	case	NOUN
cusj-5634	4	19	subset	subset	NOUN
cusj-5634	4	20	sum	sum	NOUN
cusj-5634	4	21	problem	problem	NOUN
cusj-5634	4	22	in	in	ADP
cusj-5634	4	23	polynomial	polynomial	ADJ
cusj-5634	4	24	time	time	NOUN
cusj-5634	4	25	.	.	PUNCT
cusj-5634	5	1	a	a	DET
cusj-5634	5	2	naive	naive	ADJ
cusj-5634	5	3	algorithm	algorithm	NOUN
cusj-5634	5	4	performs	perform	VERB
cusj-5634	5	5	in	in	ADP
cusj-5634	5	6	exponential	exponential	ADJ
cusj-5634	5	7	time	time	NOUN
cusj-5634	5	8	by	by	ADP
cusj-5634	5	9	cycling	cycle	VERB
cusj-5634	5	10	through	through	ADP
cusj-5634	5	11	the	the	DET
cusj-5634	5	12	possible	possible	ADJ
cusj-5634	5	13	subsets	subset	NOUN
cusj-5634	5	14	of	of	ADP
cusj-5634	5	15	a	a	PRON
cusj-5634	5	16	until	until	SCONJ
cusj-5634	5	17	it	it	PRON
cusj-5634	5	18	has	have	AUX
cusj-5634	5	19	either	either	CCONJ
cusj-5634	5	20	seen	see	VERB
cusj-5634	5	21	all	all	DET
cusj-5634	5	22	subsets	subset	NOUN
cusj-5634	5	23	or	or	CCONJ
cusj-5634	5	24	found	find	VERB
cusj-5634	5	25	one	one	NUM
cusj-5634	5	26	that	that	PRON
cusj-5634	5	27	sums	sum	VERB
cusj-5634	5	28	to	to	ADP
cusj-5634	5	29	c.	c.	PROPN
cusj-5634	5	30	a	a	DET
cusj-5634	5	31	common	common	ADJ
cusj-5634	5	32	pseudo	pseudo	ADJ
cusj-5634	5	33	-	-	ADJ
cusj-5634	5	34	polynomial	polynomial	ADJ
cusj-5634	5	35	algorithm	algorithm	NOUN
cusj-5634	5	36	employs	employ	VERB
cusj-5634	5	37	a	a	DET
cusj-5634	5	38	dynamic	dynamic	ADJ
cusj-5634	5	39	programming	programming	NOUN
cusj-5634	5	40	method	method	NOUN
cusj-5634	5	41	whose	whose	DET
cusj-5634	5	42	complexity	complexity	NOUN
cusj-5634	5	43	is	be	AUX
cusj-5634	5	44	polynomial	polynomial	ADJ
cusj-5634	5	45	with	with	ADP
cusj-5634	5	46	respect	respect	NOUN
cusj-5634	5	47	to	to	ADP
cusj-5634	5	48	the	the	DET
cusj-5634	5	49	length	length	NOUN
cusj-5634	5	50	of	of	ADP
cusj-5634	5	51	the	the	DET
cusj-5634	5	52	set	set	NOUN
cusj-5634	5	53	and	and	CCONJ
cusj-5634	5	54	the	the	DET
cusj-5634	5	55	range	range	NOUN
cusj-5634	5	56	of	of	ADP
cusj-5634	5	57	the	the	DET
cusj-5634	5	58	inputs	input	NOUN
cusj-5634	5	59	,	,	PUNCT
cusj-5634	5	60	o(n(m	o(n(m	PROPN
cusj-5634	5	61	-	-	PUNCT
cusj-5634	5	62	n	n	NUM
cusj-5634	5	63	)	)	PUNCT
cusj-5634	5	64	)	)	PUNCT
cusj-5634	5	65	,	,	PUNCT
cusj-5634	5	66	where	where	SCONJ
cusj-5634	5	67	n	n	PRON
cusj-5634	5	68	is	be	AUX
cusj-5634	5	69	the	the	DET
cusj-5634	5	70	length	length	NOUN
cusj-5634	5	71	of	of	ADP
cusj-5634	5	72	the	the	DET
cusj-5634	5	73	set	set	ADJ
cusj-5634	5	74	and	and	CCONJ
cusj-5634	5	75	m	m	NOUN
cusj-5634	5	76	-	-	PUNCT
cusj-5634	5	77	n	n	NOUN
cusj-5634	5	78	is	be	AUX
cusj-5634	5	79	the	the	DET
cusj-5634	5	80	range	range	NOUN
cusj-5634	5	81	of	of	ADP
cusj-5634	5	82	inputs	input	NOUN
cusj-5634	5	83	;	;	PUNCT
cusj-5634	5	84	however	however	ADV
cusj-5634	5	85	,	,	PUNCT
cusj-5634	5	86	this	this	DET
cusj-5634	5	87	solution	solution	NOUN
cusj-5634	5	88	is	be	AUX
cusj-5634	5	89	not	not	PART
cusj-5634	5	90	truly	truly	ADV
cusj-5634	5	91	polynomial	polynomial	ADJ
cusj-5634	5	92	,	,	PUNCT
cusj-5634	5	93	as	as	SCONJ
cusj-5634	5	94	it	it	PRON
cusj-5634	5	95	is	be	AUX
cusj-5634	5	96	polynomial	polynomial	ADJ
cusj-5634	5	97	with	with	ADP
cusj-5634	5	98	respect	respect	NOUN
cusj-5634	5	99	to	to	ADP
cusj-5634	5	100	m	m	NOUN
cusj-5634	5	101	-	-	PUNCT
cusj-5634	5	102	n	n	CCONJ
cusj-5634	5	103	,	,	PUNCT
cusj-5634	5	104	which	which	PRON
cusj-5634	5	105	is	be	AUX
cusj-5634	5	106	exponential	exponential	ADJ
cusj-5634	5	107	in	in	ADP
cusj-5634	5	108	its	its	PRON
cusj-5634	5	109	number	number	NOUN
cusj-5634	5	110	of	of	ADP
cusj-5634	5	111	bits	bit	NOUN
cusj-5634	5	112	.	.	PUNCT
cusj-5634	6	1	approximate	approximate	ADJ
cusj-5634	6	2	algorithms	algorithm	NOUN
cusj-5634	6	3	exist	exist	VERB
cusj-5634	6	4	which	which	PRON
cusj-5634	6	5	can	can	AUX
cusj-5634	6	6	be	be	AUX
cusj-5634	6	7	modified	modify	VERB
cusj-5634	6	8	to	to	PART
cusj-5634	6	9	find	find	VERB
cusj-5634	6	10	exact	exact	ADJ
cusj-5634	6	11	solutions	solution	NOUN
cusj-5634	6	12	;	;	PUNCT
cusj-5634	6	13	however	however	ADV
cusj-5634	6	14	,	,	PUNCT
cusj-5634	6	15	they	they	PRON
cusj-5634	6	16	too	too	ADV
cusj-5634	6	17	degrade	degrade	VERB
cusj-5634	6	18	to	to	ADP
cusj-5634	6	19	being	be	AUX
cusj-5634	6	20	exponential	exponential	ADJ
cusj-5634	6	21	in	in	ADP
cusj-5634	6	22	the	the	DET
cusj-5634	6	23	number	number	NOUN
cusj-5634	6	24	of	of	ADP
cusj-5634	6	25	bits	bit	NOUN
cusj-5634	6	26	required	require	VERB
cusj-5634	6	27	to	to	PART
cusj-5634	6	28	represent	represent	VERB
cusj-5634	6	29	elements	element	NOUN
cusj-5634	6	30	in	in	ADP
cusj-5634	6	31	the	the	DET
cusj-5634	6	32	set	set	NOUN
cusj-5634	6	33	.	.	PUNCT
cusj-5634	7	1	in	in	ADP
cusj-5634	7	2	contrast	contrast	NOUN
cusj-5634	7	3	to	to	ADP
cusj-5634	7	4	pre	pre	VERB
cusj-5634	7	5	-	-	ADJ
cusj-5634	7	6	existing	exist	VERB
cusj-5634	7	7	algorithms	algorithm	NOUN
cusj-5634	7	8	,	,	PUNCT
cusj-5634	7	9	the	the	DET
cusj-5634	7	10	method	method	NOUN
cusj-5634	7	11	described	describe	VERB
cusj-5634	7	12	here	here	ADV
cusj-5634	7	13	does	do	AUX
cusj-5634	7	14	not	not	PART
cusj-5634	7	15	concern	concern	VERB
cusj-5634	7	16	itself	itself	PRON
cusj-5634	7	17	with	with	ADP
cusj-5634	7	18	the	the	DET
cusj-5634	7	19	various	various	ADJ
cusj-5634	7	20	subsets	subset	NOUN
cusj-5634	7	21	that	that	PRON
cusj-5634	7	22	exist	exist	VERB
cusj-5634	7	23	within	within	ADP
cusj-5634	7	24	the	the	DET
cusj-5634	7	25	input	input	NOUN
cusj-5634	7	26	set	set	NOUN
cusj-5634	7	27	,	,	PUNCT
cusj-5634	7	28	but	but	CCONJ
cusj-5634	7	29	rather	rather	ADV
cusj-5634	7	30	searches	search	VERB
cusj-5634	7	31	the	the	DET
cusj-5634	7	32	solution	solution	NOUN
cusj-5634	7	33	space	space	NOUN
cusj-5634	7	34	of	of	ADP
cusj-5634	7	35	a	a	DET
cusj-5634	7	36	set	set	NOUN
cusj-5634	7	37	of	of	ADP
cusj-5634	7	38	linear	linear	ADJ
cusj-5634	7	39	constraints	constraint	NOUN
cusj-5634	7	40	when	when	SCONJ
cusj-5634	7	41	applied	apply	VERB
cusj-5634	7	42	to	to	ADP
cusj-5634	7	43	an	an	DET
cusj-5634	7	44	input	input	NOUN
cusj-5634	7	45	set	set	VERB
cusj-5634	7	46	to	to	PART
cusj-5634	7	47	deduce	deduce	VERB
cusj-5634	7	48	if	if	SCONJ
cusj-5634	7	49	a	a	DET
cusj-5634	7	50	solution	solution	NOUN
cusj-5634	7	51	can	can	AUX
cusj-5634	7	52	exist	exist	VERB
cusj-5634	7	53	;	;	PUNCT
cusj-5634	7	54	this	this	DET
cusj-5634	7	55	method	method	NOUN
cusj-5634	7	56	is	be	AUX
cusj-5634	7	57	a	a	DET
cusj-5634	7	58	strategy	strategy	NOUN
cusj-5634	7	59	which	which	PRON
cusj-5634	7	60	may	may	AUX
cusj-5634	7	61	be	be	AUX
cusj-5634	7	62	employed	employ	VERB
cusj-5634	7	63	to	to	PART
cusj-5634	7	64	find	find	VERB
cusj-5634	7	65	solutions	solution	NOUN
cusj-5634	7	66	satisfying	satisfy	VERB
cusj-5634	7	67	the	the	DET
cusj-5634	7	68	constraints	constraint	NOUN
cusj-5634	7	69	of	of	ADP
cusj-5634	7	70	the	the	DET
cusj-5634	7	71	subset	subset	NOUN
cusj-5634	7	72	sum	sum	NOUN
cusj-5634	7	73	problem	problem	NOUN
cusj-5634	7	74	in	in	ADP
cusj-5634	7	75	time	time	NOUN
cusj-5634	7	76	polynomial	polynomial	ADJ
cusj-5634	7	77	with	with	ADP
cusj-5634	7	78	respect	respect	NOUN
cusj-5634	7	79	only	only	ADV
cusj-5634	7	80	to	to	ADP
cusj-5634	7	81	the	the	DET
cusj-5634	7	82	length	length	NOUN
cusj-5634	7	83	of	of	ADP
cusj-5634	7	84	the	the	DET
cusj-5634	7	85	input	input	NOUN
cusj-5634	7	86	,	,	PUNCT
cusj-5634	7	87	having	have	VERB
cusj-5634	7	88	generalcase	generalcase	NOUN
cusj-5634	7	89	applicability	applicability	NOUN
cusj-5634	7	90	on	on	ADP
cusj-5634	7	91	the	the	DET
cusj-5634	7	92	basis	basis	NOUN
cusj-5634	7	93	of	of	ADP
cusj-5634	7	94	universally	universally	ADV
cusj-5634	7	95	occurring	occur	VERB
cusj-5634	7	96	properties	property	NOUN
cusj-5634	7	97	in	in	ADP
cusj-5634	7	98	sets	set	NOUN
cusj-5634	7	99	satisfying	satisfy	VERB
cusj-5634	7	100	the	the	DET
cusj-5634	7	101	problem	problem	NOUN
cusj-5634	7	102	.	.	PUNCT
cusj-5634	8	1	conventions	convention	NOUN
cusj-5634	8	2	,	,	PUNCT
cusj-5634	8	3	definitions	definition	NOUN
cusj-5634	8	4	,	,	PUNCT
cusj-5634	8	5	and	and	CCONJ
cusj-5634	8	6	properties	property	NOUN
cusj-5634	8	7	:	:	PUNCT
cusj-5634	8	8	given	give	VERB
cusj-5634	8	9	a	a	DET
cusj-5634	8	10	set	set	NOUN
cusj-5634	8	11	a	a	PRON
cusj-5634	8	12	of	of	ADP
cusj-5634	8	13	n	n	CCONJ
cusj-5634	8	14	greater	great	ADJ
cusj-5634	8	15	than	than	ADP
cusj-5634	8	16	four	four	NUM
cusj-5634	8	17	elements	element	NOUN
cusj-5634	8	18	and	and	CCONJ
cusj-5634	8	19	an	an	DET
cusj-5634	8	20	instance	instance	NOUN
cusj-5634	8	21	of	of	ADP
cusj-5634	8	22	subset	subset	ADJ
cusj-5634	8	23	sum	sum	NOUN
cusj-5634	8	24	for	for	ADP
cusj-5634	8	25	a	a	DET
cusj-5634	8	26	constant	constant	ADJ
cusj-5634	8	27	c	c	NOUN
cusj-5634	8	28	,	,	PUNCT
cusj-5634	8	29	satisfied	satisfy	VERB
cusj-5634	8	30	by	by	ADP
cusj-5634	8	31	a	a	DET
cusj-5634	8	32	subset	subset	NOUN
cusj-5634	8	33	s	s	NOUN
cusj-5634	8	34	of	of	ADP
cusj-5634	8	35	length	length	NOUN
cusj-5634	8	36	greater	great	ADJ
cusj-5634	8	37	than	than	ADP
cusj-5634	8	38	2	2	NUM
cusj-5634	8	39	(	(	PUNCT
cusj-5634	8	40	the	the	DET
cusj-5634	8	41	algorithm	algorithm	NOUN
cusj-5634	8	42	first	first	ADV
cusj-5634	8	43	catches	catch	VERB
cusj-5634	8	44	trivial	trivial	ADJ
cusj-5634	8	45	cases	case	NOUN
cusj-5634	8	46	for	for	ADP
cusj-5634	8	47	s	s	NOUN
cusj-5634	8	48	of	of	ADP
cusj-5634	8	49	length	length	NOUN
cusj-5634	8	50	1	1	NUM
cusj-5634	8	51	or	or	CCONJ
cusj-5634	8	52	2	2	NUM
cusj-5634	8	53	)	)	PUNCT
cusj-5634	8	54	,	,	PUNCT
cusj-5634	8	55	index	index	NOUN
cusj-5634	8	56	a	a	PRON
cusj-5634	8	57	as	as	SCONJ
cusj-5634	8	58	follows	follow	VERB
cusj-5634	8	59	:	:	PUNCT
cusj-5634	8	60	the	the	DET
cusj-5634	8	61	strategy	strategy	NOUN
cusj-5634	8	62	outlined	outline	VERB
cusj-5634	8	63	will	will	AUX
cusj-5634	8	64	conform	conform	VERB
cusj-5634	8	65	a	a	PRON
cusj-5634	8	66	to	to	ADP
cusj-5634	8	67	a	a	DET
cusj-5634	8	68	set	set	NOUN
cusj-5634	8	69	of	of	ADP
cusj-5634	8	70	linear	linear	ADJ
cusj-5634	8	71	constraints	constraint	NOUN
cusj-5634	8	72	which	which	PRON
cusj-5634	8	73	will	will	AUX
cusj-5634	8	74	reveal	reveal	VERB
cusj-5634	8	75	a	a	DET
cusj-5634	8	76	subset	subset	ADJ
cusj-5634	8	77	sum	sum	NOUN
cusj-5634	8	78	-	-	PUNCT
cusj-5634	8	79	satisfying	satisfying	NOUN
cusj-5634	8	80	subset	subset	NOUN
cusj-5634	8	81	if	if	SCONJ
cusj-5634	8	82	one	one	PRON
cusj-5634	8	83	exists	exist	VERB
cusj-5634	8	84	.	.	PUNCT
cusj-5634	9	1	to	to	ADP
cusj-5634	9	2	this	this	DET
cusj-5634	9	3	end	end	NOUN
cusj-5634	9	4	,	,	PUNCT
cusj-5634	9	5	define	define	VERB
cusj-5634	9	6	a	a	DET
cusj-5634	9	7	subset	subset	ADJ
cusj-5634	9	8	membership	membership	NOUN
cusj-5634	9	9	vector	vector	NOUN
cusj-5634	9	10	m	m	VERB
cusj-5634	9	11	specific	specific	ADJ
cusj-5634	9	12	to	to	ADP
cusj-5634	9	13	a	a	DET
cusj-5634	9	14	such	such	ADJ
cusj-5634	9	15	that	that	SCONJ
cusj-5634	9	16	the	the	DET
cusj-5634	9	17	ith	ith	PROPN
cusj-5634	9	18	value	value	NOUN
cusj-5634	9	19	in	in	ADP
cusj-5634	9	20	m	m	PROPN
cusj-5634	9	21	is	be	AUX
cusj-5634	9	22	1	1	NUM
cusj-5634	9	23	if	if	SCONJ
cusj-5634	9	24	the	the	DET
cusj-5634	9	25	ith	ith	PROPN
cusj-5634	9	26	element	element	NOUN
cusj-5634	9	27	of	of	ADP
cusj-5634	9	28	a	a	PRON
cusj-5634	9	29	is	be	AUX
cusj-5634	9	30	an	an	DET
cusj-5634	9	31	element	element	NOUN
cusj-5634	9	32	of	of	ADP
cusj-5634	9	33	a	a	DET
cusj-5634	9	34	given	give	VERB
cusj-5634	9	35	subset	subset	NOUN
cusj-5634	9	36	s	s	PROPN
cusj-5634	9	37	of	of	ADP
cusj-5634	9	38	a	a	DET
cusj-5634	9	39	summing	sum	VERB
cusj-5634	9	40	to	to	ADP
cusj-5634	9	41	c	c	PROPN
cusj-5634	9	42	,	,	PUNCT
cusj-5634	9	43	0	0	NUM
cusj-5634	10	1	otherwise	otherwise	ADV
cusj-5634	10	2	.	.	PUNCT
cusj-5634	11	1	if	if	SCONJ
cusj-5634	11	2	such	such	DET
cusj-5634	11	3	a	a	DET
cusj-5634	11	4	subset	subset	NOUN
cusj-5634	11	5	s	s	NOUN
cusj-5634	11	6	exists	exist	NOUN
cusj-5634	11	7	,	,	PUNCT
cusj-5634	11	8	m	m	VERB
cusj-5634	11	9	exists	exist	VERB
cusj-5634	11	10	and	and	CCONJ
cusj-5634	11	11	encodes	encodes	PRON
cusj-5634	11	12	s	s	VERB
cusj-5634	11	13	within	within	ADP
cusj-5634	11	14	a.	a.	NOUN
cusj-5634	11	15	2	2	NUM
cusj-5634	11	16	if	if	SCONJ
cusj-5634	11	17	s	s	NOUN
cusj-5634	11	18	exists	exist	VERB
cusj-5634	11	19	,	,	PUNCT
cusj-5634	11	20	the	the	DET
cusj-5634	11	21	four	four	NUM
cusj-5634	11	22	following	follow	VERB
cusj-5634	11	23	linear	linear	ADJ
cusj-5634	11	24	constraints	constraint	NOUN
cusj-5634	11	25	surrounding	surround	VERB
cusj-5634	11	26	a	a	DET
cusj-5634	11	27	,	,	PUNCT
cusj-5634	11	28	s	s	NOUN
cusj-5634	11	29	,	,	PUNCT
cusj-5634	11	30	and	and	CCONJ
cusj-5634	11	31	m	m	PROPN
cusj-5634	11	32	will	will	AUX
cusj-5634	11	33	be	be	AUX
cusj-5634	11	34	satisfied	satisfied	ADJ
cusj-5634	11	35	:	:	PUNCT
cusj-5634	11	36	1	1	X
cusj-5634	11	37	.	.	X
cusj-5634	11	38	s	s	VERB
cusj-5634	11	39	sums	sum	NOUN
cusj-5634	11	40	to	to	ADP
cusj-5634	11	41	c.	c.	PROPN
cusj-5634	11	42	2	2	NUM
cusj-5634	11	43	.	.	PUNCT
cusj-5634	12	1	s	s	PART
cusj-5634	12	2	has	have	VERB
cusj-5634	12	3	finite	finite	ADJ
cusj-5634	12	4	length	length	NOUN
cusj-5634	12	5	t.	t.	PROPN
cusj-5634	12	6	3	3	NUM
cusj-5634	12	7	.	.	PUNCT
cusj-5634	13	1	there	there	PRON
cusj-5634	13	2	exists	exist	VERB
cusj-5634	13	3	an	an	DET
cusj-5634	13	4	index	index	NOUN
cusj-5634	13	5	r	r	NOUN
cusj-5634	13	6	for	for	ADP
cusj-5634	13	7	which	which	PRON
cusj-5634	13	8	the	the	DET
cusj-5634	13	9	rth	rth	PROPN
cusj-5634	13	10	element	element	NOUN
cusj-5634	13	11	of	of	ADP
cusj-5634	13	12	a	a	PRON
cusj-5634	13	13	is	be	AUX
cusj-5634	13	14	or	or	CCONJ
cusj-5634	13	15	is	be	AUX
cusj-5634	13	16	not	not	PART
cusj-5634	13	17	in	in	ADP
cusj-5634	13	18	s.	s.	PROPN
cusj-5634	13	19	4	4	NUM
cusj-5634	13	20	.	.	PUNCT
cusj-5634	14	1	there	there	PRON
cusj-5634	14	2	exists	exist	VERB
cusj-5634	14	3	an	an	DET
cusj-5634	14	4	index	index	NOUN
cusj-5634	14	5	s	s	NOUN
cusj-5634	14	6	for	for	ADP
cusj-5634	14	7	which	which	PRON
cusj-5634	14	8	the	the	DET
cusj-5634	14	9	sth	sth	NOUN
cusj-5634	14	10	element	element	NOUN
cusj-5634	14	11	of	of	ADP
cusj-5634	14	12	a	a	PRON
cusj-5634	14	13	is	be	AUX
cusj-5634	14	14	or	or	CCONJ
cusj-5634	14	15	is	be	AUX
cusj-5634	14	16	not	not	PART
cusj-5634	14	17	in	in	ADP
cusj-5634	14	18	s.	s.	PROPN
cusj-5634	14	19	using	use	VERB
cusj-5634	14	20	the	the	DET
cusj-5634	14	21	above	above	ADJ
cusj-5634	14	22	constraints	constraint	NOUN
cusj-5634	14	23	,	,	PUNCT
cusj-5634	14	24	an	an	DET
cusj-5634	14	25	underdetermined	underdetermined	ADJ
cusj-5634	14	26	system	system	NOUN
cusj-5634	14	27	z	z	NOUN
cusj-5634	14	28	can	can	AUX
cusj-5634	14	29	be	be	AUX
cusj-5634	14	30	constructed	construct	VERB
cusj-5634	14	31	in	in	ADP
cusj-5634	14	32	the	the	DET
cusj-5634	14	33	parameters	parameter	NOUN
cusj-5634	14	34	of	of	ADP
cusj-5634	14	35	the	the	DET
cusj-5634	14	36	constraints	constraint	NOUN
cusj-5634	14	37	listed	list	VERB
cusj-5634	14	38	:	:	PUNCT
cusj-5634	14	39	the	the	DET
cusj-5634	14	40	algorithm	algorithm	NOUN
cusj-5634	14	41	given	give	VERB
cusj-5634	14	42	below	below	ADP
cusj-5634	14	43	explores	explore	NOUN
cusj-5634	14	44	the	the	DET
cusj-5634	14	45	solution	solution	NOUN
cusj-5634	14	46	spaces	space	NOUN
cusj-5634	14	47	of	of	ADP
cusj-5634	14	48	a	a	DET
cusj-5634	14	49	polynomial	polynomial	ADJ
cusj-5634	14	50	number	number	NOUN
cusj-5634	14	51	of	of	ADP
cusj-5634	14	52	forms	form	NOUN
cusj-5634	14	53	of	of	ADP
cusj-5634	14	54	z	z	NOUN
cusj-5634	14	55	to	to	PART
cusj-5634	14	56	construct	construct	VERB
cusj-5634	14	57	the	the	DET
cusj-5634	14	58	characteristic	characteristic	ADJ
cusj-5634	14	59	membership	membership	NOUN
cusj-5634	14	60	vector	vector	NOUN
cusj-5634	14	61	m	m	VERB
cusj-5634	14	62	for	for	ADP
cusj-5634	14	63	some	some	DET
cusj-5634	14	64	subset	subset	NOUN
cusj-5634	14	65	s	s	NOUN
cusj-5634	14	66	of	of	ADP
cusj-5634	14	67	a	a	DET
cusj-5634	14	68	summing	summing	NOUN
cusj-5634	14	69	to	to	ADP
cusj-5634	14	70	c	c	NOUN
cusj-5634	14	71	if	if	SCONJ
cusj-5634	14	72	one	one	PRON
cusj-5634	14	73	exists	exist	VERB
cusj-5634	14	74	.	.	PUNCT
cusj-5634	15	1	the	the	DET
cusj-5634	15	2	convention	convention	NOUN
cusj-5634	15	3	for	for	ADP
cusj-5634	15	4	the	the	DET
cusj-5634	15	5	determining	determine	VERB
cusj-5634	15	6	solution	solution	NOUN
cusj-5634	15	7	space	space	NOUN
cusj-5634	15	8	of	of	ADP
cusj-5634	15	9	z(a	z(a	PROPN
cusj-5634	15	10	,	,	PUNCT
cusj-5634	15	11	t	t	PROPN
cusj-5634	15	12	,	,	PUNCT
cusj-5634	15	13	r	r	NOUN
cusj-5634	15	14	,	,	PUNCT
cusj-5634	15	15	vr	vr	PROPN
cusj-5634	15	16	,	,	PUNCT
cusj-5634	15	17	s	s	PROPN
cusj-5634	15	18	,	,	PUNCT
cusj-5634	15	19	vs	vs	ADJ
cusj-5634	15	20	)	)	PUNCT
cusj-5634	15	21	is	be	AUX
cusj-5634	15	22	to	to	PART
cusj-5634	15	23	first	first	ADV
cusj-5634	15	24	form	form	VERB
cusj-5634	15	25	an	an	DET
cusj-5634	15	26	equivalent	equivalent	ADJ
cusj-5634	15	27	set	set	NOUN
cusj-5634	15	28	representation	representation	NOUN
cusj-5634	15	29	a	a	PRON
cusj-5634	15	30	’	'	PUNCT
cusj-5634	15	31	by	by	ADP
cusj-5634	15	32	interchanging	interchanging	ADJ
cusj-5634	15	33	index	index	NOUN
cusj-5634	15	34	3	3	NUM
cusj-5634	15	35	of	of	ADP
cusj-5634	15	36	a	a	PRON
cusj-5634	15	37	with	with	ADP
cusj-5634	15	38	index	index	NOUN
cusj-5634	15	39	r	r	NOUN
cusj-5634	15	40	,	,	PUNCT
cusj-5634	15	41	interchanging	interchanging	ADJ
cusj-5634	15	42	index	index	NOUN
cusj-5634	15	43	4	4	NUM
cusj-5634	15	44	with	with	ADP
cusj-5634	15	45	index	index	NOUN
cusj-5634	15	46	s	s	PART
cusj-5634	15	47	in	in	ADP
cusj-5634	15	48	a	a	PRON
cusj-5634	15	49	,	,	PUNCT
cusj-5634	15	50	and	and	CCONJ
cusj-5634	15	51	solving	solve	VERB
cusj-5634	15	52	z(a	z(a	NOUN
cusj-5634	15	53	’	'	PUNCT
cusj-5634	15	54	,	,	PUNCT
cusj-5634	15	55	t	t	PROPN
cusj-5634	15	56	,	,	PUNCT
cusj-5634	15	57	3	3	NUM
cusj-5634	15	58	,	,	PUNCT
cusj-5634	15	59	vr	vr	NOUN
cusj-5634	15	60	,	,	PUNCT
cusj-5634	15	61	4	4	NUM
cusj-5634	15	62	,	,	PUNCT
cusj-5634	15	63	vs	vs	ADP
cusj-5634	15	64	)	)	PUNCT
cusj-5634	15	65	for	for	ADP
cusj-5634	15	66	m	m	NOUN
cusj-5634	15	67	’	'	PUNCT
cusj-5634	15	68	equal	equal	ADJ
cusj-5634	15	69	to	to	ADP
cusj-5634	15	70	m	m	PROPN
cusj-5634	15	71	with	with	ADP
cusj-5634	15	72	likewise	likewise	ADV
cusj-5634	15	73	index	index	NOUN
cusj-5634	15	74	permutations	permutation	NOUN
cusj-5634	15	75	using	use	VERB
cusj-5634	15	76	matrices	matrix	NOUN
cusj-5634	15	77	.	.	PUNCT
cusj-5634	16	1	to	to	PART
cusj-5634	16	2	represent	represent	VERB
cusj-5634	16	3	the	the	DET
cusj-5634	16	4	solution	solution	NOUN
cusj-5634	16	5	space	space	NOUN
cusj-5634	16	6	of	of	ADP
cusj-5634	16	7	z(a	z(a	NOUN
cusj-5634	16	8	’	'	PUNCT
cusj-5634	16	9	,	,	PUNCT
cusj-5634	16	10	t	t	PROPN
cusj-5634	16	11	,	,	PUNCT
cusj-5634	16	12	3	3	NUM
cusj-5634	16	13	,	,	PUNCT
cusj-5634	16	14	vr	vr	NOUN
cusj-5634	16	15	,	,	PUNCT
cusj-5634	16	16	4	4	NUM
cusj-5634	16	17	,	,	PUNCT
cusj-5634	16	18	vs	vs	ADJ
cusj-5634	16	19	)	)	PUNCT
cusj-5634	16	20	,	,	PUNCT
cusj-5634	16	21	the	the	DET
cusj-5634	16	22	outlined	outline	VERB
cusj-5634	16	23	algorithm	algorithm	NOUN
cusj-5634	16	24	follows	follow	VERB
cusj-5634	16	25	the	the	DET
cusj-5634	16	26	convention	convention	NOUN
cusj-5634	16	27	of	of	ADP
cusj-5634	16	28	expressing	express	VERB
cusj-5634	16	29	solution	solution	NOUN
cusj-5634	16	30	space	space	NOUN
cusj-5634	16	31	with	with	ADP
cusj-5634	16	32	respect	respect	NOUN
cusj-5634	16	33	to	to	ADP
cusj-5634	16	34	a	a	DET
cusj-5634	16	35	particular	particular	ADJ
cusj-5634	16	36	solution	solution	NOUN
cusj-5634	16	37	of	of	ADP
cusj-5634	16	38	the	the	DET
cusj-5634	16	39	system	system	NOUN
cusj-5634	16	40	and	and	CCONJ
cusj-5634	16	41	any	any	DET
cusj-5634	16	42	linear	linear	ADJ
cusj-5634	16	43	combination	combination	NOUN
cusj-5634	16	44	of	of	ADP
cusj-5634	16	45	the	the	DET
cusj-5634	16	46	null	null	ADJ
cusj-5634	16	47	space	space	NOUN
cusj-5634	16	48	of	of	ADP
cusj-5634	16	49	the	the	DET
cusj-5634	16	50	multiplier	multipli	ADJ
cusj-5634	16	51	of	of	ADP
cusj-5634	16	52	z(a	z(a	NOUN
cusj-5634	16	53	’	'	PUNCT
cusj-5634	16	54	,	,	PUNCT
cusj-5634	16	55	t	t	PROPN
cusj-5634	16	56	,	,	PUNCT
cusj-5634	16	57	3	3	NUM
cusj-5634	16	58	,	,	PUNCT
cusj-5634	16	59	vr	vr	NOUN
cusj-5634	16	60	,	,	PUNCT
cusj-5634	16	61	4	4	NUM
cusj-5634	16	62	,	,	PUNCT
cusj-5634	16	63	vs	vs	ADJ
cusj-5634	16	64	)	)	PUNCT
cusj-5634	16	65	.	.	PUNCT
cusj-5634	16	66	!	!	PUNCT
cusj-5634	17	1	cusj%|%volume%9%|%spring%2015	cusj%|%volume%9%|%spring%2015	NOUN
cusj-5634	18	1	%	%	NOUN
cusj-5634	18	2	28	28	NUM
cusj-5634	18	3	%	%	NOUN
cusj-5634	18	4	1	1	NUM
cusj-5634	18	5	the	the	DET
cusj-5634	18	6	followed	follow	VERB
cusj-5634	18	7	solution	solution	NOUN
cusj-5634	18	8	convention	convention	NOUN
cusj-5634	18	9	is	be	AUX
cusj-5634	18	10	simple	simple	ADJ
cusj-5634	18	11	forward	forward	ADJ
cusj-5634	18	12	elimination	elimination	NOUN
cusj-5634	18	13	,	,	PUNCT
cusj-5634	18	14	followed	follow	VERB
cusj-5634	18	15	by	by	ADP
cusj-5634	18	16	back	back	ADJ
cusj-5634	18	17	-	-	PUNCT
cusj-5634	18	18	substitution	substitution	NOUN
cusj-5634	18	19	.	.	PUNCT
cusj-5634	19	1	the	the	DET
cusj-5634	19	2	particular	particular	ADJ
cusj-5634	19	3	solution	solution	NOUN
cusj-5634	19	4	is	be	AUX
cusj-5634	19	5	chosen	choose	VERB
cusj-5634	19	6	such	such	ADJ
cusj-5634	19	7	that	that	SCONJ
cusj-5634	19	8	all	all	DET
cusj-5634	19	9	free	free	ADJ
cusj-5634	19	10	variables	variable	NOUN
cusj-5634	19	11	(	(	PUNCT
cusj-5634	19	12	the	the	DET
cusj-5634	19	13	rank	rank	NOUN
cusj-5634	19	14	of	of	ADP
cusj-5634	19	15	the	the	DET
cusj-5634	19	16	multiplier	multipli	ADJ
cusj-5634	19	17	of	of	ADP
cusj-5634	19	18	the	the	DET
cusj-5634	19	19	system	system	NOUN
cusj-5634	19	20	is	be	AUX
cusj-5634	19	21	4	4	NUM
cusj-5634	19	22	;	;	PUNCT
cusj-5634	19	23	given	give	VERB
cusj-5634	19	24	its	its	PRON
cusj-5634	19	25	representation	representation	NOUN
cusj-5634	19	26	,	,	PUNCT
cusj-5634	19	27	the	the	DET
cusj-5634	19	28	free	free	ADJ
cusj-5634	19	29	variables	variable	NOUN
cusj-5634	19	30	are	be	AUX
cusj-5634	19	31	a’5	a’5	ADJ
cusj-5634	19	32	,	,	PUNCT
cusj-5634	19	33	.	.	PUNCT
cusj-5634	19	34	.	.	PUNCT
cusj-5634	19	35	.	.	PUNCT
cusj-5634	20	1	a’n	a’n	PROPN
cusj-5634	20	2	)	)	PUNCT
cusj-5634	21	1	are	be	AUX
cusj-5634	21	2	assumed	assume	VERB
cusj-5634	21	3	to	to	PART
cusj-5634	21	4	be	be	AUX
cusj-5634	21	5	zero	zero	NUM
cusj-5634	21	6	.	.	PUNCT
cusj-5634	22	1	the	the	DET
cusj-5634	22	2	null	null	ADJ
cusj-5634	22	3	space	space	NOUN
cusj-5634	22	4	is	be	AUX
cusj-5634	22	5	then	then	ADV
cusj-5634	22	6	composed	compose	VERB
cusj-5634	22	7	of	of	ADP
cusj-5634	22	8	n-4	n-4	PROPN
cusj-5634	22	9	special	special	ADJ
cusj-5634	22	10	solutions	solution	NOUN
cusj-5634	22	11	each	each	PRON
cusj-5634	22	12	respectively	respectively	ADV
cusj-5634	22	13	assuming	assume	VERB
cusj-5634	22	14	one	one	NUM
cusj-5634	22	15	unique	unique	ADJ
cusj-5634	22	16	mi	mi	NOUN
cusj-5634	22	17	,	,	PUNCT
cusj-5634	22	18	i	i	NOUN
cusj-5634	22	19	=	=	NOUN
cusj-5634	22	20	5	5	NUM
cusj-5634	22	21	,	,	PUNCT
cusj-5634	22	22	.	.	PUNCT
cusj-5634	22	23	.	.	PUNCT
cusj-5634	23	1	.	.	PUNCT
cusj-5634	24	1	,	,	PUNCT
cusj-5634	24	2	n	n	PART
cusj-5634	24	3	to	to	PART
cusj-5634	24	4	be	be	AUX
cusj-5634	24	5	1	1	NUM
cusj-5634	24	6	,	,	PUNCT
cusj-5634	24	7	all	all	DET
cusj-5634	24	8	other	other	ADJ
cusj-5634	24	9	mj	mj	NOUN
cusj-5634	24	10	to	to	PART
cusj-5634	24	11	be	be	AUX
cusj-5634	24	12	0	0	NUM
cusj-5634	24	13	.	.	PUNCT
cusj-5634	25	1	this	this	DET
cusj-5634	25	2	convention	convention	NOUN
cusj-5634	25	3	then	then	ADV
cusj-5634	25	4	allows	allow	VERB
cusj-5634	25	5	m	m	PRON
cusj-5634	25	6	’	'	PUNCT
cusj-5634	25	7	for	for	ADP
cusj-5634	25	8	any	any	DET
cusj-5634	25	9	a	a	PRON
cusj-5634	25	10	’	'	PUNCT
cusj-5634	25	11	to	to	PART
cusj-5634	25	12	be	be	AUX
cusj-5634	25	13	expressed	express	VERB
cusj-5634	25	14	as	as	SCONJ
cusj-5634	25	15	follows	follow	VERB
cusj-5634	25	16	:	:	PUNCT
cusj-5634	25	17	(	(	PUNCT
cusj-5634	25	18	10	10	NUM
cusj-5634	25	19	)	)	PUNCT
cusj-5634	25	20	the	the	DET
cusj-5634	25	21	prescribed	prescribed	ADJ
cusj-5634	25	22	convention	convention	NOUN
cusj-5634	25	23	thus	thus	ADV
cusj-5634	25	24	provides	provide	VERB
cusj-5634	25	25	a	a	DET
cusj-5634	25	26	representation	representation	NOUN
cusj-5634	25	27	of	of	ADP
cusj-5634	25	28	the	the	DET
cusj-5634	25	29	solution	solution	NOUN
cusj-5634	25	30	space	space	NOUN
cusj-5634	25	31	that	that	PRON
cusj-5634	25	32	may	may	AUX
cusj-5634	25	33	be	be	AUX
cusj-5634	25	34	explored	explore	VERB
cusj-5634	25	35	to	to	PART
cusj-5634	25	36	determine	determine	VERB
cusj-5634	25	37	if	if	SCONJ
cusj-5634	25	38	a	a	DET
cusj-5634	25	39	valid	valid	ADJ
cusj-5634	25	40	m	m	NOUN
cusj-5634	25	41	’	'	PUNCT
cusj-5634	25	42	satisfying	satisfy	VERB
cusj-5634	25	43	subset	subset	NOUN
cusj-5634	25	44	sum	sum	NOUN
cusj-5634	25	45	exists	exist	VERB
cusj-5634	25	46	for	for	ADP
cusj-5634	25	47	a	a	DET
cusj-5634	25	48	given	give	VERB
cusj-5634	25	49	z(a	z(a	NOUN
cusj-5634	25	50	’	'	PUNCT
cusj-5634	25	51	,	,	PUNCT
cusj-5634	25	52	t	t	PROPN
cusj-5634	25	53	,	,	PUNCT
cusj-5634	25	54	3	3	NUM
cusj-5634	25	55	,	,	PUNCT
cusj-5634	25	56	vr	vr	NOUN
cusj-5634	25	57	,	,	PUNCT
cusj-5634	25	58	4	4	NUM
cusj-5634	25	59	,	,	PUNCT
cusj-5634	25	60	vs	vs	ADP
cusj-5634	25	61	):	):	PUNCT
cusj-5634	25	62	each	each	DET
cusj-5634	25	63	vector	vector	NOUN
cusj-5634	25	64	of	of	ADP
cusj-5634	25	65	the	the	DET
cusj-5634	25	66	null	null	ADJ
cusj-5634	25	67	space	space	NOUN
cusj-5634	25	68	can	can	AUX
cusj-5634	25	69	be	be	AUX
cusj-5634	25	70	contributed	contribute	VERB
cusj-5634	25	71	to	to	ADP
cusj-5634	25	72	m	m	PROPN
cusj-5634	25	73	’	'	PUNCT
cusj-5634	25	74	one	one	NUM
cusj-5634	25	75	or	or	CCONJ
cusj-5634	25	76	zero	zero	NUM
cusj-5634	25	77	times	time	NOUN
cusj-5634	25	78	,	,	PUNCT
cusj-5634	25	79	and	and	CCONJ
cusj-5634	25	80	,	,	PUNCT
cusj-5634	25	81	together	together	ADV
cusj-5634	25	82	,	,	PUNCT
cusj-5634	25	83	the	the	DET
cusj-5634	25	84	sum	sum	NOUN
cusj-5634	25	85	of	of	ADP
cusj-5634	25	86	the	the	DET
cusj-5634	25	87	particular	particular	ADJ
cusj-5634	25	88	solutions	solution	NOUN
cusj-5634	25	89	and	and	CCONJ
cusj-5634	25	90	applicable	applicable	ADJ
cusj-5634	25	91	vectors	vector	NOUN
cusj-5634	25	92	of	of	ADP
cusj-5634	25	93	the	the	DET
cusj-5634	25	94	null	null	ADJ
cusj-5634	25	95	space	space	NOUN
cusj-5634	25	96	will	will	AUX
cusj-5634	25	97	take	take	VERB
cusj-5634	25	98	b1	b1	NOUN
cusj-5634	25	99	and	and	CCONJ
cusj-5634	25	100	b2	b2	PROPN
cusj-5634	25	101	(	(	PUNCT
cusj-5634	25	102	the	the	DET
cusj-5634	25	103	non	non	ADJ
cusj-5634	25	104	-	-	ADJ
cusj-5634	25	105	zero	zero	NUM
cusj-5634	25	106	and	and	CCONJ
cusj-5634	25	107	non	non	ADJ
cusj-5634	25	108	-	-	ADJ
cusj-5634	25	109	one	one	NUM
cusj-5634	25	110	values	value	NOUN
cusj-5634	25	111	in	in	ADP
cusj-5634	25	112	the	the	DET
cusj-5634	25	113	particular	particular	ADJ
cusj-5634	25	114	solution	solution	NOUN
cusj-5634	25	115	unique	unique	ADJ
cusj-5634	25	116	to	to	ADP
cusj-5634	25	117	the	the	DET
cusj-5634	25	118	values	value	NOUN
cusj-5634	25	119	of	of	ADP
cusj-5634	25	120	the	the	DET
cusj-5634	25	121	first	first	ADJ
cusj-5634	25	122	two	two	NUM
cusj-5634	25	123	elements	element	NOUN
cusj-5634	25	124	and	and	CCONJ
cusj-5634	25	125	the	the	DET
cusj-5634	25	126	chosen	choose	VERB
cusj-5634	25	127	vr	vr	NOUN
cusj-5634	25	128	and	and	CCONJ
cusj-5634	25	129	vs	vs	ADP
cusj-5634	25	130	)	)	PUNCT
cusj-5634	25	131	to	to	ADP
cusj-5634	25	132	0	0	NUM
cusj-5634	25	133	or	or	CCONJ
cusj-5634	25	134	1	1	NUM
cusj-5634	25	135	.	.	PUNCT
cusj-5634	26	1	for	for	ADP
cusj-5634	26	2	any	any	DET
cusj-5634	26	3	solution	solution	NOUN
cusj-5634	26	4	space	space	NOUN
cusj-5634	26	5	for	for	ADP
cusj-5634	26	6	which	which	PRON
cusj-5634	26	7	this	this	PRON
cusj-5634	26	8	applies	apply	VERB
cusj-5634	26	9	,	,	PUNCT
cusj-5634	26	10	the	the	DET
cusj-5634	26	11	resulting	result	VERB
cusj-5634	26	12	m	m	NOUN
cusj-5634	26	13	’	'	PUNCT
cusj-5634	26	14	will	will	AUX
cusj-5634	26	15	be	be	AUX
cusj-5634	26	16	a	a	DET
cusj-5634	26	17	vector	vector	NOUN
cusj-5634	26	18	of	of	ADP
cusj-5634	26	19	0s	0s	NUM
cusj-5634	26	20	and	and	CCONJ
cusj-5634	26	21	1s	1s	NUM
cusj-5634	26	22	encoding	encode	VERB
cusj-5634	26	23	the	the	DET
cusj-5634	26	24	membership	membership	NOUN
cusj-5634	26	25	of	of	ADP
cusj-5634	26	26	s.	s.	PROPN
cusj-5634	26	27	due	due	ADP
cusj-5634	26	28	to	to	ADP
cusj-5634	26	29	the	the	DET
cusj-5634	26	30	form	form	NOUN
cusj-5634	26	31	found	find	VERB
cusj-5634	26	32	as	as	ADP
cusj-5634	26	33	a	a	DET
cusj-5634	26	34	result	result	NOUN
cusj-5634	26	35	of	of	ADP
cusj-5634	26	36	convention	convention	NOUN
cusj-5634	26	37	of	of	ADP
cusj-5634	26	38	this	this	DET
cusj-5634	26	39	method	method	NOUN
cusj-5634	26	40	,	,	PUNCT
cusj-5634	26	41	the	the	DET
cusj-5634	26	42	first	first	ADJ
cusj-5634	26	43	four	four	NUM
cusj-5634	26	44	elements	element	NOUN
cusj-5634	26	45	of	of	ADP
cusj-5634	26	46	a	a	PRON
cusj-5634	26	47	’	'	PUNCT
cusj-5634	26	48	are	be	AUX
cusj-5634	26	49	referred	refer	VERB
cusj-5634	26	50	to	to	ADP
cusj-5634	26	51	as	as	ADP
cusj-5634	26	52	the	the	DET
cusj-5634	26	53	current	current	ADJ
cusj-5634	26	54	window	window	NOUN
cusj-5634	26	55	,	,	PUNCT
cusj-5634	26	56	the	the	DET
cusj-5634	26	57	first	first	ADJ
cusj-5634	26	58	two	two	NUM
cusj-5634	26	59	elements	element	NOUN
cusj-5634	26	60	are	be	AUX
cusj-5634	26	61	the	the	DET
cusj-5634	26	62	balance	balance	NOUN
cusj-5634	26	63	elements	element	NOUN
cusj-5634	26	64	,	,	PUNCT
cusj-5634	26	65	and	and	CCONJ
cusj-5634	26	66	the	the	DET
cusj-5634	26	67	second	second	ADJ
cusj-5634	26	68	two	two	NUM
cusj-5634	26	69	elements	element	NOUN
cusj-5634	26	70	are	be	AUX
cusj-5634	26	71	the	the	DET
cusj-5634	26	72	pivot	pivot	NOUN
cusj-5634	26	73	elements	element	NOUN
cusj-5634	26	74	.	.	PUNCT
cusj-5634	27	1	the	the	DET
cusj-5634	27	2	algorithm	algorithm	NOUN
cusj-5634	27	3	below	below	ADP
cusj-5634	27	4	attempts	attempt	NOUN
cusj-5634	27	5	to	to	PART
cusj-5634	27	6	reveal	reveal	VERB
cusj-5634	27	7	and	and	CCONJ
cusj-5634	27	8	exploit	exploit	VERB
cusj-5634	27	9	solution	solution	NOUN
cusj-5634	27	10	space	space	NOUN
cusj-5634	27	11	properties	property	NOUN
cusj-5634	27	12	which	which	PRON
cusj-5634	27	13	may	may	AUX
cusj-5634	27	14	exist	exist	VERB
cusj-5634	27	15	universally	universally	ADV
cusj-5634	27	16	among	among	ADP
cusj-5634	27	17	all	all	DET
cusj-5634	27	18	sets	set	NOUN
cusj-5634	27	19	for	for	ADP
cusj-5634	27	20	some	some	DET
cusj-5634	27	21	window	window	NOUN
cusj-5634	27	22	configuration	configuration	NOUN
cusj-5634	27	23	if	if	SCONJ
cusj-5634	27	24	the	the	DET
cusj-5634	27	25	set	set	NOUN
cusj-5634	27	26	satisfies	satisfie	NOUN
cusj-5634	27	27	subset	subset	VERB
cusj-5634	27	28	sum	sum	NOUN
cusj-5634	27	29	to	to	PART
cusj-5634	27	30	form	form	VERB
cusj-5634	27	31	m	m	NOUN
cusj-5634	27	32	’	'	PUNCT
cusj-5634	27	33	.	.	PUNCT
cusj-5634	28	1	if	if	SCONJ
cusj-5634	28	2	the	the	DET
cusj-5634	28	3	found	find	VERB
cusj-5634	28	4	properties	property	NOUN
cusj-5634	28	5	are	be	AUX
cusj-5634	28	6	,	,	PUNCT
cusj-5634	28	7	in	in	ADP
cusj-5634	28	8	fact	fact	NOUN
cusj-5634	28	9	,	,	PUNCT
cusj-5634	28	10	universal	universal	ADJ
cusj-5634	28	11	,	,	PUNCT
cusj-5634	28	12	the	the	DET
cusj-5634	28	13	algorithm	algorithm	NOUN
cusj-5634	28	14	outlined	outline	VERB
cusj-5634	28	15	is	be	AUX
cusj-5634	28	16	an	an	DET
cusj-5634	28	17	exact	exact	ADJ
cusj-5634	28	18	,	,	PUNCT
cusj-5634	28	19	general	general	ADJ
cusj-5634	28	20	-	-	PUNCT
cusj-5634	28	21	case	case	NOUN
cusj-5634	28	22	algorithm	algorithm	NOUN
cusj-5634	28	23	for	for	ADP
cusj-5634	28	24	the	the	DET
cusj-5634	28	25	subset	subset	NOUN
cusj-5634	28	26	sum	sum	NOUN
cusj-5634	28	27	problem	problem	NOUN
cusj-5634	28	28	.	.	PUNCT
cusj-5634	29	1	in	in	ADP
cusj-5634	29	2	order	order	NOUN
cusj-5634	29	3	to	to	PART
cusj-5634	29	4	determine	determine	VERB
cusj-5634	29	5	,	,	PUNCT
cusj-5634	29	6	view	view	NOUN
cusj-5634	29	7	,	,	PUNCT
cusj-5634	29	8	and	and	CCONJ
cusj-5634	29	9	exploit	exploit	VERB
cusj-5634	29	10	these	these	DET
cusj-5634	29	11	properties	property	NOUN
cusj-5634	29	12	,	,	PUNCT
cusj-5634	29	13	the	the	DET
cusj-5634	29	14	algorithm	algorithm	NOUN
cusj-5634	29	15	utilizes	utilize	VERB
cusj-5634	29	16	a	a	DET
cusj-5634	29	17	construct	construct	NOUN
cusj-5634	29	18	which	which	PRON
cusj-5634	29	19	will	will	AUX
cusj-5634	29	20	be	be	AUX
cusj-5634	29	21	called	call	VERB
cusj-5634	29	22	a	a	DET
cusj-5634	29	23	directional	directional	ADJ
cusj-5634	29	24	contribution	contribution	NOUN
cusj-5634	29	25	table	table	NOUN
cusj-5634	29	26	.	.	PUNCT
cusj-5634	30	1	a	a	DET
cusj-5634	30	2	directional	directional	ADJ
cusj-5634	30	3	contribution	contribution	NOUN
cusj-5634	30	4	table	table	NOUN
cusj-5634	30	5	is	be	AUX
cusj-5634	30	6	a	a	DET
cusj-5634	30	7	tabulation	tabulation	NOUN
cusj-5634	30	8	of	of	ADP
cusj-5634	30	9	the	the	DET
cusj-5634	30	10	contributions	contribution	NOUN
cusj-5634	30	11	of	of	ADP
cusj-5634	30	12	the	the	DET
cusj-5634	30	13	elements	element	NOUN
cusj-5634	30	14	of	of	ADP
cusj-5634	30	15	the	the	DET
cusj-5634	30	16	null	null	ADJ
cusj-5634	30	17	space	space	NOUN
cusj-5634	30	18	towards	towards	ADP
cusj-5634	30	19	bringing	bring	VERB
cusj-5634	30	20	the	the	DET
cusj-5634	30	21	balance	balance	NOUN
cusj-5634	30	22	values	value	NOUN
cusj-5634	30	23	of	of	ADP
cusj-5634	30	24	the	the	DET
cusj-5634	30	25	particular	particular	ADJ
cusj-5634	30	26	solution	solution	NOUN
cusj-5634	30	27	towards	towards	ADP
cusj-5634	30	28	0	0	NUM
cusj-5634	30	29	or	or	CCONJ
cusj-5634	30	30	1	1	NUM
cusj-5634	30	31	.	.	PUNCT
cusj-5634	31	1	a	a	DET
cusj-5634	31	2	directional	directional	ADJ
cusj-5634	31	3	contribution	contribution	NOUN
cusj-5634	31	4	table	table	NOUN
cusj-5634	31	5	d	d	NOUN
cusj-5634	31	6	tabulates	tabulate	VERB
cusj-5634	31	7	the	the	DET
cusj-5634	31	8	contribution	contribution	NOUN
cusj-5634	31	9	of	of	ADP
cusj-5634	31	10	a	a	DET
cusj-5634	31	11	given	give	VERB
cusj-5634	31	12	vector	vector	NOUN
cusj-5634	31	13	in	in	ADP
cusj-5634	31	14	the	the	DET
cusj-5634	31	15	null	null	ADJ
cusj-5634	31	16	space	space	NOUN
cusj-5634	31	17	of	of	ADP
cusj-5634	31	18	z	z	NOUN
cusj-5634	31	19	towards	towards	ADP
cusj-5634	31	20	paired	pair	VERB
cusj-5634	31	21	balance	balance	NOUN
cusj-5634	31	22	targets	target	NOUN
cusj-5634	31	23	and	and	CCONJ
cusj-5634	31	24	is	be	AUX
cusj-5634	31	25	defined	define	VERB
cusj-5634	31	26	with	with	ADP
cusj-5634	31	27	respect	respect	NOUN
cusj-5634	31	28	to	to	ADP
cusj-5634	31	29	the	the	DET
cusj-5634	31	30	solution	solution	NOUN
cusj-5634	31	31	space	space	NOUN
cusj-5634	31	32	(	(	PUNCT
cusj-5634	31	33	as	as	SCONJ
cusj-5634	31	34	expressed	express	VERB
cusj-5634	31	35	in	in	ADP
cusj-5634	31	36	the	the	DET
cusj-5634	31	37	previously	previously	ADV
cusj-5634	31	38	given	give	VERB
cusj-5634	31	39	convention	convention	NOUN
cusj-5634	31	40	)	)	PUNCT
cusj-5634	31	41	of	of	ADP
cusj-5634	31	42	a	a	DET
cusj-5634	31	43	system	system	NOUN
cusj-5634	31	44	s(z	s(z	PROPN
cusj-5634	31	45	)	)	PUNCT
cusj-5634	31	46	and	and	CCONJ
cusj-5634	31	47	given	give	VERB
cusj-5634	31	48	target	target	NOUN
cusj-5634	31	49	values	value	NOUN
cusj-5634	31	50	of	of	ADP
cusj-5634	31	51	the	the	DET
cusj-5634	31	52	balance	balance	NOUN
cusj-5634	31	53	points	point	NOUN
cusj-5634	31	54	within	within	ADP
cusj-5634	31	55	the	the	DET
cusj-5634	31	56	particular	particular	ADJ
cusj-5634	31	57	solution	solution	NOUN
cusj-5634	31	58	.	.	PUNCT
cusj-5634	32	1	2	2	NUM
cusj-5634	32	2	(	(	PUNCT
cusj-5634	32	3	11	11	NUM
cusj-5634	32	4	)	)	PUNCT
cusj-5634	32	5	for	for	ADP
cusj-5634	32	6	a	a	DET
cusj-5634	32	7	given	give	VERB
cusj-5634	32	8	set	set	VERB
cusj-5634	32	9	a	a	DET
cusj-5634	32	10	satisfying	satisfying	NOUN
cusj-5634	32	11	subset	subset	NOUN
cusj-5634	32	12	sum	sum	NOUN
cusj-5634	32	13	,	,	PUNCT
cusj-5634	32	14	there	there	PRON
cusj-5634	32	15	appears	appear	VERB
cusj-5634	32	16	to	to	PART
cusj-5634	32	17	exit	exit	VERB
cusj-5634	32	18	a	a	DET
cusj-5634	32	19	window	window	NOUN
cusj-5634	32	20	configuration	configuration	NOUN
cusj-5634	32	21	for	for	ADP
cusj-5634	32	22	which	which	PRON
cusj-5634	32	23	in	in	ADP
cusj-5634	32	24	z(a	z(a	NOUN
cusj-5634	32	25	’	'	PUNCT
cusj-5634	32	26	,	,	PUNCT
cusj-5634	32	27	t	t	PROPN
cusj-5634	32	28	,	,	PUNCT
cusj-5634	32	29	3	3	NUM
cusj-5634	32	30	,	,	PUNCT
cusj-5634	32	31	vr	vr	NOUN
cusj-5634	32	32	,	,	PUNCT
cusj-5634	32	33	4	4	NUM
cusj-5634	32	34	,	,	PUNCT
cusj-5634	32	35	vs	vs	ADP
cusj-5634	32	36	)	)	PUNCT
cusj-5634	32	37	and	and	CCONJ
cusj-5634	32	38	d(s(z	d(s(z	NOUN
cusj-5634	32	39	)	)	PUNCT
cusj-5634	32	40	,	,	PUNCT
cusj-5634	32	41	t1	t1	NOUN
cusj-5634	32	42	,	,	PUNCT
cusj-5634	32	43	t2	t2	NOUN
cusj-5634	32	44	)	)	PUNCT
cusj-5634	32	45	,	,	PUNCT
cusj-5634	32	46	t	t	PROPN
cusj-5634	32	47	,	,	PUNCT
cusj-5634	32	48	vr	vr	PROPN
cusj-5634	32	49	,	,	PUNCT
cusj-5634	32	50	vs	vs	ADP
cusj-5634	32	51	,	,	PUNCT
cusj-5634	32	52	t1	t1	NOUN
cusj-5634	32	53	,	,	PUNCT
cusj-5634	32	54	and	and	CCONJ
cusj-5634	32	55	t2	t2	NOUN
cusj-5634	32	56	apply	apply	VERB
cusj-5634	32	57	to	to	ADP
cusj-5634	32	58	an	an	DET
cusj-5634	32	59	extant	extant	ADJ
cusj-5634	32	60	s	s	NOUN
cusj-5634	32	61	,	,	PUNCT
cusj-5634	32	62	characterized	characterize	VERB
cusj-5634	32	63	by	by	ADP
cusj-5634	32	64	specific	specific	ADJ
cusj-5634	32	65	properties	property	NOUN
cusj-5634	32	66	within	within	ADP
cusj-5634	32	67	d.	d.	PROPN
cusj-5634	32	68	the	the	DET
cusj-5634	32	69	following	follow	VERB
cusj-5634	32	70	(	(	PUNCT
cusj-5634	32	71	possibly	possibly	ADV
cusj-5634	32	72	non	non	ADJ
cusj-5634	32	73	-	-	ADJ
cusj-5634	32	74	exhaustive	exhaustive	ADJ
cusj-5634	32	75	)	)	PUNCT
cusj-5634	32	76	property	property	NOUN
cusj-5634	32	77	has	have	AUX
cusj-5634	32	78	been	be	AUX
cusj-5634	32	79	determined	determine	VERB
cusj-5634	32	80	and	and	CCONJ
cusj-5634	32	81	is	be	AUX
cusj-5634	32	82	employed	employ	VERB
cusj-5634	32	83	by	by	ADP
cusj-5634	32	84	the	the	DET
cusj-5634	32	85	algorithm	algorithm	NOUN
cusj-5634	32	86	to	to	PART
cusj-5634	32	87	determine	determine	VERB
cusj-5634	32	88	m	m	NOUN
cusj-5634	32	89	’	'	PUNCT
cusj-5634	32	90	encoding	encode	VERB
cusj-5634	32	91	s	s	PRON
cusj-5634	32	92	within	within	ADP
cusj-5634	32	93	a	a	DET
cusj-5634	32	94	’	'	PUNCT
cusj-5634	32	95	:	:	PUNCT
cusj-5634	32	96	(	(	PUNCT
cusj-5634	32	97	a	a	X
cusj-5634	32	98	)	)	PUNCT
cusj-5634	32	99	if	if	SCONJ
cusj-5634	32	100	the	the	DET
cusj-5634	32	101	length	length	NOUN
cusj-5634	32	102	of	of	ADP
cusj-5634	32	103	s	s	NOUN
cusj-5634	32	104	is	be	AUX
cusj-5634	32	105	4	4	NUM
cusj-5634	32	106	,	,	PUNCT
cusj-5634	32	107	m	m	VERB
cusj-5634	32	108	’	'	PUNCT
cusj-5634	32	109	is	be	AUX
cusj-5634	32	110	the	the	DET
cusj-5634	32	111	exact	exact	ADJ
cusj-5634	32	112	solution	solution	NOUN
cusj-5634	32	113	of	of	ADP
cusj-5634	32	114	s(z	s(z	PROPN
cusj-5634	32	115	)	)	PUNCT
cusj-5634	32	116	when	when	SCONJ
cusj-5634	32	117	the	the	DET
cusj-5634	32	118	elements	element	NOUN
cusj-5634	32	119	of	of	ADP
cusj-5634	32	120	the	the	DET
cusj-5634	32	121	window	window	NOUN
cusj-5634	32	122	are	be	AUX
cusj-5634	32	123	the	the	DET
cusj-5634	32	124	elements	element	NOUN
cusj-5634	32	125	of	of	ADP
cusj-5634	32	126	s	s	NOUN
cusj-5634	32	127	and	and	CCONJ
cusj-5634	32	128	membership	membership	NOUN
cusj-5634	32	129	variables	variable	NOUN
cusj-5634	32	130	are	be	AUX
cusj-5634	32	131	set	set	VERB
cusj-5634	32	132	appropriately	appropriately	ADV
cusj-5634	32	133	.	.	PUNCT
cusj-5634	33	1	if	if	SCONJ
cusj-5634	33	2	the	the	DET
cusj-5634	33	3	length	length	NOUN
cusj-5634	33	4	of	of	ADP
cusj-5634	33	5	s	s	NOUN
cusj-5634	33	6	is	be	AUX
cusj-5634	33	7	5	5	NUM
cusj-5634	33	8	,	,	PUNCT
cusj-5634	33	9	m	m	PRON
cusj-5634	33	10	’	'	PUNCT
cusj-5634	33	11	is	be	AUX
cusj-5634	33	12	the	the	DET
cusj-5634	33	13	exact	exact	ADJ
cusj-5634	33	14	solution	solution	NOUN
cusj-5634	33	15	of	of	ADP
cusj-5634	33	16	s(z	s(z	PROPN
cusj-5634	33	17	)	)	PUNCT
cusj-5634	33	18	plus	plus	CCONJ
cusj-5634	33	19	the	the	DET
cusj-5634	33	20	vector	vector	NOUN
cusj-5634	33	21	representing	represent	VERB
cusj-5634	33	22	the	the	DET
cusj-5634	33	23	column	column	NOUN
cusj-5634	33	24	of	of	ADP
cusj-5634	33	25	d	d	PROPN
cusj-5634	33	26	for	for	ADP
cusj-5634	33	27	which	which	PRON
cusj-5634	33	28	d1,i	d1,i	PROPN
cusj-5634	33	29	and	and	CCONJ
cusj-5634	33	30	d2,i	d2,i	PROPN
cusj-5634	33	31	are	be	AUX
cusj-5634	33	32	both	both	PRON
cusj-5634	33	33	1	1	NUM
cusj-5634	33	34	when	when	SCONJ
cusj-5634	33	35	membership	membership	NOUN
cusj-5634	33	36	variables	variable	NOUN
cusj-5634	33	37	are	be	AUX
cusj-5634	33	38	set	set	VERB
cusj-5634	33	39	appropriately	appropriately	ADV
cusj-5634	33	40	.	.	PUNCT
cusj-5634	34	1	in	in	ADP
cusj-5634	34	2	all	all	DET
cusj-5634	34	3	other	other	ADJ
cusj-5634	34	4	cases	case	NOUN
cusj-5634	34	5	for	for	ADP
cusj-5634	34	6	a	a	DET
cusj-5634	34	7	set	set	NOUN
cusj-5634	34	8	a	a	PRON
cusj-5634	34	9	of	of	ADP
cusj-5634	34	10	length	length	NOUN
cusj-5634	34	11	greater	great	ADJ
cusj-5634	34	12	than	than	ADP
cusj-5634	34	13	four	four	NUM
cusj-5634	34	14	,	,	PUNCT
cusj-5634	34	15	m	m	VERB
cusj-5634	34	16	’	'	PUNCT
cusj-5634	34	17	may	may	AUX
cusj-5634	34	18	be	be	AUX
cusj-5634	34	19	formed	form	VERB
cusj-5634	34	20	by	by	ADP
cusj-5634	34	21	taking	take	VERB
cusj-5634	34	22	the	the	DET
cusj-5634	34	23	vectors	vector	NOUN
cusj-5634	34	24	represented	represent	VERB
cusj-5634	34	25	by	by	ADP
cusj-5634	34	26	each	each	DET
cusj-5634	34	27	column	column	NOUN
cusj-5634	34	28	i	i	PRON
cusj-5634	34	29	for	for	ADP
cusj-5634	34	30	which	which	PRON
cusj-5634	34	31	the	the	DET
cusj-5634	34	32	absolute	absolute	ADJ
cusj-5634	34	33	value	value	NOUN
cusj-5634	34	34	of	of	ADP
cusj-5634	34	35	d3,i	d3,i	PROPN
cusj-5634	34	36	is	be	AUX
cusj-5634	34	37	less	less	ADJ
cusj-5634	34	38	than	than	ADP
cusj-5634	34	39	one	one	NUM
cusj-5634	34	40	.	.	PUNCT
cusj-5634	35	1	justification	justification	NOUN
cusj-5634	35	2	of	of	ADP
cusj-5634	35	3	properties	property	NOUN
cusj-5634	35	4	:	:	PUNCT
cusj-5634	35	5	within	within	ADP
cusj-5634	35	6	the	the	DET
cusj-5634	35	7	parameters	parameter	NOUN
cusj-5634	35	8	of	of	ADP
cusj-5634	35	9	the	the	DET
cusj-5634	35	10	convention	convention	NOUN
cusj-5634	35	11	listed	list	VERB
cusj-5634	35	12	above	above	ADV
cusj-5634	35	13	,	,	PUNCT
cusj-5634	35	14	manual	manual	ADJ
cusj-5634	35	15	algebraic	algebraic	ADJ
cusj-5634	35	16	reduction	reduction	NOUN
cusj-5634	35	17	in	in	ADP
cusj-5634	35	18	the	the	DET
cusj-5634	35	19	general	general	ADJ
cusj-5634	35	20	case	case	NOUN
cusj-5634	35	21	yields	yield	VERB
cusj-5634	35	22	the	the	DET
cusj-5634	35	23	following	follow	VERB
cusj-5634	35	24	closed	closed	ADJ
cusj-5634	35	25	forms	form	NOUN
cusj-5634	35	26	for	for	ADP
cusj-5634	35	27	the	the	DET
cusj-5634	35	28	variables	variable	NOUN
cusj-5634	35	29	of	of	ADP
cusj-5634	35	30	the	the	DET
cusj-5634	35	31	particular	particular	ADJ
cusj-5634	35	32	solution	solution	NOUN
cusj-5634	35	33	of	of	ADP
cusj-5634	35	34	s(z	s(z	PROPN
cusj-5634	35	35	)	)	PUNCT
cusj-5634	35	36	,	,	PUNCT
cusj-5634	35	37	the	the	DET
cusj-5634	35	38	null	null	ADJ
cusj-5634	35	39	space	space	NOUN
cusj-5634	35	40	of	of	ADP
cusj-5634	35	41	s(z	s(z	PROPN
cusj-5634	35	42	)	)	PUNCT
cusj-5634	35	43	,	,	PUNCT
cusj-5634	35	44	and	and	CCONJ
cusj-5634	35	45	values	value	NOUN
cusj-5634	35	46	within	within	ADP
cusj-5634	35	47	the	the	DET
cusj-5634	35	48	directional	directional	ADJ
cusj-5634	35	49	contribution	contribution	NOUN
cusj-5634	35	50	table	table	NOUN
cusj-5634	35	51	:	:	PUNCT
cusj-5634	35	52	(	(	PUNCT
cusj-5634	35	53	(	(	PUNCT
cusj-5634	35	54	17	17	NUM
cusj-5634	35	55	)	)	PUNCT
cusj-5634	35	56	(	(	PUNCT
cusj-5634	35	57	19	19	NUM
cusj-5634	35	58	)	)	PUNCT
cusj-5634	35	59	!	!	PUNCT
cusj-5634	36	1	cusj%|%volume%9%|%spring%2015	cusj%|%volume%9%|%spring%2015	NOUN
cusj-5634	36	2	%	%	NOUN
cusj-5634	36	3	29	29	NUM
cusj-5634	36	4	%	%	NOUN
cusj-5634	36	5	1	1	NUM
cusj-5634	36	6	property	property	NOUN
cusj-5634	36	7	(	(	PUNCT
cusj-5634	36	8	a	a	X
cusj-5634	36	9	)	)	PUNCT
cusj-5634	36	10	is	be	AUX
cusj-5634	36	11	to	to	PART
cusj-5634	36	12	say	say	VERB
cusj-5634	36	13	that	that	SCONJ
cusj-5634	36	14	an	an	DET
cusj-5634	36	15	instance	instance	NOUN
cusj-5634	36	16	of	of	ADP
cusj-5634	36	17	a	a	DET
cusj-5634	36	18	subset	subset	NOUN
cusj-5634	36	19	s	s	NOUN
cusj-5634	36	20	of	of	ADP
cusj-5634	36	21	a	a	DET
cusj-5634	36	22	summing	summing	NOUN
cusj-5634	36	23	to	to	ADP
cusj-5634	36	24	c	c	PROPN
cusj-5634	36	25	exists	exist	VERB
cusj-5634	36	26	under	under	ADP
cusj-5634	36	27	the	the	DET
cusj-5634	36	28	following	follow	VERB
cusj-5634	36	29	constraints	constraint	NOUN
cusj-5634	36	30	:	:	PUNCT
cusj-5634	36	31	(	(	PUNCT
cusj-5634	36	32	1	1	X
cusj-5634	36	33	)	)	PUNCT
cusj-5634	36	34	the	the	DET
cusj-5634	36	35	length	length	NOUN
cusj-5634	36	36	of	of	ADP
cusj-5634	36	37	s	s	NOUN
cusj-5634	36	38	is	be	AUX
cusj-5634	36	39	four	four	NUM
cusj-5634	36	40	,	,	PUNCT
cusj-5634	36	41	and	and	CCONJ
cusj-5634	36	42	when	when	SCONJ
cusj-5634	36	43	the	the	DET
cusj-5634	36	44	elements	element	NOUN
cusj-5634	36	45	of	of	ADP
cusj-5634	36	46	s	s	NOUN
cusj-5634	36	47	are	be	AUX
cusj-5634	36	48	set	set	VERB
cusj-5634	36	49	as	as	ADP
cusj-5634	36	50	the	the	DET
cusj-5634	36	51	window	window	NOUN
cusj-5634	36	52	of	of	ADP
cusj-5634	36	53	a	a	PRON
cusj-5634	36	54	’	'	PUNCT
cusj-5634	36	55	,	,	PUNCT
cusj-5634	36	56	m	m	PRON
cusj-5634	36	57	’	'	PUNCT
cusj-5634	36	58	is	be	AUX
cusj-5634	36	59	found	find	VERB
cusj-5634	36	60	encoding	encode	VERB
cusj-5634	36	61	s	s	PRON
cusj-5634	36	62	within	within	ADP
cusj-5634	36	63	a.	a.	NOUN
cusj-5634	36	64	assume	assume	VERB
cusj-5634	36	65	all	all	DET
cusj-5634	36	66	members	member	NOUN
cusj-5634	36	67	of	of	ADP
cusj-5634	36	68	s	s	PRON
cusj-5634	36	69	are	be	AUX
cusj-5634	36	70	the	the	DET
cusj-5634	36	71	current	current	ADJ
cusj-5634	36	72	window	window	NOUN
cusj-5634	36	73	of	of	ADP
cusj-5634	36	74	a	a	PRON
cusj-5634	36	75	’	'	PUNCT
cusj-5634	36	76	,	,	PUNCT
cusj-5634	36	77	and	and	CCONJ
cusj-5634	36	78	set	set	VERB
cusj-5634	36	79	membership	membership	NOUN
cusj-5634	36	80	to	to	ADP
cusj-5634	36	81	t1	t1	NOUN
cusj-5634	36	82	=	=	SYM
cusj-5634	36	83	1	1	NUM
cusj-5634	36	84	,	,	PUNCT
cusj-5634	36	85	t2	t2	NOUN
cusj-5634	36	86	=	=	SYM
cusj-5634	36	87	1	1	NUM
cusj-5634	36	88	,	,	PUNCT
cusj-5634	36	89	vr	vr	NOUN
cusj-5634	36	90	=	=	SYM
cusj-5634	36	91	1	1	NUM
cusj-5634	36	92	,	,	PUNCT
cusj-5634	36	93	vs	vs	ADP
cusj-5634	36	94	=	=	NOUN
cusj-5634	36	95	1	1	NUM
cusj-5634	36	96	.	.	PUNCT
cusj-5634	37	1	thus	thus	ADV
cusj-5634	37	2	,	,	PUNCT
cusj-5634	37	3	the	the	DET
cusj-5634	37	4	particular	particular	ADJ
cusj-5634	37	5	solution	solution	NOUN
cusj-5634	37	6	of	of	ADP
cusj-5634	37	7	s(z	s(z	PROPN
cusj-5634	37	8	)	)	PUNCT
cusj-5634	37	9	for	for	ADP
cusj-5634	37	10	this	this	DET
cusj-5634	37	11	configuration	configuration	NOUN
cusj-5634	37	12	is	be	AUX
cusj-5634	37	13	encoding	encode	VERB
cusj-5634	37	14	s	s	PRON
cusj-5634	37	15	and	and	CCONJ
cusj-5634	37	16	showing	show	VERB
cusj-5634	37	17	(	(	PUNCT
cusj-5634	37	18	1	1	NUM
cusj-5634	37	19	)	)	PUNCT
cusj-5634	37	20	to	to	PART
cusj-5634	37	21	be	be	AUX
cusj-5634	37	22	true	true	ADJ
cusj-5634	37	23	.	.	PUNCT
cusj-5634	38	1	the	the	DET
cusj-5634	38	2	above	above	ADJ
cusj-5634	38	3	also	also	ADV
cusj-5634	38	4	extends	extend	VERB
cusj-5634	38	5	to	to	PART
cusj-5634	38	6	show	show	VERB
cusj-5634	38	7	that	that	SCONJ
cusj-5634	38	8	(	(	PUNCT
cusj-5634	38	9	1	1	X
cusj-5634	38	10	)	)	PUNCT
cusj-5634	38	11	is	be	AUX
cusj-5634	38	12	true	true	ADJ
cusj-5634	38	13	for	for	ADP
cusj-5634	38	14	any	any	DET
cusj-5634	38	15	instance	instance	NOUN
cusj-5634	38	16	of	of	ADP
cusj-5634	38	17	s	s	AUX
cusj-5634	38	18	having	have	VERB
cusj-5634	38	19	length	length	NOUN
cusj-5634	38	20	less	less	ADJ
cusj-5634	38	21	than	than	ADP
cusj-5634	38	22	four	four	NUM
cusj-5634	38	23	for	for	ADP
cusj-5634	38	24	which	which	PRON
cusj-5634	38	25	all	all	DET
cusj-5634	38	26	elements	element	NOUN
cusj-5634	38	27	of	of	ADP
cusj-5634	38	28	s	s	NOUN
cusj-5634	38	29	are	be	AUX
cusj-5634	38	30	within	within	ADP
cusj-5634	38	31	the	the	DET
cusj-5634	38	32	window	window	NOUN
cusj-5634	38	33	of	of	ADP
cusj-5634	38	34	a	a	PRON
cusj-5634	38	35	’	'	PUNCT
cusj-5634	38	36	and	and	CCONJ
cusj-5634	38	37	membership	membership	NOUN
cusj-5634	38	38	is	be	AUX
cusj-5634	38	39	set	set	VERB
cusj-5634	38	40	appropriately	appropriately	ADV
cusj-5634	38	41	.	.	PUNCT
cusj-5634	39	1	the	the	DET
cusj-5634	39	2	length	length	NOUN
cusj-5634	39	3	of	of	ADP
cusj-5634	39	4	s	s	NOUN
cusj-5634	39	5	is	be	AUX
cusj-5634	39	6	5	5	NUM
cusj-5634	39	7	,	,	PUNCT
cusj-5634	39	8	and	and	CCONJ
cusj-5634	39	9	when	when	SCONJ
cusj-5634	39	10	all	all	DET
cusj-5634	39	11	but	but	SCONJ
cusj-5634	39	12	one	one	NUM
cusj-5634	39	13	element	element	NOUN
cusj-5634	39	14	of	of	ADP
cusj-5634	39	15	s	s	PROPN
cusj-5634	39	16	is	be	AUX
cusj-5634	39	17	set	set	VERB
cusj-5634	39	18	as	as	ADP
cusj-5634	39	19	the	the	DET
cusj-5634	39	20	window	window	NOUN
cusj-5634	39	21	of	of	ADP
cusj-5634	39	22	a	a	PRON
cusj-5634	39	23	’	'	PUNCT
cusj-5634	39	24	,	,	PUNCT
cusj-5634	39	25	m	m	NOUN
cusj-5634	39	26	’	'	PUNCT
cusj-5634	39	27	encoding	encode	VERB
cusj-5634	39	28	s	s	PRON
cusj-5634	39	29	within	within	ADP
cusj-5634	39	30	a	a	PRON
cusj-5634	39	31	’	'	PUNCT
cusj-5634	39	32	is	be	AUX
cusj-5634	39	33	found	find	VERB
cusj-5634	39	34	by	by	ADP
cusj-5634	39	35	adding	add	VERB
cusj-5634	39	36	to	to	ADP
cusj-5634	39	37	the	the	DET
cusj-5634	39	38	particular	particular	ADJ
cusj-5634	39	39	solution	solution	NOUN
cusj-5634	39	40	the	the	DET
cusj-5634	39	41	vector	vector	NOUN
cusj-5634	39	42	of	of	ADP
cusj-5634	39	43	the	the	DET
cusj-5634	39	44	null	null	ADJ
cusj-5634	39	45	space	space	NOUN
cusj-5634	39	46	corresponding	correspond	VERB
cusj-5634	39	47	to	to	ADP
cusj-5634	39	48	d1,r	d1,r	PROPN
cusj-5634	39	49	=	=	SYM
cusj-5634	39	50	d2,r	d2,r	PROPN
cusj-5634	39	51	=	=	SYM
cusj-5634	39	52	1	1	X
cusj-5634	39	53	.	.	X
cusj-5634	39	54	assume	assume	VERB
cusj-5634	39	55	four	four	NUM
cusj-5634	39	56	members	member	NOUN
cusj-5634	39	57	of	of	ADP
cusj-5634	39	58	s	s	NOUN
cusj-5634	39	59	are	be	AUX
cusj-5634	39	60	the	the	DET
cusj-5634	39	61	current	current	ADJ
cusj-5634	39	62	window	window	NOUN
cusj-5634	39	63	of	of	ADP
cusj-5634	39	64	a	a	PRON
cusj-5634	39	65	’	'	PUNCT
cusj-5634	39	66	,	,	PUNCT
cusj-5634	39	67	and	and	CCONJ
cusj-5634	39	68	set	set	VERB
cusj-5634	39	69	membership	membership	NOUN
cusj-5634	39	70	to	to	ADP
cusj-5634	39	71	t1	t1	NOUN
cusj-5634	39	72	=	=	SYM
cusj-5634	39	73	1	1	NUM
cusj-5634	39	74	,	,	PUNCT
cusj-5634	39	75	t2	t2	NOUN
cusj-5634	39	76	=	=	SYM
cusj-5634	39	77	1	1	NUM
cusj-5634	39	78	,	,	PUNCT
cusj-5634	39	79	vr	vr	NOUN
cusj-5634	39	80	=	=	SYM
cusj-5634	39	81	1	1	NUM
cusj-5634	39	82	,	,	PUNCT
cusj-5634	39	83	vs	vs	ADP
cusj-5634	39	84	=	=	NOUN
cusj-5634	39	85	1	1	NUM
cusj-5634	39	86	.	.	NOUN
cusj-5634	39	87	2	2	NUM
cusj-5634	39	88	solving	solving	NOUN
cusj-5634	39	89	for	for	ADP
cusj-5634	39	90	the	the	DET
cusj-5634	39	91	values	value	NOUN
cusj-5634	39	92	in	in	ADP
cusj-5634	39	93	the	the	DET
cusj-5634	39	94	directional	directional	ADJ
cusj-5634	39	95	contribution	contribution	NOUN
cusj-5634	39	96	table	table	NOUN
cusj-5634	39	97	:	:	PUNCT
cusj-5634	39	98	showing	show	VERB
cusj-5634	39	99	(	(	PUNCT
cusj-5634	39	100	2	2	NUM
cusj-5634	39	101	)	)	PUNCT
cusj-5634	39	102	to	to	PART
cusj-5634	39	103	be	be	AUX
cusj-5634	39	104	true	true	ADJ
cusj-5634	39	105	.	.	PUNCT
cusj-5634	40	1	the	the	DET
cusj-5634	40	2	above	above	ADJ
cusj-5634	40	3	may	may	AUX
cusj-5634	40	4	also	also	ADV
cusj-5634	40	5	be	be	AUX
cusj-5634	40	6	generalized	generalize	VERB
cusj-5634	40	7	for	for	ADP
cusj-5634	40	8	any	any	PRON
cusj-5634	40	9	s	s	AUX
cusj-5634	40	10	having	have	VERB
cusj-5634	40	11	length	length	NOUN
cusj-5634	40	12	less	less	ADJ
cusj-5634	40	13	than	than	ADP
cusj-5634	40	14	or	or	CCONJ
cusj-5634	40	15	equal	equal	ADJ
cusj-5634	40	16	to	to	ADP
cusj-5634	40	17	five	five	NUM
cusj-5634	40	18	for	for	SCONJ
cusj-5634	40	19	which	which	PRON
cusj-5634	40	20	all	all	PRON
cusj-5634	40	21	but	but	SCONJ
cusj-5634	40	22	one	one	NUM
cusj-5634	40	23	element	element	NOUN
cusj-5634	40	24	of	of	ADP
cusj-5634	40	25	the	the	DET
cusj-5634	40	26	subset	subset	NOUN
cusj-5634	40	27	exists	exist	VERB
cusj-5634	40	28	within	within	ADP
cusj-5634	40	29	the	the	DET
cusj-5634	40	30	window	window	NOUN
cusj-5634	40	31	and	and	CCONJ
cusj-5634	40	32	membership	membership	NOUN
cusj-5634	40	33	is	be	AUX
cusj-5634	40	34	set	set	VERB
cusj-5634	40	35	appropriately	appropriately	ADV
cusj-5634	40	36	.	.	PUNCT
cusj-5634	41	1	(	(	PUNCT
cusj-5634	41	2	3	3	X
cusj-5634	41	3	)	)	PUNCT
cusj-5634	41	4	in	in	ADP
cusj-5634	41	5	all	all	DET
cusj-5634	41	6	other	other	ADJ
cusj-5634	41	7	cases	case	NOUN
cusj-5634	41	8	,	,	PUNCT
cusj-5634	41	9	s	s	VERB
cusj-5634	41	10	of	of	ADP
cusj-5634	41	11	length	length	NOUN
cusj-5634	41	12	t	t	PROPN
cusj-5634	42	1	>	>	X
cusj-5634	42	2	5	5	NUM
cusj-5634	42	3	of	of	ADP
cusj-5634	42	4	a	a	DET
cusj-5634	42	5	exists	exist	NOUN
cusj-5634	42	6	if	if	SCONJ
cusj-5634	42	7	and	and	CCONJ
cusj-5634	42	8	only	only	ADV
cusj-5634	42	9	if	if	SCONJ
cusj-5634	42	10	there	there	PRON
cusj-5634	42	11	exists	exist	VERB
cusj-5634	42	12	a	a	DET
cusj-5634	42	13	window	window	NOUN
cusj-5634	42	14	configuration	configuration	NOUN
cusj-5634	42	15	and	and	CCONJ
cusj-5634	42	16	membership	membership	NOUN
cusj-5634	42	17	assignment	assignment	NOUN
cusj-5634	42	18	t1	t1	PROPN
cusj-5634	42	19	,	,	PUNCT
cusj-5634	42	20	t2	t2	NOUN
cusj-5634	42	21	,	,	PUNCT
cusj-5634	42	22	vr	vr	NOUN
cusj-5634	42	23	,	,	PUNCT
cusj-5634	42	24	vs	vs	ADP
cusj-5634	42	25	such	such	ADJ
cusj-5634	42	26	that	that	SCONJ
cusj-5634	42	27	there	there	PRON
cusj-5634	42	28	exists	exist	VERB
cusj-5634	42	29	a	a	DET
cusj-5634	42	30	set	set	NOUN
cusj-5634	42	31	i	i	PRON
cusj-5634	42	32	,	,	PUNCT
cusj-5634	42	33	length	length	NOUN
cusj-5634	42	34	t	t	PROPN
cusj-5634	42	35	’	'	PUNCT
cusj-5634	42	36	=	=	SYM
cusj-5634	42	37	t	t	PROPN
cusj-5634	42	38	t1	t1	NOUN
cusj-5634	42	39	t2	t2	PROPN
cusj-5634	42	40	vr	vr	PROPN
cusj-5634	42	41	vs	vs	ADP
cusj-5634	42	42	satisfying	satisfy	VERB
cusj-5634	42	43	d3,ij	d3,ij	PROPN
cusj-5634	42	44	<	<	X
cusj-5634	42	45	1	1	NUM
cusj-5634	42	46	and	and	CCONJ
cusj-5634	42	47	σd1,ij=	σd1,ij=	X
cusj-5634	42	48	σd2,ij	σd2,ij	NOUN
cusj-5634	42	49	=	=	SYM
cusj-5634	42	50	1	1	NUM
cusj-5634	42	51	for	for	ADP
cusj-5634	42	52	all	all	DET
cusj-5634	42	53	j	j	PROPN
cusj-5634	42	54	in	in	ADP
cusj-5634	42	55	the	the	DET
cusj-5634	42	56	range	range	NOUN
cusj-5634	42	57	of	of	ADP
cusj-5634	42	58	the	the	DET
cusj-5634	42	59	length	length	NOUN
cusj-5634	42	60	of	of	ADP
cusj-5634	42	61	i.	i.	PROPN
cusj-5634	42	62	suppose	suppose	VERB
cusj-5634	42	63	that	that	SCONJ
cusj-5634	42	64	such	such	DET
cusj-5634	42	65	a	a	DET
cusj-5634	42	66	window	window	NOUN
cusj-5634	42	67	exists	exist	VERB
cusj-5634	42	68	.	.	PUNCT
cusj-5634	43	1	it	it	PRON
cusj-5634	43	2	is	be	AUX
cusj-5634	43	3	given	give	VERB
cusj-5634	43	4	that	that	PRON
cusj-5634	43	5	and	and	CCONJ
cusj-5634	43	6	using	use	VERB
cusj-5634	43	7	the	the	DET
cusj-5634	43	8	closed	closed	ADJ
cusj-5634	43	9	forms	form	NOUN
cusj-5634	43	10	derived	derive	VERB
cusj-5634	43	11	earlier	early	ADV
cusj-5634	43	12	in	in	ADP
cusj-5634	43	13	this	this	DET
cusj-5634	43	14	section	section	NOUN
cusj-5634	43	15	:	:	PUNCT
cusj-5634	43	16	!	!	PUNCT
cusj-5634	44	1	cusj%|%volume%9%|%spring%2015	cusj%|%volume%9%|%spring%2015	NOUN
cusj-5634	44	2	%	%	NOUN
cusj-5634	44	3	30	30	NUM
cusj-5634	44	4	%	%	NOUN
cusj-5634	44	5	1	1	NUM
cusj-5634	44	6	repeating	repeat	VERB
cusj-5634	44	7	the	the	DET
cusj-5634	44	8	same	same	ADJ
cusj-5634	44	9	process	process	NOUN
cusj-5634	44	10	as	as	SCONJ
cusj-5634	44	11	was	be	AUX
cusj-5634	44	12	used	use	VERB
cusj-5634	44	13	in	in	ADP
cusj-5634	44	14	the	the	DET
cusj-5634	44	15	justification	justification	NOUN
cusj-5634	44	16	of	of	ADP
cusj-5634	44	17	(	(	PUNCT
cusj-5634	44	18	1	1	NUM
cusj-5634	44	19	)	)	PUNCT
cusj-5634	44	20	,	,	PUNCT
cusj-5634	44	21	m	m	PRON
cusj-5634	44	22	’	'	PUNCT
cusj-5634	44	23	is	be	AUX
cusj-5634	44	24	derived	derive	VERB
cusj-5634	44	25	encoding	encode	VERB
cusj-5634	44	26	s	s	PRON
cusj-5634	44	27	within	within	ADP
cusj-5634	44	28	a	a	PRON
cusj-5634	44	29	’	'	PUNCT
cusj-5634	44	30	:	:	PUNCT
cusj-5634	44	31	thus	thus	ADV
cusj-5634	44	32	,	,	PUNCT
cusj-5634	44	33	if	if	SCONJ
cusj-5634	44	34	such	such	DET
cusj-5634	44	35	a	a	DET
cusj-5634	44	36	window	window	NOUN
cusj-5634	44	37	exists	exist	VERB
cusj-5634	44	38	,	,	PUNCT
cusj-5634	44	39	a	a	DET
cusj-5634	44	40	s	s	NOUN
cusj-5634	44	41	of	of	ADP
cusj-5634	44	42	a	a	PRON
cusj-5634	44	43	’	'	PUNCT
cusj-5634	44	44	of	of	ADP
cusj-5634	44	45	length	length	NOUN
cusj-5634	44	46	t	t	PROPN
cusj-5634	44	47	exists	exist	VERB
cusj-5634	44	48	and	and	CCONJ
cusj-5634	44	49	is	be	AUX
cusj-5634	44	50	encoded	encode	VERB
cusj-5634	44	51	by	by	ADP
cusj-5634	44	52	the	the	DET
cusj-5634	44	53	derivable	derivable	ADJ
cusj-5634	44	54	m	m	NOUN
cusj-5634	44	55	’	'	PUNCT
cusj-5634	44	56	.	.	PUNCT
cusj-5634	45	1	suppose	suppose	VERB
cusj-5634	45	2	s	s	PRON
cusj-5634	45	3	of	of	ADP
cusj-5634	45	4	length	length	NOUN
cusj-5634	45	5	t	t	PROPN
cusj-5634	45	6	of	of	ADP
cusj-5634	45	7	a	a	DET
cusj-5634	45	8	’	'	PUNCT
cusj-5634	45	9	exists	exist	NOUN
cusj-5634	45	10	.	.	PUNCT
cusj-5634	46	1	let	let	VERB
cusj-5634	46	2	call	call	VERB
cusj-5634	46	3	window	window	NOUN
cusj-5634	47	1	w	w	NOUN
cusj-5634	47	2	=	=	PRON
cusj-5634	47	3	{	{	PUNCT
cusj-5634	47	4	a’1	a’1	ADJ
cusj-5634	47	5	,	,	PUNCT
cusj-5634	47	6	a’2	a’2	ADV
cusj-5634	47	7	,	,	PUNCT
cusj-5634	47	8	a’3	a’3	NOUN
cusj-5634	47	9	,	,	PUNCT
cusj-5634	47	10	a’4	a’4	ADV
cusj-5634	47	11	}	}	PUNCT
cusj-5634	47	12	and	and	CCONJ
cusj-5634	47	13	define	define	VERB
cusj-5634	47	14	membership	membership	NOUN
cusj-5634	47	15	of	of	ADP
cusj-5634	47	16	the	the	DET
cusj-5634	47	17	window	window	NOUN
cusj-5634	47	18	as	as	SCONJ
cusj-5634	47	19	follows	follow	VERB
cusj-5634	47	20	:	:	PUNCT
cusj-5634	47	21	under	under	ADP
cusj-5634	47	22	this	this	DET
cusj-5634	47	23	membership	membership	NOUN
cusj-5634	47	24	assignment	assignment	NOUN
cusj-5634	47	25	,	,	PUNCT
cusj-5634	47	26	2	2	NUM
cusj-5634	47	27	likewise	likewise	ADV
cusj-5634	47	28	,	,	PUNCT
cusj-5634	47	29	thus	thus	ADV
cusj-5634	47	30	,	,	PUNCT
cusj-5634	47	31	if	if	SCONJ
cusj-5634	47	32	s	s	VERB
cusj-5634	47	33	of	of	ADP
cusj-5634	47	34	a	a	DET
cusj-5634	47	35	exists	exist	NOUN
cusj-5634	47	36	,	,	PUNCT
cusj-5634	47	37	σd2	σd2	X
cusj-5634	47	38	,	,	PUNCT
cusj-5634	47	39	ij	ij	NOUN
cusj-5634	47	40	=	=	PUNCT
cusj-5634	47	41	σd1,ij	σd1,ij	PROPN
cusj-5634	48	1	=	=	PROPN
cusj-5634	48	2	1	1	X
cusj-5634	48	3	.	.	PUNCT
cusj-5634	48	4	by	by	ADP
cusj-5634	48	5	(	(	PUNCT
cusj-5634	48	6	3	3	NUM
cusj-5634	48	7	)	)	PUNCT
cusj-5634	48	8	,	,	PUNCT
cusj-5634	48	9	all	all	DET
cusj-5634	48	10	d3,ij	d3,ij	PROPN
cusj-5634	48	11	for	for	ADP
cusj-5634	48	12	the	the	DET
cusj-5634	48	13	window	window	NOUN
cusj-5634	48	14	must	must	AUX
cusj-5634	48	15	satisfy	satisfy	VERB
cusj-5634	48	16	expanding	expand	VERB
cusj-5634	48	17	the	the	DET
cusj-5634	48	18	variables	variable	NOUN
cusj-5634	48	19	and	and	CCONJ
cusj-5634	48	20	simplifying	simplify	VERB
cusj-5634	48	21	,	,	PUNCT
cusj-5634	48	22	for	for	ADP
cusj-5634	48	23	δ1δ2	δ1δ2	PROPN
cusj-5634	48	24	>	>	SYM
cusj-5634	48	25	0	0	NUM
cusj-5634	48	26	,	,	PUNCT
cusj-5634	48	27	and	and	CCONJ
cusj-5634	48	28	for	for	ADP
cusj-5634	48	29	δ1δ2	δ1δ2	X
cusj-5634	48	30	<	<	X
cusj-5634	48	31	0	0	NUM
cusj-5634	48	32	,	,	PUNCT
cusj-5634	48	33	it	it	PRON
cusj-5634	48	34	can	can	AUX
cusj-5634	48	35	be	be	AUX
cusj-5634	48	36	shown	show	VERB
cusj-5634	48	37	that	that	SCONJ
cusj-5634	48	38	the	the	DET
cusj-5634	48	39	above	above	ADJ
cusj-5634	48	40	is	be	AUX
cusj-5634	48	41	satisfied	satisfied	ADJ
cusj-5634	48	42	for	for	ADP
cusj-5634	48	43	some	some	DET
cusj-5634	48	44	window	window	NOUN
cusj-5634	48	45	configuration	configuration	NOUN
cusj-5634	48	46	by	by	ADP
cusj-5634	48	47	showing	show	VERB
cusj-5634	48	48	that	that	SCONJ
cusj-5634	48	49	a	a	DET
cusj-5634	48	50	tighter	tight	ADJ
cusj-5634	48	51	contained	contain	VERB
cusj-5634	48	52	constraint	constraint	NOUN
cusj-5634	48	53	is	be	AUX
cusj-5634	48	54	also	also	ADV
cusj-5634	48	55	satisfied	satisfied	ADJ
cusj-5634	48	56	for	for	ADP
cusj-5634	48	57	some	some	DET
cusj-5634	48	58	window	window	NOUN
cusj-5634	48	59	:	:	PUNCT
cusj-5634	48	60	summing	sum	VERB
cusj-5634	48	61	the	the	DET
cusj-5634	48	62	d3,ij	d3,ij	PROPN
cusj-5634	48	63	,	,	PUNCT
cusj-5634	48	64	!	!	PUNCT
cusj-5634	49	1	cusj%|%volume%9%|%spring%2015	cusj%|%volume%9%|%spring%2015	NOUN
cusj-5634	49	2	%	%	NOUN
cusj-5634	49	3	31	31	NUM
cusj-5634	49	4	%	%	NOUN
cusj-5634	49	5	1	1	NUM
cusj-5634	49	6	the	the	DET
cusj-5634	49	7	numerator	numerator	NOUN
cusj-5634	49	8	and	and	CCONJ
cusj-5634	49	9	denominator	denominator	NOUN
cusj-5634	49	10	of	of	ADP
cusj-5634	49	11	this	this	DET
cusj-5634	49	12	expression	expression	NOUN
cusj-5634	49	13	are	be	AUX
cusj-5634	49	14	both	both	ADV
cusj-5634	49	15	polynomial	polynomial	ADJ
cusj-5634	49	16	with	with	ADP
cusj-5634	49	17	respect	respect	NOUN
cusj-5634	49	18	to	to	ADP
cusj-5634	49	19	t	t	PROPN
cusj-5634	49	20	’	'	PUNCT
cusj-5634	49	21	(	(	PUNCT
cusj-5634	49	22	the	the	DET
cusj-5634	49	23	numerator	numerator	NOUN
cusj-5634	49	24	is	be	AUX
cusj-5634	49	25	of	of	ADP
cusj-5634	49	26	degree	degree	NOUN
cusj-5634	49	27	1	1	NUM
cusj-5634	49	28	,	,	PUNCT
cusj-5634	49	29	and	and	CCONJ
cusj-5634	49	30	the	the	DET
cusj-5634	49	31	denominator	denominator	NOUN
cusj-5634	49	32	of	of	ADP
cusj-5634	49	33	degree	degree	NOUN
cusj-5634	49	34	2	2	NUM
cusj-5634	49	35	)	)	PUNCT
cusj-5634	49	36	;	;	PUNCT
cusj-5634	49	37	given	give	VERB
cusj-5634	49	38	that	that	DET
cusj-5634	49	39	t	t	NOUN
cusj-5634	49	40	’	'	PUNCT
cusj-5634	49	41	>	>	PROPN
cusj-5634	49	42	1	1	NUM
cusj-5634	49	43	,	,	PUNCT
cusj-5634	49	44	all	all	DET
cusj-5634	49	45	coefficients	coefficient	NOUN
cusj-5634	49	46	of	of	ADP
cusj-5634	49	47	t	t	NOUN
cusj-5634	49	48	’	'	PUNCT
cusj-5634	49	49	in	in	ADP
cusj-5634	49	50	the	the	DET
cusj-5634	49	51	numerator	numerator	NOUN
cusj-5634	49	52	appear	appear	VERB
cusj-5634	49	53	as	as	ADP
cusj-5634	49	54	a	a	DET
cusj-5634	49	55	product	product	NOUN
cusj-5634	49	56	in	in	ADP
cusj-5634	49	57	the	the	DET
cusj-5634	49	58	denominator	denominator	NOUN
cusj-5634	49	59	,	,	PUNCT
cusj-5634	49	60	and	and	CCONJ
cusj-5634	49	61	all	all	DET
cusj-5634	49	62	non	non	ADJ
cusj-5634	49	63	-	-	ADJ
cusj-5634	49	64	t	t	ADJ
cusj-5634	49	65	’	'	PUNCT
cusj-5634	49	66	constants	constant	NOUN
cusj-5634	49	67	in	in	ADP
cusj-5634	49	68	the	the	DET
cusj-5634	49	69	numerator	numerator	NOUN
cusj-5634	49	70	appear	appear	VERB
cusj-5634	49	71	in	in	ADP
cusj-5634	49	72	the	the	DET
cusj-5634	49	73	denominator	denominator	NOUN
cusj-5634	49	74	,	,	PUNCT
cusj-5634	49	75	the	the	DET
cusj-5634	49	76	result	result	NOUN
cusj-5634	49	77	is	be	AUX
cusj-5634	49	78	bounded	bound	VERB
cusj-5634	49	79	by	by	ADP
cusj-5634	49	80	(	(	PUNCT
cusj-5634	49	81	-t	-t	NOUN
cusj-5634	49	82	’	'	PUNCT
cusj-5634	49	83	,	,	PUNCT
cusj-5634	49	84	t	t	PROPN
cusj-5634	49	85	’	'	PUNCT
cusj-5634	49	86	)	)	PUNCT
cusj-5634	49	87	.	.	PUNCT
cusj-5634	50	1	given	give	VERB
cusj-5634	50	2	that	that	SCONJ
cusj-5634	50	3	the	the	DET
cusj-5634	50	4	above	above	ADJ
cusj-5634	50	5	is	be	AUX
cusj-5634	50	6	bounded	bound	VERB
cusj-5634	50	7	,	,	PUNCT
cusj-5634	50	8	viewing	view	VERB
cusj-5634	50	9	the	the	DET
cusj-5634	50	10	second	second	ADJ
cusj-5634	50	11	constraint	constraint	NOUN
cusj-5634	50	12	,	,	PUNCT
cusj-5634	50	13	assert	assert	VERB
cusj-5634	50	14	that	that	SCONJ
cusj-5634	50	15	thus	thus	ADV
cusj-5634	50	16	meaning	mean	VERB
cusj-5634	50	17	noting	note	VERB
cusj-5634	50	18	that	that	SCONJ
cusj-5634	50	19	it	it	PRON
cusj-5634	50	20	can	can	AUX
cusj-5634	50	21	be	be	AUX
cusj-5634	50	22	seen	see	VERB
cusj-5634	50	23	that	that	SCONJ
cusj-5634	50	24	a	a	DET
cusj-5634	50	25	window	window	NOUN
cusj-5634	50	26	configuration	configuration	NOUN
cusj-5634	50	27	composed	compose	VERB
cusj-5634	50	28	of	of	ADP
cusj-5634	50	29	the	the	DET
cusj-5634	50	30	minima	minima	NOUN
cusj-5634	50	31	and/or	and/or	CCONJ
cusj-5634	50	32	maxima	maxima	PROPN
cusj-5634	50	33	(	(	PUNCT
cusj-5634	50	34	and/or	and/or	CCONJ
cusj-5634	50	35	points	point	VERB
cusj-5634	50	36	whose	whose	DET
cusj-5634	50	37	values	value	NOUN
cusj-5634	50	38	are	be	AUX
cusj-5634	50	39	set	set	VERB
cusj-5634	50	40	according	accord	VERB
cusj-5634	50	41	to	to	ADP
cusj-5634	50	42	these	these	PRON
cusj-5634	50	43	)	)	PUNCT
cusj-5634	50	44	with	with	ADP
cusj-5634	50	45	membership	membership	NOUN
cusj-5634	50	46	appropriately	appropriately	ADV
cusj-5634	50	47	set	set	VERB
cusj-5634	50	48	of	of	ADP
cusj-5634	50	49	si	si	X
cusj-5634	50	50	can	can	AUX
cusj-5634	50	51	be	be	AUX
cusj-5634	50	52	made	make	VERB
cusj-5634	50	53	among	among	ADP
cusj-5634	50	54	the	the	DET
cusj-5634	50	55	set	set	NOUN
cusj-5634	50	56	(	(	PUNCT
cusj-5634	50	57	or	or	CCONJ
cusj-5634	50	58	possibly	possibly	ADV
cusj-5634	50	59	created	create	VERB
cusj-5634	50	60	)	)	PUNCT
cusj-5634	50	61	to	to	PART
cusj-5634	50	62	satisfy	satisfy	VERB
cusj-5634	50	63	both	both	DET
cusj-5634	50	64	these	these	PRON
cusj-5634	50	65	(	(	PUNCT
cusj-5634	50	66	and	and	CCONJ
cusj-5634	50	67	thus	thus	ADV
cusj-5634	50	68	the	the	DET
cusj-5634	50	69	primary	primary	ADJ
cusj-5634	50	70	)	)	PUNCT
cusj-5634	50	71	constraints	constraint	NOUN
cusj-5634	50	72	.	.	PUNCT
cusj-5634	51	1	additionally	additionally	ADV
cusj-5634	51	2	,	,	PUNCT
cusj-5634	51	3	note	note	VERB
cusj-5634	51	4	that	that	SCONJ
cusj-5634	51	5	if	if	SCONJ
cusj-5634	51	6	an	an	DET
cusj-5634	51	7	initial	initial	ADJ
cusj-5634	51	8	ordering	ordering	NOUN
cusj-5634	51	9	of	of	ADP
cusj-5634	51	10	the	the	DET
cusj-5634	51	11	set	set	NOUN
cusj-5634	51	12	is	be	AUX
cusj-5634	51	13	enforced	enforce	VERB
cusj-5634	51	14	in	in	ADP
cusj-5634	51	15	which	which	PRON
cusj-5634	51	16	the	the	DET
cusj-5634	51	17	set	set	NOUN
cusj-5634	51	18	is	be	AUX
cusj-5634	51	19	ordered	order	VERB
cusj-5634	51	20	by	by	ADP
cusj-5634	51	21	the	the	DET
cusj-5634	51	22	absolute	absolute	ADJ
cusj-5634	51	23	value	value	NOUN
cusj-5634	51	24	of	of	ADP
cusj-5634	51	25	its	its	PRON
cusj-5634	51	26	elements	element	NOUN
cusj-5634	51	27	(	(	PUNCT
cusj-5634	51	28	increasing	increase	VERB
cusj-5634	51	29	or	or	CCONJ
cusj-5634	51	30	decreasing	decrease	VERB
cusj-5634	51	31	)	)	PUNCT
cusj-5634	51	32	,	,	PUNCT
cusj-5634	51	33	enumerating	enumerate	VERB
cusj-5634	51	34	and	and	CCONJ
cusj-5634	51	35	swapping	swap	VERB
cusj-5634	51	36	all	all	DET
cusj-5634	51	37	possible	possible	ADJ
cusj-5634	51	38	windows	window	NOUN
cusj-5634	51	39	of	of	ADP
cusj-5634	51	40	a	a	PRON
cusj-5634	51	41	in	in	ADP
cusj-5634	51	42	a	a	DET
cusj-5634	51	43	pair	pair	NOUN
cusj-5634	51	44	-	-	PUNCT
cusj-5634	51	45	wise	wise	ADJ
cusj-5634	51	46	order	order	NOUN
cusj-5634	51	47	(	(	PUNCT
cusj-5634	51	48	1	1	NUM
cusj-5634	51	49	with	with	ADP
cusj-5634	51	50	2	2	NUM
cusj-5634	51	51	,	,	PUNCT
cusj-5634	51	52	1	1	NUM
cusj-5634	51	53	with	with	ADP
cusj-5634	51	54	3	3	NUM
cusj-5634	51	55	,	,	PUNCT
cusj-5634	51	56	.	.	PUNCT
cusj-5634	51	57	.	.	PUNCT
cusj-5634	52	1	.	.	PUNCT
cusj-5634	53	1	,	,	PUNCT
cusj-5634	53	2	2	2	NUM
cusj-5634	53	3	with	with	ADP
cusj-5634	53	4	3	3	NUM
cusj-5634	53	5	;	;	PUNCT
cusj-5634	53	6	followed	follow	VERB
cusj-5634	53	7	by	by	ADP
cusj-5634	53	8	pair	pair	NOUN
cusj-5634	53	9	1	1	NUM
cusj-5634	53	10	with	with	ADP
cusj-5634	53	11	pair	pair	NOUN
cusj-5634	53	12	2	2	NUM
cusj-5634	53	13	..	..	PUNCT
cusj-5634	53	14	.	.	PUNCT
cusj-5634	53	15	.	.	PUNCT
cusj-5634	54	1	pair	pair	NOUN
cusj-5634	54	2	2	2	NUM
cusj-5634	54	3	with	with	ADP
cusj-5634	54	4	pair	pair	NOUN
cusj-5634	54	5	3	3	NUM
cusj-5634	54	6	)	)	PUNCT
cusj-5634	54	7	creates	create	VERB
cusj-5634	54	8	such	such	DET
cusj-5634	54	9	a	a	DET
cusj-5634	54	10	set	set	NOUN
cusj-5634	54	11	ordering	ordering	NOUN
cusj-5634	54	12	for	for	ADP
cusj-5634	54	13	which	which	PRON
cusj-5634	54	14	a	a	DET
cusj-5634	54	15	window	window	NOUN
cusj-5634	54	16	may	may	AUX
cusj-5634	54	17	satisfy	satisfy	VERB
cusj-5634	54	18	in	in	ADP
cusj-5634	54	19	the	the	DET
cusj-5634	54	20	same	same	ADJ
cusj-5634	54	21	window	window	NOUN
cusj-5634	54	22	assignment	assignment	NOUN
cusj-5634	54	23	as	as	ADP
cusj-5634	54	24	the	the	DET
cusj-5634	54	25	previous	previous	ADJ
cusj-5634	54	26	constraint	constraint	NOUN
cusj-5634	54	27	.	.	PUNCT
cusj-5634	55	1	this	this	DET
cusj-5634	55	2	shows	show	NOUN
cusj-5634	55	3	,	,	PUNCT
cusj-5634	55	4	then	then	ADV
cusj-5634	55	5	,	,	PUNCT
cusj-5634	55	6	that	that	SCONJ
cusj-5634	55	7	if	if	SCONJ
cusj-5634	55	8	s	s	VERB
cusj-5634	55	9	of	of	ADP
cusj-5634	55	10	length	length	NOUN
cusj-5634	55	11	t	t	PROPN
cusj-5634	55	12	of	of	ADP
cusj-5634	55	13	a	a	DET
cusj-5634	55	14	exists	exist	NOUN
cusj-5634	55	15	,	,	PUNCT
cusj-5634	55	16	there	there	PRON
cusj-5634	55	17	exists	exist	VERB
cusj-5634	55	18	a	a	DET
cusj-5634	55	19	window	window	NOUN
cusj-5634	55	20	configuration	configuration	NOUN
cusj-5634	55	21	and	and	CCONJ
cusj-5634	55	22	membership	membership	NOUN
cusj-5634	55	23	assignment	assignment	NOUN
cusj-5634	55	24	t1	t1	PROPN
cusj-5634	55	25	,	,	PUNCT
cusj-5634	55	26	t2	t2	NOUN
cusj-5634	55	27	,	,	PUNCT
cusj-5634	55	28	2	2	NUM
cusj-5634	55	29	vr	vr	NOUN
cusj-5634	55	30	,	,	PUNCT
cusj-5634	55	31	vs	vs	ADP
cusj-5634	55	32	such	such	ADJ
cusj-5634	55	33	that	that	SCONJ
cusj-5634	55	34	there	there	PRON
cusj-5634	55	35	exists	exist	VERB
cusj-5634	55	36	a	a	DET
cusj-5634	55	37	set	set	NOUN
cusj-5634	55	38	i	i	PRON
cusj-5634	55	39	,	,	PUNCT
cusj-5634	55	40	length	length	NOUN
cusj-5634	55	41	t	t	PROPN
cusj-5634	55	42	’	'	PUNCT
cusj-5634	55	43	=	=	SYM
cusj-5634	55	44	t	t	PROPN
cusj-5634	55	45	t1	t1	NOUN
cusj-5634	55	46	t2	t2	PROPN
cusj-5634	55	47	vr	vr	PROPN
cusj-5634	55	48	vs	vs	ADP
cusj-5634	55	49	satisfying	satisfy	VERB
cusj-5634	55	50	d3,ij	d3,ij	PROPN
cusj-5634	55	51	<	<	PROPN
cusj-5634	55	52	1	1	NUM
cusj-5634	55	53	and	and	CCONJ
cusj-5634	55	54	σd1,ij	σd1,ij	NOUN
cusj-5634	55	55	=	=	PUNCT
cusj-5634	55	56	σd2,ij	σd2,ij	PUNCT
cusj-5634	56	1	=	=	PUNCT
cusj-5634	56	2	1	1	NUM
cusj-5634	56	3	for	for	ADP
cusj-5634	56	4	all	all	DET
cusj-5634	56	5	j	j	PROPN
cusj-5634	56	6	in	in	ADP
cusj-5634	56	7	the	the	DET
cusj-5634	56	8	range	range	NOUN
cusj-5634	56	9	of	of	ADP
cusj-5634	56	10	the	the	DET
cusj-5634	56	11	length	length	NOUN
cusj-5634	56	12	of	of	ADP
cusj-5634	56	13	i.	i.	PROPN
cusj-5634	56	14	algorithm	algorithm	PROPN
cusj-5634	56	15	&	&	CCONJ
cusj-5634	56	16	complexity	complexity	PROPN
cusj-5634	56	17	:	:	PUNCT
cusj-5634	56	18	available	available	ADJ
cusj-5634	56	19	upon	upon	SCONJ
cusj-5634	56	20	request	request	NOUN
cusj-5634	56	21	to	to	PART
cusj-5634	56	22	cusj	cusj	VERB
cusj-5634	56	23	.	.	PUNCT
cusj-5634	57	1	discussion	discussion	NOUN
cusj-5634	57	2	:	:	PUNCT
cusj-5634	57	3	a	a	DET
cusj-5634	57	4	simple	simple	ADJ
cusj-5634	57	5	implementation	implementation	NOUN
cusj-5634	57	6	of	of	ADP
cusj-5634	57	7	the	the	DET
cusj-5634	57	8	algorithm	algorithm	NOUN
cusj-5634	57	9	was	be	AUX
cusj-5634	57	10	written	write	VERB
cusj-5634	57	11	in	in	ADP
cusj-5634	57	12	java	java	NOUN
cusj-5634	57	13	using	use	VERB
cusj-5634	57	14	64	64	NUM
cusj-5634	57	15	-	-	PUNCT
cusj-5634	57	16	bit	bit	NOUN
cusj-5634	57	17	long	long	ADJ
cusj-5634	57	18	integers	integer	NOUN
cusj-5634	57	19	and	and	CCONJ
cusj-5634	57	20	tested	test	VERB
cusj-5634	57	21	for	for	ADP
cusj-5634	57	22	accuracy	accuracy	NOUN
cusj-5634	57	23	to	to	PART
cusj-5634	57	24	reveal	reveal	VERB
cusj-5634	57	25	efficacy	efficacy	NOUN
cusj-5634	57	26	of	of	ADP
cusj-5634	57	27	the	the	DET
cusj-5634	57	28	algorithm	algorithm	NOUN
cusj-5634	57	29	.	.	PUNCT
cusj-5634	58	1	to	to	PART
cusj-5634	58	2	test	test	VERB
cusj-5634	58	3	and	and	CCONJ
cusj-5634	58	4	explore	explore	VERB
cusj-5634	58	5	the	the	DET
cusj-5634	58	6	algorithm	algorithm	NOUN
cusj-5634	58	7	’s	’s	PART
cusj-5634	58	8	performance	performance	NOUN
cusj-5634	58	9	,	,	PUNCT
cusj-5634	58	10	a	a	DET
cusj-5634	58	11	driver	driver	NOUN
cusj-5634	58	12	was	be	AUX
cusj-5634	58	13	implemented	implement	VERB
cusj-5634	58	14	which	which	PRON
cusj-5634	58	15	generates	generate	VERB
cusj-5634	58	16	random	random	ADJ
cusj-5634	58	17	sets	set	NOUN
cusj-5634	58	18	of	of	ADP
cusj-5634	58	19	integers	integer	NOUN
cusj-5634	58	20	of	of	ADP
cusj-5634	58	21	a	a	DET
cusj-5634	58	22	given	give	VERB
cusj-5634	58	23	length	length	NOUN
cusj-5634	58	24	n	n	CCONJ
cusj-5634	58	25	,	,	PUNCT
cusj-5634	58	26	having	have	VERB
cusj-5634	58	27	range	range	NOUN
cusj-5634	58	28	-2n2	-2n2	VERB
cusj-5634	58	29	to	to	ADP
cusj-5634	58	30	2n2	2n2	NUM
cusj-5634	58	31	and	and	CCONJ
cusj-5634	58	32	tests	test	VERB
cusj-5634	58	33	whether	whether	SCONJ
cusj-5634	58	34	the	the	DET
cusj-5634	58	35	set	set	NOUN
cusj-5634	58	36	satisfies	satisfie	NOUN
cusj-5634	58	37	subset	subset	VERB
cusj-5634	58	38	sum	sum	NOUN
cusj-5634	58	39	for	for	ADP
cusj-5634	58	40	c	c	PROPN
cusj-5634	58	41	equal	equal	ADJ
cusj-5634	58	42	either	either	ADV
cusj-5634	58	43	to	to	ADP
cusj-5634	58	44	the	the	DET
cusj-5634	58	45	sum	sum	NOUN
cusj-5634	58	46	of	of	ADP
cusj-5634	58	47	a	a	DET
cusj-5634	58	48	randomly	randomly	ADV
cusj-5634	58	49	chosen	choose	VERB
cusj-5634	58	50	subset	subset	NOUN
cusj-5634	58	51	or	or	CCONJ
cusj-5634	58	52	a	a	DET
cusj-5634	58	53	random	random	ADJ
cusj-5634	58	54	number	number	NOUN
cusj-5634	58	55	unrelated	unrelated	ADJ
cusj-5634	58	56	to	to	ADP
cusj-5634	58	57	the	the	DET
cusj-5634	58	58	set	set	NOUN
cusj-5634	58	59	using	use	VERB
cusj-5634	58	60	(	(	PUNCT
cusj-5634	58	61	a	a	X
cusj-5634	58	62	)	)	PUNCT
cusj-5634	58	63	a	a	DET
cusj-5634	58	64	conventional	conventional	ADJ
cusj-5634	58	65	exponential	exponential	ADJ
cusj-5634	58	66	algorithm	algorithm	NOUN
cusj-5634	58	67	and	and	CCONJ
cusj-5634	58	68	(	(	PUNCT
cusj-5634	58	69	b	b	X
cusj-5634	58	70	)	)	PUNCT
cusj-5634	58	71	the	the	DET
cusj-5634	58	72	subsetsum	subsetsum	NOUN
cusj-5634	58	73	routine	routine	NOUN
cusj-5634	58	74	for	for	ADP
cusj-5634	58	75	n	n	NOUN
cusj-5634	58	76	permutations	permutation	NOUN
cusj-5634	58	77	of	of	ADP
cusj-5634	58	78	the	the	DET
cusj-5634	58	79	set	set	NOUN
cusj-5634	58	80	.	.	PUNCT
cusj-5634	59	1	under	under	ADP
cusj-5634	59	2	the	the	DET
cusj-5634	59	3	parameters	parameter	NOUN
cusj-5634	59	4	of	of	ADP
cusj-5634	59	5	this	this	DET
cusj-5634	59	6	test	test	NOUN
cusj-5634	59	7	,	,	PUNCT
cusj-5634	59	8	failure	failure	NOUN
cusj-5634	59	9	occurs	occur	VERB
cusj-5634	59	10	when	when	SCONJ
cusj-5634	59	11	the	the	DET
cusj-5634	59	12	output	output	NOUN
cusj-5634	59	13	of	of	ADP
cusj-5634	59	14	(	(	PUNCT
cusj-5634	59	15	b	b	NOUN
cusj-5634	59	16	)	)	PUNCT
cusj-5634	59	17	differs	differ	VERB
cusj-5634	59	18	from	from	ADP
cusj-5634	59	19	that	that	PRON
cusj-5634	59	20	of	of	ADP
cusj-5634	59	21	(	(	PUNCT
cusj-5634	59	22	a	a	NOUN
cusj-5634	59	23	)	)	PUNCT
cusj-5634	59	24	.	.	PUNCT
cusj-5634	60	1	for	for	ADP
cusj-5634	60	2	each	each	DET
cusj-5634	60	3	n	n	NOUN
cusj-5634	60	4	from	from	ADP
cusj-5634	60	5	1	1	NUM
cusj-5634	60	6	to	to	ADP
cusj-5634	60	7	20	20	NUM
cusj-5634	60	8	,	,	PUNCT
cusj-5634	60	9	1,000,000	1,000,000	NUM
cusj-5634	60	10	such	such	ADJ
cusj-5634	60	11	sets	set	NOUN
cusj-5634	60	12	were	be	AUX
cusj-5634	60	13	generated	generate	VERB
cusj-5634	60	14	and	and	CCONJ
cusj-5634	60	15	used	use	VERB
cusj-5634	60	16	to	to	PART
cusj-5634	60	17	test	test	VERB
cusj-5634	60	18	the	the	DET
cusj-5634	60	19	implementation	implementation	NOUN
cusj-5634	60	20	of	of	ADP
cusj-5634	60	21	the	the	DET
cusj-5634	60	22	algorithm	algorithm	NOUN
cusj-5634	60	23	.	.	PUNCT
cusj-5634	61	1	following	follow	VERB
cusj-5634	61	2	all	all	DET
cusj-5634	61	3	20,000,000	20,000,000	NUM
cusj-5634	61	4	trials	trial	NOUN
cusj-5634	61	5	,	,	PUNCT
cusj-5634	61	6	the	the	DET
cusj-5634	61	7	success	success	NOUN
cusj-5634	61	8	rate	rate	NOUN
cusj-5634	61	9	was	be	AUX
cusj-5634	61	10	100	100	NUM
cusj-5634	61	11	%	%	NOUN
cusj-5634	61	12	,	,	PUNCT
cusj-5634	61	13	exhibiting	exhibit	VERB
cusj-5634	61	14	precisely	precisely	ADV
cusj-5634	61	15	0	0	NUM
cusj-5634	61	16	failures	failure	NOUN
cusj-5634	61	17	.	.	PUNCT
cusj-5634	62	1	to	to	PART
cusj-5634	62	2	further	far	ADV
cusj-5634	62	3	explore	explore	VERB
cusj-5634	62	4	general	general	ADJ
cusj-5634	62	5	-	-	PUNCT
cusj-5634	62	6	case	case	NOUN
cusj-5634	62	7	applicability	applicability	NOUN
cusj-5634	62	8	of	of	ADP
cusj-5634	62	9	the	the	DET
cusj-5634	62	10	algorithm	algorithm	NOUN
cusj-5634	62	11	,	,	PUNCT
cusj-5634	62	12	a	a	DET
cusj-5634	62	13	reduction	reduction	NOUN
cusj-5634	62	14	to	to	PART
cusj-5634	62	15	subset	subset	VERB
cusj-5634	62	16	sum	sum	NOUN
cusj-5634	62	17	from	from	ADP
cusj-5634	62	18	3	3	NUM
cusj-5634	62	19	-	-	PUNCT
cusj-5634	62	20	sat	sit	VERB
cusj-5634	62	21	,	,	PUNCT
cusj-5634	62	22	another	another	DET
cusj-5634	62	23	np	np	NOUN
cusj-5634	62	24	-	-	PUNCT
cusj-5634	62	25	complete	complete	ADJ
cusj-5634	62	26	problem	problem	NOUN
cusj-5634	62	27	,	,	PUNCT
cusj-5634	62	28	was	be	AUX
cusj-5634	62	29	implemented	implement	VERB
cusj-5634	62	30	and	and	CCONJ
cusj-5634	62	31	tested	test	VERB
cusj-5634	62	32	,	,	PUNCT
cusj-5634	62	33	also	also	ADV
cusj-5634	62	34	exhibiting	exhibit	VERB
cusj-5634	62	35	precisely	precisely	ADV
cusj-5634	62	36	0	0	NUM
cusj-5634	62	37	failures	failure	NOUN
cusj-5634	62	38	over	over	ADP
cusj-5634	62	39	all	all	DET
cusj-5634	62	40	trials	trial	NOUN
cusj-5634	62	41	.	.	PUNCT
cusj-5634	63	1	the	the	DET
cusj-5634	63	2	method	method	NOUN
cusj-5634	63	3	can	can	AUX
cusj-5634	63	4	be	be	AUX
cusj-5634	63	5	reduced	reduce	VERB
cusj-5634	63	6	to	to	ADP
cusj-5634	63	7	an	an	DET
cusj-5634	63	8	o(n4	o(n4	NOUN
cusj-5634	63	9	)	)	PUNCT
cusj-5634	63	10	approximation	approximation	NOUN
cusj-5634	63	11	method	method	NOUN
cusj-5634	63	12	by	by	ADP
cusj-5634	63	13	only	only	ADV
cusj-5634	63	14	using	use	VERB
cusj-5634	63	15	the	the	DET
cusj-5634	63	16	subset	subset	NOUN
cusj-5634	63	17	of	of	ADP
cusj-5634	63	18	possible	possible	ADJ
cusj-5634	63	19	window	window	NOUN
cusj-5634	63	20	configurations	configuration	NOUN
cusj-5634	63	21	represented	represent	VERB
cusj-5634	63	22	by	by	ADP
cusj-5634	63	23	shifting	shift	VERB
cusj-5634	63	24	the	the	DET
cusj-5634	63	25	entire	entire	ADJ
cusj-5634	63	26	set	set	NOUN
cusj-5634	63	27	to	to	ADP
cusj-5634	63	28	the	the	DET
cusj-5634	63	29	left	left	NOUN
cusj-5634	63	30	(	(	PUNCT
cusj-5634	63	31	wrapping	wrap	VERB
cusj-5634	63	32	the	the	DET
cusj-5634	63	33	element	element	NOUN
cusj-5634	63	34	of	of	ADP
cusj-5634	63	35	the	the	DET
cusj-5634	63	36	first	first	ADJ
cusj-5634	63	37	index	index	NOUN
cusj-5634	63	38	to	to	ADP
cusj-5634	63	39	the	the	DET
cusj-5634	63	40	last	last	ADJ
cusj-5634	63	41	position	position	NOUN
cusj-5634	63	42	in	in	ADP
cusj-5634	63	43	the	the	DET
cusj-5634	63	44	set	set	NOUN
cusj-5634	63	45	)	)	PUNCT
cusj-5634	63	46	n	n	NUM
cusj-5634	63	47	times	time	NOUN
cusj-5634	63	48	and	and	CCONJ
cusj-5634	63	49	repeating	repeat	VERB
cusj-5634	63	50	the	the	DET
cusj-5634	63	51	constrain	constrain	NOUN
cusj-5634	63	52	procedure	procedure	NOUN
cusj-5634	63	53	.	.	PUNCT
cusj-5634	64	1	performing	perform	VERB
cusj-5634	64	2	the	the	DET
cusj-5634	64	3	same	same	ADJ
cusj-5634	64	4	testing	testing	NOUN
cusj-5634	64	5	as	as	SCONJ
cusj-5634	64	6	was	be	AUX
cusj-5634	64	7	performed	perform	VERB
cusj-5634	64	8	on	on	ADP
cusj-5634	64	9	the	the	DET
cusj-5634	64	10	exact	exact	ADJ
cusj-5634	64	11	method	method	NOUN
cusj-5634	64	12	as	as	SCONJ
cusj-5634	64	13	was	be	AUX
cusj-5634	64	14	outlined	outline	VERB
cusj-5634	64	15	in	in	ADP
cusj-5634	64	16	section	section	NOUN
cusj-5634	64	17	2.2	2.2	NUM
cusj-5634	64	18	,	,	PUNCT
cusj-5634	64	19	yielding	yield	VERB
cusj-5634	64	20	a	a	DET
cusj-5634	64	21	success	success	NOUN
cusj-5634	64	22	rate	rate	NOUN
cusj-5634	64	23	of	of	ADP
cusj-5634	64	24	99.95	99.95	NUM
cusj-5634	64	25	%	%	NOUN
cusj-5634	64	26	over	over	ADP
cusj-5634	64	27	20,000,000	20,000,000	NUM
cusj-5634	64	28	trials	trial	NOUN
cusj-5634	64	29	.	.	PUNCT
cusj-5634	65	1	the	the	DET
cusj-5634	65	2	fact	fact	NOUN
cusj-5634	65	3	that	that	SCONJ
cusj-5634	65	4	such	such	ADJ
cusj-5634	65	5	accuracy	accuracy	NOUN
cusj-5634	65	6	is	be	AUX
cusj-5634	65	7	yielded	yield	VERB
cusj-5634	65	8	from	from	ADP
cusj-5634	65	9	a	a	DET
cusj-5634	65	10	derived	derive	VERB
cusj-5634	65	11	approximation	approximation	NOUN
cusj-5634	65	12	which	which	PRON
cusj-5634	65	13	performs	perform	VERB
cusj-5634	65	14	in	in	ADP
cusj-5634	65	15	the	the	DET
cusj-5634	65	16	somewhat	somewhat	ADV
cusj-5634	65	17	practical	practical	ADJ
cusj-5634	65	18	time	time	NOUN
cusj-5634	65	19	of	of	ADP
cusj-5634	65	20	o(n4	o(n4	NOUN
cusj-5634	65	21	)	)	PUNCT
cusj-5634	65	22	gives	give	VERB
cusj-5634	65	23	reason	reason	NOUN
cusj-5634	65	24	to	to	PART
cusj-5634	65	25	believe	believe	VERB
cusj-5634	65	26	that	that	SCONJ
cusj-5634	65	27	such	such	DET
cusj-5634	65	28	a	a	DET
cusj-5634	65	29	method	method	NOUN
cusj-5634	65	30	may	may	AUX
cusj-5634	65	31	call	call	VERB
cusj-5634	65	32	into	into	ADP
cusj-5634	65	33	question	question	NOUN
cusj-5634	65	34	the	the	DET
cusj-5634	65	35	reliability	reliability	NOUN
cusj-5634	65	36	of	of	ADP
cusj-5634	65	37	the	the	DET
cusj-5634	65	38	assumption	assumption	NOUN
cusj-5634	65	39	that	that	SCONJ
cusj-5634	65	40	“	"	PUNCT
cusj-5634	65	41	practically	practically	ADV
cusj-5634	65	42	many	many	ADJ
cusj-5634	65	43	”	"	PUNCT
cusj-5634	65	44	naturally	naturally	ADV
cusj-5634	65	45	occurring	occur	VERB
cusj-5634	65	46	instances	instance	NOUN
cusj-5634	65	47	of	of	ADP
cusj-5634	65	48	npcomplete	npcomplete	ADJ
cusj-5634	65	49	problems	problem	NOUN
cusj-5634	65	50	can	can	AUX
cusj-5634	65	51	not	not	PART
cusj-5634	65	52	be	be	AUX
cusj-5634	65	53	solved	solve	VERB
cusj-5634	65	54	in	in	ADP
cusj-5634	65	55	polynomial	polynomial	ADJ
cusj-5634	65	56	time	time	NOUN
cusj-5634	65	57	.	.	PUNCT
cusj-5634	66	1	conclusion	conclusion	NOUN
cusj-5634	66	2	:	:	PUNCT
cusj-5634	66	3	an	an	DET
cusj-5634	66	4	algorithm	algorithm	NOUN
cusj-5634	66	5	has	have	AUX
cusj-5634	66	6	been	be	AUX
cusj-5634	66	7	made	make	VERB
cusj-5634	66	8	that	that	PRON
cusj-5634	66	9	reduces	reduce	VERB
cusj-5634	66	10	the	the	DET
cusj-5634	66	11	conditions	condition	NOUN
cusj-5634	66	12	under	under	ADP
cusj-5634	66	13	which	which	PRON
cusj-5634	66	14	a	a	DET
cusj-5634	66	15	given	give	VERB
cusj-5634	66	16	set	set	NOUN
cusj-5634	66	17	satisfies	satisfie	NOUN
cusj-5634	66	18	the	the	DET
cusj-5634	66	19	stipulations	stipulation	NOUN
cusj-5634	66	20	of	of	ADP
cusj-5634	66	21	the	the	DET
cusj-5634	66	22	subset	subset	ADJ
cusj-5634	66	23	sum	sum	NOUN
cusj-5634	66	24	proposition	proposition	NOUN
cusj-5634	66	25	to	to	ADP
cusj-5634	66	26	a	a	DET
cusj-5634	66	27	set	set	NOUN
cusj-5634	66	28	of	of	ADP
cusj-5634	66	29	linear	linear	ADJ
cusj-5634	66	30	relationships	relationship	NOUN
cusj-5634	66	31	,	,	PUNCT
cusj-5634	66	32	answering	answer	VERB
cusj-5634	66	33	question	question	NOUN
cusj-5634	66	34	of	of	ADP
cusj-5634	66	35	whether	whether	SCONJ
cusj-5634	66	36	a	a	DET
cusj-5634	66	37	set	set	NOUN
cusj-5634	66	38	satisfies	satisfie	NOUN
cusj-5634	66	39	subset	subset	VERB
cusj-5634	66	40	sum	sum	NOUN
cusj-5634	66	41	may	may	AUX
cusj-5634	66	42	be	be	AUX
cusj-5634	66	43	answered	answer	VERB
cusj-5634	66	44	in	in	ADP
cusj-5634	66	45	a	a	DET
cusj-5634	66	46	number	number	NOUN
cusj-5634	66	47	of	of	ADP
cusj-5634	66	48	steps	step	NOUN
cusj-5634	66	49	strongly	strongly	ADV
cusj-5634	66	50	polynomial	polynomial	ADJ
cusj-5634	66	51	with	with	ADP
cusj-5634	66	52	respect	respect	NOUN
cusj-5634	66	53	to	to	ADP
cusj-5634	66	54	the	the	DET
cusj-5634	66	55	length	length	NOUN
cusj-5634	66	56	of	of	ADP
cusj-5634	66	57	the	the	DET
cusj-5634	66	58	input	input	NOUN
cusj-5634	66	59	.	.	PUNCT
cusj-5634	67	1	following	follow	VERB
cusj-5634	67	2	the	the	DET
cusj-5634	67	3	justification	justification	NOUN
cusj-5634	67	4	,	,	PUNCT
cusj-5634	67	5	implementation	implementation	NOUN
cusj-5634	67	6	and	and	CCONJ
cusj-5634	67	7	exploration	exploration	NOUN
cusj-5634	67	8	of	of	ADP
cusj-5634	67	9	applications	application	NOUN
cusj-5634	67	10	,	,	PUNCT
cusj-5634	67	11	as	as	ADV
cusj-5634	67	12	well	well	ADV
cusj-5634	67	13	as	as	ADP
cusj-5634	67	14	testing	testing	NOUN
cusj-5634	67	15	of	of	ADP
cusj-5634	67	16	this	this	DET
cusj-5634	67	17	algorithm	algorithm	NOUN
cusj-5634	67	18	,	,	PUNCT
cusj-5634	67	19	a	a	DET
cusj-5634	67	20	rate	rate	NOUN
cusj-5634	67	21	of	of	ADP
cusj-5634	67	22	accuracy	accuracy	NOUN
cusj-5634	67	23	and	and	CCONJ
cusj-5634	67	24	observed	observed	ADJ
cusj-5634	67	25	applicability	applicability	NOUN
cusj-5634	67	26	was	be	AUX
cusj-5634	67	27	found	find	VERB
cusj-5634	67	28	that	that	SCONJ
cusj-5634	67	29	calls	call	VERB
cusj-5634	67	30	to	to	PART
cusj-5634	67	31	question	question	VERB
cusj-5634	67	32	the	the	DET
cusj-5634	67	33	reliability	reliability	NOUN
cusj-5634	67	34	of	of	ADP
cusj-5634	67	35	assumption	assumption	NOUN
cusj-5634	67	36	that	that	SCONJ
cusj-5634	67	37	“	"	PUNCT
cusj-5634	67	38	practically	practically	ADV
cusj-5634	67	39	many	many	ADJ
cusj-5634	67	40	”	"	PUNCT
cusj-5634	67	41	naturally	naturally	ADV
cusj-5634	67	42	occurring	occur	VERB
cusj-5634	67	43	instances	instance	NOUN
cusj-5634	67	44	of	of	ADP
cusj-5634	67	45	np	np	NOUN
cusj-5634	67	46	-	-	PUNCT
cusj-5634	67	47	complete	complete	ADJ
cusj-5634	67	48	problems	problem	NOUN
cusj-5634	67	49	can	can	AUX
cusj-5634	67	50	not	not	PART
cusj-5634	67	51	be	be	AUX
cusj-5634	67	52	solved	solve	VERB
cusj-5634	67	53	in	in	ADP
cusj-5634	67	54	polynomial	polynomial	ADJ
cusj-5634	67	55	time	time	NOUN
cusj-5634	67	56	.	.	PUNCT