id	sid	tid	token	lemma	pos
app01-4651	1	1	acta	acta	PROPN
app01-4651	1	2	polytechnica	polytechnica	PROPN
app01-4651	1	3	ctu	ctu	PROPN
app01-4651	1	4	proceedings	proceeding	NOUN
app01-4651	1	5	doi:10.14311	doi:10.14311	NOUN
app01-4651	1	6	/	/	SYM
app01-4651	1	7	app.2017.13.0135	app.2017.13.0135	NOUN
app01-4651	1	8	acta	acta	PROPN
app01-4651	1	9	polytechnica	polytechnica	NOUN
app01-4651	1	10	ctu	ctu	NOUN
app01-4651	1	11	proceedings	proceeding	NOUN
app01-4651	1	12	13:135–141	13:135–141	NUM
app01-4651	1	13	,	,	PUNCT
app01-4651	1	14	2017	2017	NUM
app01-4651	1	15	©	©	PROPN
app01-4651	1	16	czech	czech	PROPN
app01-4651	1	17	technical	technical	PROPN
app01-4651	1	18	university	university	PROPN
app01-4651	1	19	in	in	ADP
app01-4651	1	20	prague	prague	PROPN
app01-4651	1	21	,	,	PUNCT
app01-4651	1	22	2017	2017	NUM
app01-4651	1	23	available	available	ADJ
app01-4651	1	24	online	online	ADV
app01-4651	1	25	at	at	ADP
app01-4651	1	26	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-4651	1	27	optimization	optimization	NOUN
app01-4651	1	28	-	-	PUNCT
app01-4651	1	29	based	base	VERB
app01-4651	1	30	approach	approach	NOUN
app01-4651	1	31	to	to	ADP
app01-4651	1	32	tiling	tile	VERB
app01-4651	1	33	of	of	ADP
app01-4651	1	34	finite	finite	ADJ
app01-4651	1	35	areas	area	NOUN
app01-4651	1	36	with	with	ADP
app01-4651	1	37	arbitrary	arbitrary	ADJ
app01-4651	1	38	sets	set	NOUN
app01-4651	1	39	of	of	ADP
app01-4651	1	40	wang	wang	PROPN
app01-4651	1	41	tiles	tiles	PROPN
app01-4651	1	42	marek	marek	PROPN
app01-4651	1	43	tyburec∗	tyburec∗	PROPN
app01-4651	1	44	,	,	PUNCT
app01-4651	1	45	jan	jan	PROPN
app01-4651	1	46	zeman	zeman	PROPN
app01-4651	1	47	czech	czech	PROPN
app01-4651	1	48	technical	technical	PROPN
app01-4651	1	49	university	university	PROPN
app01-4651	1	50	in	in	ADP
app01-4651	1	51	prague	prague	PROPN
app01-4651	1	52	,	,	PUNCT
app01-4651	1	53	faculty	faculty	NOUN
app01-4651	1	54	of	of	ADP
app01-4651	1	55	civil	civil	ADJ
app01-4651	1	56	engineering	engineering	NOUN
app01-4651	1	57	,	,	PUNCT
app01-4651	1	58	department	department	NOUN
app01-4651	1	59	of	of	ADP
app01-4651	1	60	mechanics	mechanic	NOUN
app01-4651	1	61	,	,	PUNCT
app01-4651	1	62	thákurova	thákurova	X
app01-4651	1	63	7	7	NUM
app01-4651	1	64	,	,	PUNCT
app01-4651	1	65	166	166	NUM
app01-4651	1	66	29	29	NUM
app01-4651	1	67	prague	prague	NOUN
app01-4651	1	68	6	6	NUM
app01-4651	1	69	,	,	PUNCT
app01-4651	1	70	czech	czech	PROPN
app01-4651	1	71	republic	republic	NOUN
app01-4651	1	72	∗	∗	NOUN
app01-4651	1	73	corresponding	correspond	VERB
app01-4651	1	74	author	author	NOUN
app01-4651	1	75	:	:	PUNCT
app01-4651	1	76	marek.tyburec@fsv.cvut.cz	marek.tyburec@fsv.cvut.cz	NUM
app01-4651	1	77	abstract	abstract	NOUN
app01-4651	1	78	.	.	PUNCT
app01-4651	2	1	wang	wang	PROPN
app01-4651	2	2	tiles	tile	NOUN
app01-4651	2	3	proved	prove	VERB
app01-4651	2	4	to	to	PART
app01-4651	2	5	be	be	AUX
app01-4651	2	6	a	a	DET
app01-4651	2	7	convenient	convenient	ADJ
app01-4651	2	8	tool	tool	NOUN
app01-4651	2	9	for	for	ADP
app01-4651	2	10	the	the	DET
app01-4651	2	11	design	design	NOUN
app01-4651	2	12	of	of	ADP
app01-4651	2	13	aperiodic	aperiodic	ADJ
app01-4651	2	14	tilings	tiling	NOUN
app01-4651	2	15	in	in	ADP
app01-4651	2	16	computer	computer	NOUN
app01-4651	2	17	graphics	graphic	NOUN
app01-4651	2	18	and	and	CCONJ
app01-4651	2	19	in	in	ADP
app01-4651	2	20	materials	material	NOUN
app01-4651	2	21	engineering	engineering	NOUN
app01-4651	2	22	.	.	PUNCT
app01-4651	3	1	while	while	SCONJ
app01-4651	3	2	there	there	PRON
app01-4651	3	3	are	be	VERB
app01-4651	3	4	several	several	ADJ
app01-4651	3	5	algorithms	algorithm	NOUN
app01-4651	3	6	for	for	ADP
app01-4651	3	7	generation	generation	NOUN
app01-4651	3	8	of	of	ADP
app01-4651	3	9	finite	finite	ADJ
app01-4651	3	10	-	-	ADJ
app01-4651	3	11	sized	sized	ADJ
app01-4651	3	12	tilings	tiling	NOUN
app01-4651	3	13	,	,	PUNCT
app01-4651	3	14	they	they	PRON
app01-4651	3	15	exploit	exploit	VERB
app01-4651	3	16	the	the	DET
app01-4651	3	17	specific	specific	ADJ
app01-4651	3	18	structure	structure	NOUN
app01-4651	3	19	of	of	ADP
app01-4651	3	20	individual	individual	ADJ
app01-4651	3	21	tile	tile	NOUN
app01-4651	3	22	sets	set	NOUN
app01-4651	3	23	,	,	PUNCT
app01-4651	3	24	which	which	PRON
app01-4651	3	25	prevents	prevent	VERB
app01-4651	3	26	their	their	PRON
app01-4651	3	27	general	general	ADJ
app01-4651	3	28	usage	usage	NOUN
app01-4651	3	29	.	.	PUNCT
app01-4651	4	1	in	in	ADP
app01-4651	4	2	this	this	DET
app01-4651	4	3	contribution	contribution	NOUN
app01-4651	4	4	,	,	PUNCT
app01-4651	4	5	we	we	PRON
app01-4651	4	6	reformulate	reformulate	VERB
app01-4651	4	7	the	the	DET
app01-4651	4	8	np	np	NOUN
app01-4651	4	9	-	-	PUNCT
app01-4651	4	10	complete	complete	ADJ
app01-4651	4	11	tiling	tiling	NOUN
app01-4651	4	12	generation	generation	NOUN
app01-4651	4	13	problem	problem	NOUN
app01-4651	4	14	as	as	ADP
app01-4651	4	15	a	a	DET
app01-4651	4	16	binary	binary	ADJ
app01-4651	4	17	linear	linear	PROPN
app01-4651	4	18	program	program	NOUN
app01-4651	4	19	,	,	PUNCT
app01-4651	4	20	together	together	ADV
app01-4651	4	21	with	with	ADP
app01-4651	4	22	its	its	PRON
app01-4651	4	23	linear	linear	ADJ
app01-4651	4	24	and	and	CCONJ
app01-4651	4	25	semidefinite	semidefinite	ADJ
app01-4651	4	26	relaxations	relaxation	NOUN
app01-4651	4	27	suitable	suitable	ADJ
app01-4651	4	28	for	for	ADP
app01-4651	4	29	the	the	DET
app01-4651	4	30	branch	branch	NOUN
app01-4651	4	31	and	and	CCONJ
app01-4651	4	32	bound	bind	VERB
app01-4651	4	33	method	method	NOUN
app01-4651	4	34	.	.	PUNCT
app01-4651	5	1	finally	finally	ADV
app01-4651	5	2	,	,	PUNCT
app01-4651	5	3	we	we	PRON
app01-4651	5	4	assess	assess	VERB
app01-4651	5	5	the	the	DET
app01-4651	5	6	performance	performance	NOUN
app01-4651	5	7	of	of	ADP
app01-4651	5	8	the	the	DET
app01-4651	5	9	established	establish	VERB
app01-4651	5	10	formulations	formulation	NOUN
app01-4651	5	11	on	on	ADP
app01-4651	5	12	generations	generation	NOUN
app01-4651	5	13	of	of	ADP
app01-4651	5	14	several	several	ADJ
app01-4651	5	15	aperiodic	aperiodic	ADJ
app01-4651	5	16	tilings	tiling	NOUN
app01-4651	5	17	reported	report	VERB
app01-4651	5	18	in	in	ADP
app01-4651	5	19	the	the	DET
app01-4651	5	20	literature	literature	NOUN
app01-4651	5	21	,	,	PUNCT
app01-4651	5	22	and	and	CCONJ
app01-4651	5	23	conclude	conclude	VERB
app01-4651	5	24	that	that	SCONJ
app01-4651	5	25	the	the	DET
app01-4651	5	26	linear	linear	ADJ
app01-4651	5	27	relaxation	relaxation	NOUN
app01-4651	5	28	is	be	AUX
app01-4651	5	29	better	well	ADV
app01-4651	5	30	suited	suited	ADJ
app01-4651	5	31	for	for	ADP
app01-4651	5	32	the	the	DET
app01-4651	5	33	problem	problem	NOUN
app01-4651	5	34	.	.	PUNCT
app01-4651	6	1	keywords	keyword	NOUN
app01-4651	6	2	:	:	PUNCT
app01-4651	6	3	wang	wang	PROPN
app01-4651	6	4	tiles	tiles	PROPN
app01-4651	6	5	,	,	PUNCT
app01-4651	6	6	binary	binary	ADJ
app01-4651	6	7	and	and	CCONJ
app01-4651	6	8	continuous	continuous	ADJ
app01-4651	6	9	linear	linear	ADJ
app01-4651	6	10	programming	programming	NOUN
app01-4651	6	11	,	,	PUNCT
app01-4651	6	12	semidefinite	semidefinite	PROPN
app01-4651	6	13	programming	programming	PROPN
app01-4651	6	14	,	,	PUNCT
app01-4651	6	15	aperiodic	aperiodic	ADJ
app01-4651	6	16	tilings	tiling	NOUN
app01-4651	6	17	,	,	PUNCT
app01-4651	6	18	relaxation	relaxation	NOUN
app01-4651	6	19	.	.	PUNCT
app01-4651	7	1	1	1	X
app01-4651	7	2	.	.	X
app01-4651	7	3	introduction	introduction	NOUN
app01-4651	7	4	wang	wang	PROPN
app01-4651	7	5	tiles	tiles	PROPN
app01-4651	7	6	,	,	PUNCT
app01-4651	7	7	squares	square	NOUN
app01-4651	7	8	with	with	ADP
app01-4651	7	9	colored	colored	ADJ
app01-4651	7	10	edges	edge	NOUN
app01-4651	7	11	,	,	PUNCT
app01-4651	7	12	were	be	AUX
app01-4651	7	13	invented	invent	VERB
app01-4651	7	14	by	by	ADP
app01-4651	7	15	and	and	CCONJ
app01-4651	7	16	named	name	VERB
app01-4651	7	17	in	in	ADP
app01-4651	7	18	honor	honor	NOUN
app01-4651	7	19	of	of	ADP
app01-4651	7	20	hao	hao	PROPN
app01-4651	7	21	wang	wang	PROPN
app01-4651	7	22	,	,	PUNCT
app01-4651	7	23	originally	originally	ADV
app01-4651	7	24	serving	serve	VERB
app01-4651	7	25	as	as	ADP
app01-4651	7	26	a	a	DET
app01-4651	7	27	tool	tool	NOUN
app01-4651	7	28	for	for	ADP
app01-4651	7	29	studying	study	VERB
app01-4651	7	30	the	the	DET
app01-4651	7	31	∀∃∀	∀∃∀	NOUN
app01-4651	7	32	decidability	decidability	NOUN
app01-4651	7	33	problem	problem	NOUN
app01-4651	7	34	of	of	ADP
app01-4651	7	35	the	the	DET
app01-4651	7	36	predicate	predicate	NOUN
app01-4651	7	37	calculus	calculus	NOUN
app01-4651	7	38	[	[	X
app01-4651	7	39	1	1	NUM
app01-4651	7	40	]	]	PUNCT
app01-4651	7	41	.	.	PUNCT
app01-4651	8	1	wang	wang	PROPN
app01-4651	8	2	showed	show	VERB
app01-4651	8	3	that	that	SCONJ
app01-4651	8	4	the	the	DET
app01-4651	8	5	decidability	decidability	NOUN
app01-4651	8	6	problem	problem	NOUN
app01-4651	8	7	is	be	AUX
app01-4651	8	8	equivalent	equivalent	ADJ
app01-4651	8	9	to	to	ADP
app01-4651	8	10	the	the	DET
app01-4651	8	11	domino	domino	NOUN
app01-4651	8	12	problem	problem	NOUN
app01-4651	8	13	:	:	PUNCT
app01-4651	8	14	assume	assume	VERB
app01-4651	8	15	a	a	DET
app01-4651	8	16	set	set	NOUN
app01-4651	8	17	of	of	ADP
app01-4651	8	18	non	non	ADJ
app01-4651	8	19	-	-	ADJ
app01-4651	8	20	rotatable	rotatable	ADJ
app01-4651	8	21	unit	unit	NOUN
app01-4651	8	22	-	-	PUNCT
app01-4651	8	23	sized	sized	ADJ
app01-4651	8	24	(	(	PUNCT
app01-4651	8	25	wang	wang	PROPN
app01-4651	8	26	)	)	PUNCT
app01-4651	8	27	tiles	tile	NOUN
app01-4651	8	28	with	with	ADP
app01-4651	8	29	edges	edge	NOUN
app01-4651	8	30	colored	color	VERB
app01-4651	8	31	according	accord	VERB
app01-4651	8	32	to	to	ADP
app01-4651	8	33	the	the	DET
app01-4651	8	34	∀∃∀	∀∃∀	NOUN
app01-4651	8	35	problem	problem	NOUN
app01-4651	8	36	.	.	PUNCT
app01-4651	9	1	if	if	SCONJ
app01-4651	9	2	it	it	PRON
app01-4651	9	3	is	be	AUX
app01-4651	9	4	feasible	feasible	ADJ
app01-4651	9	5	to	to	PART
app01-4651	9	6	cover	cover	VERB
app01-4651	9	7	the	the	DET
app01-4651	9	8	infinite	infinite	ADJ
app01-4651	9	9	plane	plane	NOUN
app01-4651	9	10	by	by	ADP
app01-4651	9	11	translating	translate	VERB
app01-4651	9	12	copies	copy	NOUN
app01-4651	9	13	of	of	ADP
app01-4651	9	14	the	the	DET
app01-4651	9	15	tiles	tile	NOUN
app01-4651	9	16	,	,	PUNCT
app01-4651	9	17	such	such	ADJ
app01-4651	9	18	that	that	SCONJ
app01-4651	9	19	all	all	DET
app01-4651	9	20	their	their	PRON
app01-4651	9	21	vertices	vertex	NOUN
app01-4651	9	22	lie	lie	VERB
app01-4651	9	23	at	at	ADP
app01-4651	9	24	the	the	DET
app01-4651	9	25	integer	integer	NOUN
app01-4651	9	26	lattice	lattice	PROPN
app01-4651	9	27	points	point	NOUN
app01-4651	9	28	of	of	ADP
app01-4651	9	29	the	the	DET
app01-4651	9	30	plane	plane	NOUN
app01-4651	9	31	and	and	CCONJ
app01-4651	9	32	the	the	DET
app01-4651	9	33	adjoining	adjoining	ADJ
app01-4651	9	34	edges	edge	NOUN
app01-4651	9	35	share	share	VERB
app01-4651	9	36	the	the	DET
app01-4651	9	37	same	same	ADJ
app01-4651	9	38	color	color	NOUN
app01-4651	9	39	,	,	PUNCT
app01-4651	9	40	the	the	DET
app01-4651	9	41	problem	problem	NOUN
app01-4651	9	42	is	be	AUX
app01-4651	9	43	said	say	VERB
app01-4651	9	44	to	to	PART
app01-4651	9	45	be	be	AUX
app01-4651	9	46	solvable	solvable	ADJ
app01-4651	9	47	;	;	PUNCT
app01-4651	9	48	unsolvable	unsolvable	ADJ
app01-4651	9	49	otherwise	otherwise	ADV
app01-4651	9	50	.	.	PUNCT
app01-4651	10	1	for	for	ADP
app01-4651	10	2	an	an	DET
app01-4651	10	3	illustration	illustration	NOUN
app01-4651	10	4	of	of	ADP
app01-4651	10	5	a	a	DET
app01-4651	10	6	sample	sample	NOUN
app01-4651	10	7	2×	2×	NUM
app01-4651	10	8	3	3	NUM
app01-4651	10	9	wang	wang	PROPN
app01-4651	10	10	tiling	tiling	NOUN
app01-4651	10	11	,	,	PUNCT
app01-4651	10	12	see	see	VERB
app01-4651	10	13	fig	fig	NOUN
app01-4651	10	14	.	.	PUNCT
app01-4651	11	1	1	1	X
app01-4651	11	2	.	.	X
app01-4651	12	1	in	in	ADP
app01-4651	12	2	[	[	X
app01-4651	12	3	2	2	NUM
app01-4651	12	4	]	]	PUNCT
app01-4651	12	5	,	,	PUNCT
app01-4651	12	6	wang	wang	PROPN
app01-4651	12	7	made	make	VERB
app01-4651	12	8	a	a	DET
app01-4651	12	9	fundamental	fundamental	ADJ
app01-4651	12	10	conjecture	conjecture	NOUN
app01-4651	12	11	stating	state	VERB
app01-4651	12	12	that	that	SCONJ
app01-4651	12	13	the	the	DET
app01-4651	12	14	domino	domino	NOUN
app01-4651	12	15	problem	problem	NOUN
app01-4651	12	16	is	be	AUX
app01-4651	12	17	solvable	solvable	ADJ
app01-4651	12	18	if	if	SCONJ
app01-4651	12	19	and	and	CCONJ
app01-4651	12	20	only	only	ADV
app01-4651	12	21	if	if	SCONJ
app01-4651	12	22	the	the	DET
app01-4651	12	23	tiling	tiling	NOUN
app01-4651	12	24	was	be	AUX
app01-4651	12	25	periodic	periodic	ADJ
app01-4651	12	26	,	,	PUNCT
app01-4651	12	27	i.e.	i.e.	X
app01-4651	12	28	,	,	PUNCT
app01-4651	12	29	if	if	SCONJ
app01-4651	12	30	there	there	PRON
app01-4651	12	31	existed	exist	VERB
app01-4651	12	32	a	a	DET
app01-4651	12	33	rectangular	rectangular	ADJ
app01-4651	12	34	region	region	NOUN
app01-4651	12	35	of	of	ADP
app01-4651	12	36	the	the	DET
app01-4651	12	37	tiling	tiling	NOUN
app01-4651	12	38	with	with	ADP
app01-4651	12	39	identically	identically	ADV
app01-4651	12	40	colored	color	VERB
app01-4651	12	41	horizontal	horizontal	ADJ
app01-4651	12	42	,	,	PUNCT
app01-4651	12	43	and	and	CCONJ
app01-4651	12	44	vertical	vertical	ADJ
app01-4651	12	45	edges	edge	NOUN
app01-4651	12	46	,	,	PUNCT
app01-4651	12	47	respectively	respectively	ADV
app01-4651	12	48	.	.	PUNCT
app01-4651	13	1	a	a	DET
app01-4651	13	2	year	year	NOUN
app01-4651	13	3	later	later	ADV
app01-4651	13	4	,	,	PUNCT
app01-4651	13	5	kahr	kahr	PROPN
app01-4651	13	6	reduced	reduce	VERB
app01-4651	13	7	the	the	DET
app01-4651	13	8	turing	ture	VERB
app01-4651	13	9	machine	machine	NOUN
app01-4651	13	10	halting	halting	ADJ
app01-4651	13	11	problem	problem	NOUN
app01-4651	13	12	[	[	X
app01-4651	13	13	3	3	NUM
app01-4651	13	14	,	,	PUNCT
app01-4651	13	15	4	4	NUM
app01-4651	13	16	]	]	PUNCT
app01-4651	13	17	into	into	ADP
app01-4651	13	18	the	the	DET
app01-4651	13	19	origin	origin	NOUN
app01-4651	13	20	-	-	PUNCT
app01-4651	13	21	constrained	constrain	VERB
app01-4651	13	22	domino	domino	NOUN
app01-4651	13	23	problem	problem	NOUN
app01-4651	13	24	[	[	X
app01-4651	13	25	5	5	NUM
app01-4651	13	26	]	]	PUNCT
app01-4651	13	27	,	,	PUNCT
app01-4651	13	28	which	which	PRON
app01-4651	13	29	implies	imply	VERB
app01-4651	13	30	the	the	DET
app01-4651	13	31	domino	domino	NOUN
app01-4651	13	32	problem	problem	NOUN
app01-4651	13	33	is	be	AUX
app01-4651	13	34	also	also	ADV
app01-4651	13	35	undecidable	undecidable	ADJ
app01-4651	13	36	.	.	PUNCT
app01-4651	14	1	this	this	PRON
app01-4651	14	2	can	can	AUX
app01-4651	14	3	be	be	AUX
app01-4651	14	4	illustrated	illustrate	VERB
app01-4651	14	5	by	by	ADP
app01-4651	14	6	introducing	introduce	VERB
app01-4651	14	7	a	a	DET
app01-4651	14	8	turing	ture	VERB
app01-4651	14	9	machine	machine	NOUN
app01-4651	14	10	for	for	ADP
app01-4651	14	11	each	each	DET
app01-4651	14	12	tile	tile	NOUN
app01-4651	14	13	set	set	NOUN
app01-4651	14	14	,	,	PUNCT
app01-4651	14	15	halting	halt	VERB
app01-4651	14	16	only	only	ADV
app01-4651	14	17	if	if	SCONJ
app01-4651	14	18	the	the	DET
app01-4651	14	19	domino	domino	NOUN
app01-4651	14	20	problem	problem	NOUN
app01-4651	14	21	is	be	AUX
app01-4651	14	22	unsolvable	unsolvable	ADJ
app01-4651	14	23	.	.	PUNCT
app01-4651	15	1	however	however	ADV
app01-4651	15	2	,	,	PUNCT
app01-4651	15	3	there	there	PRON
app01-4651	15	4	is	be	VERB
app01-4651	15	5	an	an	DET
app01-4651	15	6	infinite	infinite	ADJ
app01-4651	15	7	number	number	NOUN
app01-4651	15	8	of	of	ADP
app01-4651	15	9	such	such	ADJ
app01-4651	15	10	tile	tile	NOUN
app01-4651	15	11	sets	set	NOUN
app01-4651	15	12	,	,	PUNCT
app01-4651	15	13	making	make	VERB
app01-4651	15	14	the	the	DET
app01-4651	15	15	domino	domino	NOUN
app01-4651	15	16	problem	problem	NOUN
app01-4651	15	17	undecidable	undecidable	ADJ
app01-4651	15	18	as	as	ADV
app01-4651	15	19	well	well	ADV
app01-4651	15	20	,	,	PUNCT
app01-4651	15	21	and	and	CCONJ
app01-4651	15	22	forbidding	forbid	VERB
app01-4651	15	23	existence	existence	NOUN
app01-4651	15	24	of	of	ADP
app01-4651	15	25	a	a	DET
app01-4651	15	26	general	general	ADJ
app01-4651	15	27	finite	finite	ADJ
app01-4651	15	28	algorithm	algorithm	NOUN
app01-4651	15	29	for	for	ADP
app01-4651	15	30	the	the	DET
app01-4651	15	31	generation	generation	NOUN
app01-4651	15	32	of	of	ADP
app01-4651	15	33	infinite	infinite	ADJ
app01-4651	15	34	tilings	tiling	NOUN
app01-4651	15	35	.	.	PUNCT
app01-4651	16	1	1.1	1.1	NUM
app01-4651	16	2	.	.	PUNCT
app01-4651	16	3	aperiodic	aperiodic	ADJ
app01-4651	16	4	tile	tile	NOUN
app01-4651	16	5	sets	set	VERB
app01-4651	16	6	undecidability	undecidability	NOUN
app01-4651	16	7	of	of	ADP
app01-4651	16	8	the	the	DET
app01-4651	16	9	domino	domino	NOUN
app01-4651	16	10	problem	problem	NOUN
app01-4651	16	11	was	be	AUX
app01-4651	16	12	also	also	ADV
app01-4651	16	13	proved	prove	VERB
app01-4651	16	14	by	by	ADP
app01-4651	16	15	wang	wang	PROPN
app01-4651	16	16	’s	’s	PROPN
app01-4651	16	17	student	student	PROPN
app01-4651	16	18	berger	berger	PROPN
app01-4651	16	19	,	,	PUNCT
app01-4651	16	20	who	who	PRON
app01-4651	16	21	used	use	VERB
app01-4651	16	22	the	the	DET
app01-4651	16	23	principle	principle	NOUN
app01-4651	16	24	of	of	ADP
app01-4651	16	25	expanding	expand	VERB
app01-4651	16	26	squares	square	NOUN
app01-4651	16	27	for	for	ADP
app01-4651	16	28	developing	develop	VERB
app01-4651	16	29	the	the	DET
app01-4651	16	30	sets	set	NOUN
app01-4651	16	31	of	of	ADP
app01-4651	16	32	20	20	NUM
app01-4651	16	33	,	,	PUNCT
app01-4651	16	34	426	426	NUM
app01-4651	17	1	[	[	X
app01-4651	17	2	6	6	NUM
app01-4651	17	3	]	]	PUNCT
app01-4651	17	4	and	and	CCONJ
app01-4651	17	5	104	104	NUM
app01-4651	17	6	tiles	tile	NOUN
app01-4651	17	7	[	[	X
app01-4651	17	8	7	7	X
app01-4651	17	9	]	]	PUNCT
app01-4651	17	10	that	that	PRON
app01-4651	17	11	admit	admit	VERB
app01-4651	17	12	only	only	ADV
app01-4651	17	13	aperiodic	aperiodic	ADJ
app01-4651	17	14	tilings	tiling	NOUN
app01-4651	17	15	of	of	ADP
app01-4651	17	16	the	the	DET
app01-4651	17	17	infinite	infinite	ADJ
app01-4651	17	18	plane	plane	NOUN
app01-4651	17	19	,	,	PUNCT
app01-4651	17	20	contrary	contrary	ADV
app01-4651	17	21	to	to	ADP
app01-4651	17	22	the	the	DET
app01-4651	17	23	wang	wang	PROPN
app01-4651	17	24	fundamental	fundamental	ADJ
app01-4651	17	25	conjecture	conjecture	NOUN
app01-4651	17	26	.	.	PUNCT
app01-4651	18	1	✓	✓	ADJ
app01-4651	18	2	✗	✗	PROPN
app01-4651	18	3	figure	figure	NOUN
app01-4651	18	4	1	1	NUM
app01-4651	18	5	.	.	PUNCT
app01-4651	18	6	periodic	periodic	ADJ
app01-4651	18	7	tiling	tiling	NOUN
app01-4651	18	8	composed	compose	VERB
app01-4651	18	9	of	of	ADP
app01-4651	18	10	2	2	NUM
app01-4651	18	11	wang	wang	PROPN
app01-4651	18	12	tiles	tile	NOUN
app01-4651	18	13	over	over	ADP
app01-4651	18	14	2	2	NUM
app01-4651	18	15	colors	color	NOUN
app01-4651	18	16	.	.	PUNCT
app01-4651	19	1	aiming	aim	VERB
app01-4651	19	2	to	to	PART
app01-4651	19	3	simplify	simplify	VERB
app01-4651	19	4	the	the	DET
app01-4651	19	5	berger	berger	PROPN
app01-4651	19	6	’s	’s	PART
app01-4651	19	7	proof	proof	NOUN
app01-4651	19	8	,	,	PUNCT
app01-4651	19	9	smaller	small	ADJ
app01-4651	19	10	aperiodic	aperiodic	ADJ
app01-4651	19	11	sets	set	NOUN
app01-4651	19	12	of	of	ADP
app01-4651	19	13	wang	wang	PROPN
app01-4651	19	14	tiles	tile	NOUN
app01-4651	19	15	have	have	AUX
app01-4651	19	16	been	be	AUX
app01-4651	19	17	constructed	construct	VERB
app01-4651	19	18	.	.	PUNCT
app01-4651	20	1	in	in	ADP
app01-4651	20	2	1966	1966	NUM
app01-4651	20	3	,	,	PUNCT
app01-4651	20	4	läuchli	läuchli	NOUN
app01-4651	20	5	sent	send	VERB
app01-4651	20	6	to	to	ADP
app01-4651	20	7	professor	professor	PROPN
app01-4651	20	8	wang	wang	PROPN
app01-4651	20	9	an	an	DET
app01-4651	20	10	aperiodic	aperiodic	ADJ
app01-4651	20	11	set	set	NOUN
app01-4651	20	12	of	of	ADP
app01-4651	20	13	40	40	NUM
app01-4651	20	14	tiles	tile	NOUN
app01-4651	20	15	over	over	ADP
app01-4651	20	16	16	16	NUM
app01-4651	20	17	colors	color	NOUN
app01-4651	20	18	,	,	PUNCT
app01-4651	20	19	but	but	CCONJ
app01-4651	20	20	it	it	PRON
app01-4651	20	21	remained	remain	VERB
app01-4651	20	22	unpublished	unpublished	ADJ
app01-4651	20	23	until	until	ADP
app01-4651	20	24	1975	1975	NUM
app01-4651	20	25	[	[	X
app01-4651	20	26	8	8	NUM
app01-4651	20	27	]	]	PUNCT
app01-4651	20	28	.	.	PUNCT
app01-4651	21	1	meanwhile	meanwhile	ADV
app01-4651	21	2	,	,	PUNCT
app01-4651	21	3	unaware	unaware	ADJ
app01-4651	21	4	of	of	ADP
app01-4651	21	5	läuchli	läuchli	PROPN
app01-4651	21	6	’s	’s	PART
app01-4651	21	7	result	result	NOUN
app01-4651	21	8	,	,	PUNCT
app01-4651	21	9	knuth	knuth	PROPN
app01-4651	21	10	simplified	simplify	VERB
app01-4651	21	11	berger	berger	PROPN
app01-4651	21	12	’s	’s	PART
app01-4651	21	13	set	set	VERB
app01-4651	21	14	to	to	ADP
app01-4651	21	15	92	92	NUM
app01-4651	21	16	tiles	tile	NOUN
app01-4651	21	17	over	over	ADP
app01-4651	21	18	26	26	NUM
app01-4651	21	19	colors	color	NOUN
app01-4651	21	20	[	[	X
app01-4651	21	21	9	9	NUM
app01-4651	21	22	]	]	PUNCT
app01-4651	21	23	;	;	PUNCT
app01-4651	21	24	and	and	CCONJ
app01-4651	21	25	robinson	robinson	PROPN
app01-4651	21	26	developed	develop	VERB
app01-4651	21	27	sets	set	NOUN
app01-4651	21	28	of	of	ADP
app01-4651	21	29	104	104	NUM
app01-4651	21	30	and	and	CCONJ
app01-4651	21	31	52	52	NUM
app01-4651	21	32	tiles	tile	NOUN
app01-4651	21	33	in	in	ADP
app01-4651	21	34	1967	1967	NUM
app01-4651	21	35	[	[	X
app01-4651	21	36	10	10	NUM
app01-4651	21	37	]	]	PUNCT
app01-4651	21	38	,	,	PUNCT
app01-4651	21	39	of	of	ADP
app01-4651	21	40	56	56	NUM
app01-4651	21	41	tiles	tile	NOUN
app01-4651	21	42	over	over	ADP
app01-4651	21	43	12	12	NUM
app01-4651	21	44	colors	color	NOUN
app01-4651	21	45	in	in	ADP
app01-4651	21	46	1971	1971	NUM
app01-4651	21	47	[	[	X
app01-4651	21	48	11	11	NUM
app01-4651	21	49	]	]	PUNCT
app01-4651	21	50	,	,	PUNCT
app01-4651	21	51	and	and	CCONJ
app01-4651	21	52	marked	mark	VERB
app01-4651	21	53	existence	existence	NOUN
app01-4651	21	54	of	of	ADP
app01-4651	21	55	a	a	DET
app01-4651	21	56	set	set	NOUN
app01-4651	21	57	of	of	ADP
app01-4651	21	58	35	35	NUM
app01-4651	21	59	tiles	tile	NOUN
app01-4651	21	60	[	[	X
app01-4651	21	61	11	11	NUM
app01-4651	21	62	]	]	PUNCT
app01-4651	21	63	.	.	PUNCT
app01-4651	22	1	in	in	ADP
app01-4651	22	2	1973	1973	NUM
app01-4651	22	3	,	,	PUNCT
app01-4651	22	4	penrose	penrose	PROPN
app01-4651	22	5	developed	develop	VERB
app01-4651	22	6	a	a	DET
app01-4651	22	7	new	new	ADJ
app01-4651	22	8	approach	approach	NOUN
app01-4651	22	9	based	base	VERB
app01-4651	22	10	on	on	ADP
app01-4651	22	11	kites	kite	NOUN
app01-4651	22	12	and	and	CCONJ
app01-4651	22	13	darts	dart	NOUN
app01-4651	22	14	tiling	tile	VERB
app01-4651	22	15	,	,	PUNCT
app01-4651	22	16	leading	lead	VERB
app01-4651	22	17	to	to	ADP
app01-4651	22	18	a	a	DET
app01-4651	22	19	set	set	NOUN
app01-4651	22	20	of	of	ADP
app01-4651	22	21	34	34	NUM
app01-4651	22	22	tiles	tile	NOUN
app01-4651	22	23	.	.	PUNCT
app01-4651	23	1	robinson	robinson	PROPN
app01-4651	23	2	,	,	PUNCT
app01-4651	23	3	being	be	AUX
app01-4651	23	4	in	in	ADP
app01-4651	23	5	contact	contact	NOUN
app01-4651	23	6	with	with	ADP
app01-4651	23	7	penrose	penrose	PROPN
app01-4651	23	8	,	,	PUNCT
app01-4651	23	9	modified	modify	VERB
app01-4651	23	10	the	the	DET
app01-4651	23	11	penrose	penrose	NOUN
app01-4651	23	12	’s	’s	PART
app01-4651	23	13	approach	approach	NOUN
app01-4651	23	14	to	to	PART
app01-4651	23	15	reach	reach	VERB
app01-4651	23	16	a	a	DET
app01-4651	23	17	reduced	reduce	VERB
app01-4651	23	18	set	set	NOUN
app01-4651	23	19	of	of	ADP
app01-4651	23	20	32	32	NUM
app01-4651	23	21	tiles	tile	NOUN
app01-4651	23	22	over	over	ADP
app01-4651	23	23	16	16	NUM
app01-4651	23	24	colors	color	NOUN
app01-4651	23	25	[	[	X
app01-4651	23	26	12	12	NUM
app01-4651	23	27	]	]	PUNCT
app01-4651	23	28	.	.	PUNCT
app01-4651	24	1	using	use	VERB
app01-4651	24	2	the	the	DET
app01-4651	24	3	same	same	ADJ
app01-4651	24	4	technique	technique	NOUN
app01-4651	24	5	together	together	ADV
app01-4651	24	6	with	with	ADP
app01-4651	24	7	penrose	penrose	PROPN
app01-4651	24	8	rhombs	rhomb	VERB
app01-4651	24	9	tiling	tiling	NOUN
app01-4651	24	10	,	,	PUNCT
app01-4651	24	11	grünbaum	grünbaum	NOUN
app01-4651	24	12	obtained	obtain	VERB
app01-4651	24	13	a	a	DET
app01-4651	24	14	set	set	NOUN
app01-4651	24	15	of	of	ADP
app01-4651	24	16	24	24	NUM
app01-4651	24	17	tiles	tile	NOUN
app01-4651	24	18	over	over	ADP
app01-4651	24	19	9	9	NUM
app01-4651	24	20	colors	color	NOUN
app01-4651	24	21	in	in	ADP
app01-4651	24	22	1987	1987	NUM
app01-4651	24	23	[	[	X
app01-4651	24	24	12	12	NUM
app01-4651	24	25	]	]	PUNCT
app01-4651	24	26	.	.	PUNCT
app01-4651	25	1	another	another	DET
app01-4651	25	2	two	two	NUM
app01-4651	25	3	tile	tile	NOUN
app01-4651	25	4	sets	set	NOUN
app01-4651	25	5	were	be	AUX
app01-4651	25	6	discovered	discover	VERB
app01-4651	25	7	due	due	ADP
app01-4651	25	8	to	to	ADP
app01-4651	25	9	ammann	ammann	NOUN
app01-4651	25	10	.	.	PUNCT
app01-4651	26	1	in	in	ADP
app01-4651	26	2	1978	1978	NUM
app01-4651	26	3	,	,	PUNCT
app01-4651	26	4	he	he	PRON
app01-4651	26	5	used	use	VERB
app01-4651	26	6	ammann	ammann	PROPN
app01-4651	26	7	bars	bar	NOUN
app01-4651	26	8	to	to	PART
app01-4651	26	9	reach	reach	VERB
app01-4651	26	10	16	16	NUM
app01-4651	26	11	tiles	tile	NOUN
app01-4651	26	12	over	over	ADP
app01-4651	26	13	6	6	NUM
app01-4651	26	14	colors	color	NOUN
app01-4651	26	15	[	[	PUNCT
app01-4651	26	16	13	13	NUM
app01-4651	26	17	]	]	PUNCT
app01-4651	26	18	.	.	PUNCT
app01-4651	27	1	building	build	VERB
app01-4651	27	2	on	on	ADP
app01-4651	27	3	the	the	DET
app01-4651	27	4	ammann	ammann	PROPN
app01-4651	27	5	’s	’s	PART
app01-4651	27	6	a2	a2	PROPN
app01-4651	27	7	tiling	tile	VERB
app01-4651	27	8	,	,	PUNCT
app01-4651	27	9	see	see	VERB
app01-4651	27	10	,	,	PUNCT
app01-4651	27	11	e.g.	e.g.	ADV
app01-4651	27	12	,	,	PUNCT
app01-4651	27	13	[	[	X
app01-4651	27	14	12	12	NUM
app01-4651	27	15	]	]	PUNCT
app01-4651	27	16	,	,	PUNCT
app01-4651	27	17	robinson	robinson	PROPN
app01-4651	27	18	obtained	obtain	VERB
app01-4651	27	19	a	a	DET
app01-4651	27	20	set	set	NOUN
app01-4651	27	21	of	of	ADP
app01-4651	27	22	24	24	NUM
app01-4651	27	23	tiles	tile	NOUN
app01-4651	27	24	over	over	ADP
app01-4651	27	25	24	24	NUM
app01-4651	27	26	colors	color	NOUN
app01-4651	27	27	in	in	ADP
app01-4651	27	28	1977	1977	NUM
app01-4651	27	29	.	.	PUNCT
app01-4651	28	1	subsequent	subsequent	ADJ
app01-4651	28	2	size	size	NOUN
app01-4651	28	3	reduction	reduction	NOUN
app01-4651	28	4	of	of	ADP
app01-4651	28	5	the	the	DET
app01-4651	28	6	smallest	small	ADJ
app01-4651	28	7	aperiodic	aperiodic	ADJ
app01-4651	28	8	set	set	NOUN
app01-4651	28	9	occurred	occur	VERB
app01-4651	28	10	in	in	ADP
app01-4651	28	11	1996	1996	NUM
app01-4651	28	12	,	,	PUNCT
app01-4651	28	13	as	as	SCONJ
app01-4651	28	14	kari	kari	X
app01-4651	28	15	developed	develop	VERB
app01-4651	28	16	a	a	DET
app01-4651	28	17	new	new	ADJ
app01-4651	28	18	method	method	NOUN
app01-4651	28	19	based	base	VERB
app01-4651	28	20	on	on	ADP
app01-4651	28	21	mealy	mealy	PROPN
app01-4651	28	22	machines	machine	NOUN
app01-4651	28	23	multiplying	multiply	VERB
app01-4651	28	24	beatty	beatty	PROPN
app01-4651	28	25	sequences	sequences	PROPN
app01-4651	28	26	,	,	PUNCT
app01-4651	28	27	and	and	CCONJ
app01-4651	28	28	presented	present	VERB
app01-4651	28	29	a	a	DET
app01-4651	28	30	set	set	NOUN
app01-4651	28	31	of	of	ADP
app01-4651	28	32	14	14	NUM
app01-4651	28	33	tiles	tile	NOUN
app01-4651	28	34	over	over	ADP
app01-4651	28	35	6	6	NUM
app01-4651	28	36	colors	color	NOUN
app01-4651	28	37	[	[	X
app01-4651	28	38	14	14	NUM
app01-4651	28	39	]	]	PUNCT
app01-4651	28	40	.	.	PUNCT
app01-4651	29	1	čulík	čulík	PROPN
app01-4651	29	2	,	,	PUNCT
app01-4651	29	3	using	use	VERB
app01-4651	29	4	the	the	DET
app01-4651	29	5	same	same	ADJ
app01-4651	29	6	approach	approach	NOUN
app01-4651	29	7	,	,	PUNCT
app01-4651	29	8	reduced	reduce	VERB
app01-4651	29	9	the	the	DET
app01-4651	29	10	set	set	NOUN
app01-4651	29	11	even	even	ADV
app01-4651	29	12	further	far	ADV
app01-4651	29	13	to	to	ADP
app01-4651	29	14	13	13	NUM
app01-4651	29	15	tiles	tile	NOUN
app01-4651	29	16	over	over	ADP
app01-4651	29	17	5	5	NUM
app01-4651	29	18	colors	color	NOUN
app01-4651	29	19	[	[	X
app01-4651	29	20	15	15	NUM
app01-4651	29	21	]	]	PUNCT
app01-4651	29	22	.	.	PUNCT
app01-4651	30	1	135	135	NUM
app01-4651	31	1	http://dx.doi.org/10.14311/app.2017.13.0135	http://dx.doi.org/10.14311/app.2017.13.0135	PROPN
app01-4651	31	2	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-4651	31	3	marek	marek	PROPN
app01-4651	31	4	tyburec	tyburec	NOUN
app01-4651	31	5	,	,	PUNCT
app01-4651	31	6	jan	jan	PROPN
app01-4651	31	7	zeman	zeman	PROPN
app01-4651	31	8	acta	acta	PROPN
app01-4651	31	9	polytechnica	polytechnica	PROPN
app01-4651	31	10	ctu	ctu	NOUN
app01-4651	31	11	proceedings	proceeding	NOUN
app01-4651	31	12	the	the	DET
app01-4651	31	13	search	search	NOUN
app01-4651	31	14	for	for	ADP
app01-4651	31	15	the	the	DET
app01-4651	31	16	minimal	minimal	ADJ
app01-4651	31	17	aperiodic	aperiodic	ADJ
app01-4651	31	18	set	set	NOUN
app01-4651	31	19	is	be	AUX
app01-4651	31	20	concluded	conclude	VERB
app01-4651	31	21	by	by	ADP
app01-4651	31	22	jeandel	jeandel	PROPN
app01-4651	31	23	,	,	PUNCT
app01-4651	31	24	who	who	PRON
app01-4651	31	25	used	use	VERB
app01-4651	31	26	a	a	DET
app01-4651	31	27	brute	brute	ADJ
app01-4651	31	28	-	-	PUNCT
app01-4651	31	29	force	force	NOUN
app01-4651	31	30	enumeration	enumeration	NOUN
app01-4651	31	31	approach	approach	NOUN
app01-4651	31	32	to	to	PART
app01-4651	31	33	find	find	VERB
app01-4651	31	34	aperiodic	aperiodic	ADJ
app01-4651	31	35	sets	set	NOUN
app01-4651	31	36	of	of	ADP
app01-4651	31	37	11	11	NUM
app01-4651	31	38	tiles	tile	NOUN
app01-4651	31	39	over	over	ADP
app01-4651	31	40	4	4	NUM
app01-4651	31	41	and	and	CCONJ
app01-4651	31	42	5	5	NUM
app01-4651	31	43	colors	color	NOUN
app01-4651	31	44	;	;	PUNCT
app01-4651	31	45	and	and	CCONJ
app01-4651	31	46	proved	prove	VERB
app01-4651	31	47	both	both	PRON
app01-4651	31	48	that	that	SCONJ
app01-4651	31	49	there	there	PRON
app01-4651	31	50	does	do	AUX
app01-4651	31	51	not	not	PART
app01-4651	31	52	exist	exist	VERB
app01-4651	31	53	an	an	DET
app01-4651	31	54	aperiodic	aperiodic	ADJ
app01-4651	31	55	set	set	NOUN
app01-4651	31	56	with	with	ADP
app01-4651	31	57	10	10	NUM
app01-4651	31	58	or	or	CCONJ
app01-4651	31	59	fewer	few	ADJ
app01-4651	31	60	tiles	tile	NOUN
app01-4651	31	61	and	and	CCONJ
app01-4651	31	62	with	with	ADP
app01-4651	31	63	less	less	ADJ
app01-4651	31	64	than	than	ADP
app01-4651	31	65	4	4	NUM
app01-4651	31	66	colors	color	NOUN
app01-4651	31	67	[	[	X
app01-4651	31	68	16	16	NUM
app01-4651	31	69	]	]	PUNCT
app01-4651	31	70	.	.	PUNCT
app01-4651	32	1	in	in	ADP
app01-4651	32	2	addition	addition	NOUN
app01-4651	32	3	to	to	ADP
app01-4651	32	4	the	the	DET
app01-4651	32	5	classical	classical	ADJ
app01-4651	32	6	wang	wang	PROPN
app01-4651	32	7	tiles	tile	NOUN
app01-4651	32	8	,	,	PUNCT
app01-4651	32	9	in	in	ADP
app01-4651	32	10	2006	2006	NUM
app01-4651	32	11	,	,	PUNCT
app01-4651	32	12	lagae	lagae	PROPN
app01-4651	32	13	introduced	introduce	VERB
app01-4651	32	14	a	a	DET
app01-4651	32	15	subset	subset	NOUN
app01-4651	32	16	of	of	ADP
app01-4651	32	17	the	the	DET
app01-4651	32	18	wang	wang	PROPN
app01-4651	32	19	tiles	tiles	PROPN
app01-4651	32	20	,	,	PUNCT
app01-4651	32	21	the	the	DET
app01-4651	32	22	corner	corner	NOUN
app01-4651	32	23	tiles	tile	NOUN
app01-4651	32	24	,	,	PUNCT
app01-4651	32	25	with	with	ADP
app01-4651	32	26	the	the	DET
app01-4651	32	27	connectivity	connectivity	NOUN
app01-4651	32	28	information	information	NOUN
app01-4651	32	29	stored	store	VERB
app01-4651	32	30	in	in	ADP
app01-4651	32	31	the	the	DET
app01-4651	32	32	colored	colored	ADJ
app01-4651	32	33	corners	corner	NOUN
app01-4651	32	34	instead	instead	ADV
app01-4651	32	35	of	of	ADP
app01-4651	32	36	the	the	DET
app01-4651	32	37	edges	edge	NOUN
app01-4651	32	38	[	[	X
app01-4651	32	39	17	17	NUM
app01-4651	32	40	]	]	PUNCT
app01-4651	32	41	.	.	PUNCT
app01-4651	33	1	in	in	ADP
app01-4651	33	2	the	the	DET
app01-4651	33	3	same	same	ADJ
app01-4651	33	4	year	year	NOUN
app01-4651	33	5	,	,	PUNCT
app01-4651	33	6	he	he	PRON
app01-4651	33	7	constructed	construct	VERB
app01-4651	33	8	an	an	DET
app01-4651	33	9	aperiodic	aperiodic	ADJ
app01-4651	33	10	set	set	NOUN
app01-4651	33	11	of	of	ADP
app01-4651	33	12	44	44	NUM
app01-4651	33	13	corner	corner	NOUN
app01-4651	33	14	tiles	tile	NOUN
app01-4651	33	15	over	over	ADP
app01-4651	33	16	6	6	NUM
app01-4651	33	17	colors	color	NOUN
app01-4651	33	18	[	[	X
app01-4651	33	19	18	18	NUM
app01-4651	33	20	]	]	PUNCT
app01-4651	33	21	.	.	PUNCT
app01-4651	34	1	the	the	DET
app01-4651	34	2	set	set	NOUN
app01-4651	34	3	was	be	AUX
app01-4651	34	4	further	far	ADV
app01-4651	34	5	simplified	simplify	VERB
app01-4651	34	6	by	by	ADP
app01-4651	34	7	nurmi	nurmi	NOUN
app01-4651	34	8	to	to	ADP
app01-4651	34	9	30	30	NUM
app01-4651	34	10	corner	corner	NOUN
app01-4651	34	11	tiles	tile	NOUN
app01-4651	34	12	over	over	ADP
app01-4651	34	13	6	6	NUM
app01-4651	34	14	colors	color	NOUN
app01-4651	34	15	[	[	X
app01-4651	34	16	19	19	NUM
app01-4651	34	17	]	]	PUNCT
app01-4651	34	18	.	.	PUNCT
app01-4651	35	1	note	note	VERB
app01-4651	35	2	that	that	SCONJ
app01-4651	35	3	because	because	SCONJ
app01-4651	35	4	the	the	DET
app01-4651	35	5	corner	corner	NOUN
app01-4651	35	6	tiles	tile	NOUN
app01-4651	35	7	can	can	AUX
app01-4651	35	8	be	be	AUX
app01-4651	35	9	straightforwardly	straightforwardly	ADV
app01-4651	35	10	converted	convert	VERB
app01-4651	35	11	to	to	ADP
app01-4651	35	12	the	the	DET
app01-4651	35	13	edge	edge	NOUN
app01-4651	35	14	-	-	PUNCT
app01-4651	35	15	based	base	VERB
app01-4651	35	16	wang	wang	PROPN
app01-4651	35	17	tiles	tiles	PROPN
app01-4651	35	18	[	[	X
app01-4651	35	19	17	17	NUM
app01-4651	35	20	]	]	PUNCT
app01-4651	35	21	,	,	PUNCT
app01-4651	35	22	our	our	PRON
app01-4651	35	23	approach	approach	NOUN
app01-4651	35	24	naturally	naturally	ADV
app01-4651	35	25	extends	extend	VERB
app01-4651	35	26	to	to	ADP
app01-4651	35	27	the	the	DET
app01-4651	35	28	corner	corner	NOUN
app01-4651	35	29	tiles	tile	NOUN
app01-4651	35	30	,	,	PUNCT
app01-4651	35	31	see	see	VERB
app01-4651	35	32	section	section	NOUN
app01-4651	35	33	4	4	NUM
app01-4651	35	34	for	for	ADP
app01-4651	35	35	a	a	DET
app01-4651	35	36	specific	specific	ADJ
app01-4651	35	37	example	example	NOUN
app01-4651	35	38	.	.	PUNCT
app01-4651	36	1	1.2	1.2	NUM
app01-4651	36	2	.	.	PUNCT
app01-4651	36	3	selected	select	VERB
app01-4651	36	4	applications	application	NOUN
app01-4651	36	5	due	due	ADP
app01-4651	36	6	to	to	ADP
app01-4651	36	7	the	the	DET
app01-4651	36	8	ability	ability	NOUN
app01-4651	36	9	of	of	ADP
app01-4651	36	10	some	some	DET
app01-4651	36	11	tile	tile	NOUN
app01-4651	36	12	sets	set	NOUN
app01-4651	36	13	to	to	PART
app01-4651	36	14	generate	generate	VERB
app01-4651	36	15	aperiodic	aperiodic	ADJ
app01-4651	36	16	patterns	pattern	NOUN
app01-4651	36	17	,	,	PUNCT
app01-4651	36	18	wang	wang	PROPN
app01-4651	36	19	tiles	tiles	PROPN
app01-4651	36	20	received	receive	VERB
app01-4651	36	21	a	a	DET
app01-4651	36	22	broad	broad	ADJ
app01-4651	36	23	interest	interest	NOUN
app01-4651	36	24	among	among	ADP
app01-4651	36	25	disciplines	discipline	NOUN
app01-4651	36	26	.	.	PUNCT
app01-4651	37	1	also	also	ADV
app01-4651	37	2	,	,	PUNCT
app01-4651	37	3	their	their	PRON
app01-4651	37	4	original	original	ADJ
app01-4651	37	5	significance	significance	NOUN
app01-4651	37	6	for	for	ADP
app01-4651	37	7	automated	automate	VERB
app01-4651	37	8	theorem	theorem	NOUN
app01-4651	37	9	proving	prove	VERB
app01-4651	37	10	[	[	X
app01-4651	37	11	2	2	NUM
app01-4651	37	12	]	]	PUNCT
app01-4651	37	13	was	be	AUX
app01-4651	37	14	supplemented	supplement	VERB
app01-4651	37	15	by	by	ADP
app01-4651	37	16	proofs	proof	NOUN
app01-4651	37	17	in	in	ADP
app01-4651	37	18	cellular	cellular	ADJ
app01-4651	37	19	automata	automata	NOUN
app01-4651	37	20	theory	theory	NOUN
app01-4651	37	21	[	[	X
app01-4651	37	22	20	20	NUM
app01-4651	37	23	]	]	PUNCT
app01-4651	37	24	.	.	PUNCT
app01-4651	38	1	in	in	ADP
app01-4651	38	2	2003	2003	NUM
app01-4651	38	3	,	,	PUNCT
app01-4651	38	4	cohen	cohen	PROPN
app01-4651	38	5	et	et	PROPN
app01-4651	38	6	al	al	PROPN
app01-4651	38	7	.	.	PROPN
app01-4651	38	8	introduced	introduce	VERB
app01-4651	38	9	wang	wang	PROPN
app01-4651	38	10	tiles	tile	NOUN
app01-4651	38	11	to	to	ADP
app01-4651	38	12	the	the	DET
app01-4651	38	13	computer	computer	NOUN
app01-4651	38	14	graphics	graphic	NOUN
app01-4651	38	15	community	community	NOUN
app01-4651	38	16	[	[	X
app01-4651	38	17	21	21	NUM
app01-4651	38	18	]	]	PUNCT
app01-4651	38	19	.	.	PUNCT
app01-4651	39	1	since	since	SCONJ
app01-4651	39	2	then	then	ADV
app01-4651	39	3	,	,	PUNCT
app01-4651	39	4	wang	wang	PROPN
app01-4651	39	5	tiles	tile	NOUN
app01-4651	39	6	have	have	AUX
app01-4651	39	7	been	be	AUX
app01-4651	39	8	successfully	successfully	ADV
app01-4651	39	9	used	use	VERB
app01-4651	39	10	,	,	PUNCT
app01-4651	39	11	e.g.	e.g.	ADV
app01-4651	39	12	,	,	PUNCT
app01-4651	39	13	for	for	ADP
app01-4651	39	14	efficient	efficient	ADJ
app01-4651	39	15	synthesis	synthesis	NOUN
app01-4651	39	16	of	of	ADP
app01-4651	39	17	stochastic	stochastic	ADJ
app01-4651	39	18	textures	texture	NOUN
app01-4651	39	19	or	or	CCONJ
app01-4651	39	20	for	for	ADP
app01-4651	39	21	generation	generation	NOUN
app01-4651	39	22	of	of	ADP
app01-4651	39	23	poisson	poisson	NOUN
app01-4651	39	24	disk	disk	NOUN
app01-4651	39	25	distributions	distribution	NOUN
app01-4651	39	26	.	.	PUNCT
app01-4651	40	1	molecular	molecular	ADJ
app01-4651	40	2	realization	realization	NOUN
app01-4651	40	3	of	of	ADP
app01-4651	40	4	wang	wang	PROPN
app01-4651	40	5	tiles	tile	NOUN
app01-4651	40	6	is	be	AUX
app01-4651	40	7	due	due	ADJ
app01-4651	40	8	to	to	ADP
app01-4651	40	9	winfree	winfree	NOUN
app01-4651	40	10	,	,	PUNCT
app01-4651	40	11	who	who	PRON
app01-4651	40	12	introduced	introduce	VERB
app01-4651	40	13	a	a	DET
app01-4651	40	14	self	self	NOUN
app01-4651	40	15	-	-	PUNCT
app01-4651	40	16	assembly	assembly	NOUN
app01-4651	40	17	of	of	ADP
app01-4651	40	18	biological	biological	ADJ
app01-4651	40	19	nanostructures	nanostructure	NOUN
app01-4651	40	20	into	into	ADP
app01-4651	40	21	aperiodic	aperiodic	ADJ
app01-4651	40	22	crystals	crystal	NOUN
app01-4651	40	23	[	[	X
app01-4651	40	24	22	22	NUM
app01-4651	40	25	]	]	PUNCT
app01-4651	40	26	.	.	PUNCT
app01-4651	41	1	novák	novák	PROPN
app01-4651	41	2	was	be	AUX
app01-4651	41	3	probably	probably	ADV
app01-4651	41	4	the	the	DET
app01-4651	41	5	first	first	ADJ
app01-4651	41	6	one	one	NUM
app01-4651	41	7	who	who	PRON
app01-4651	41	8	used	use	VERB
app01-4651	41	9	wang	wang	PROPN
app01-4651	41	10	tiles	tile	NOUN
app01-4651	41	11	in	in	ADP
app01-4651	41	12	materials	material	NOUN
app01-4651	41	13	engineering	engineering	NOUN
app01-4651	41	14	for	for	ADP
app01-4651	41	15	efficient	efficient	ADJ
app01-4651	41	16	compression	compression	NOUN
app01-4651	41	17	of	of	ADP
app01-4651	41	18	microstructures	microstructure	NOUN
app01-4651	41	19	[	[	X
app01-4651	41	20	23	23	NUM
app01-4651	41	21	]	]	PUNCT
app01-4651	41	22	;	;	PUNCT
app01-4651	41	23	doškář	doškář	VERB
app01-4651	41	24	for	for	ADP
app01-4651	41	25	their	their	PRON
app01-4651	41	26	reconstruction	reconstruction	NOUN
app01-4651	41	27	[	[	X
app01-4651	41	28	24	24	NUM
app01-4651	41	29	]	]	PUNCT
app01-4651	41	30	.	.	PUNCT
app01-4651	42	1	doškář	doškář	PROPN
app01-4651	42	2	further	far	ADV
app01-4651	42	3	generated	generate	VERB
app01-4651	42	4	large	large	ADJ
app01-4651	42	5	stochastic	stochastic	ADJ
app01-4651	42	6	samples	sample	NOUN
app01-4651	42	7	of	of	ADP
app01-4651	42	8	the	the	DET
app01-4651	42	9	alporas	alporas	ADJ
app01-4651	42	10	®	®	NOUN
app01-4651	42	11	foam	foam	NOUN
app01-4651	42	12	and	and	CCONJ
app01-4651	42	13	its	its	PRON
app01-4651	42	14	finiteelement	finiteelement	NOUN
app01-4651	42	15	representations	representation	NOUN
app01-4651	42	16	in	in	ADP
app01-4651	42	17	[	[	X
app01-4651	42	18	25	25	NUM
app01-4651	42	19	]	]	PUNCT
app01-4651	42	20	.	.	PUNCT
app01-4651	43	1	in	in	ADP
app01-4651	43	2	[	[	X
app01-4651	43	3	26	26	NUM
app01-4651	43	4	]	]	PUNCT
app01-4651	43	5	,	,	PUNCT
app01-4651	43	6	tyburec	tyburec	PROPN
app01-4651	43	7	used	use	VERB
app01-4651	43	8	wang	wang	PROPN
app01-4651	43	9	tiles	tile	NOUN
app01-4651	43	10	to	to	PART
app01-4651	43	11	describe	describe	VERB
app01-4651	43	12	modular	modular	ADJ
app01-4651	43	13	assembly	assembly	NOUN
app01-4651	43	14	of	of	ADP
app01-4651	43	15	structures	structure	NOUN
app01-4651	43	16	,	,	PUNCT
app01-4651	43	17	whereas	whereas	SCONJ
app01-4651	43	18	both	both	CCONJ
app01-4651	43	19	the	the	DET
app01-4651	43	20	topology	topology	NOUN
app01-4651	43	21	and	and	CCONJ
app01-4651	43	22	arrangement	arrangement	NOUN
app01-4651	43	23	of	of	ADP
app01-4651	43	24	modules	module	NOUN
app01-4651	43	25	were	be	AUX
app01-4651	43	26	subjects	subject	NOUN
app01-4651	43	27	of	of	ADP
app01-4651	43	28	optimization	optimization	NOUN
app01-4651	43	29	.	.	PUNCT
app01-4651	44	1	1.3	1.3	NUM
app01-4651	44	2	.	.	PUNCT
app01-4651	44	3	tiling	tile	VERB
app01-4651	44	4	generation	generation	NOUN
app01-4651	44	5	algorithms	algorithm	NOUN
app01-4651	44	6	existing	exist	VERB
app01-4651	44	7	tiling	tile	VERB
app01-4651	44	8	generation	generation	NOUN
app01-4651	44	9	algorithms	algorithm	NOUN
app01-4651	44	10	are	be	AUX
app01-4651	44	11	designed	design	VERB
app01-4651	44	12	specifically	specifically	ADV
app01-4651	44	13	to	to	ADP
app01-4651	44	14	the	the	DET
app01-4651	44	15	tile	tile	NOUN
app01-4651	44	16	sets	set	VERB
app01-4651	44	17	they	they	PRON
app01-4651	44	18	handle	handle	VERB
app01-4651	44	19	.	.	PUNCT
app01-4651	45	1	in	in	ADP
app01-4651	45	2	computer	computer	NOUN
app01-4651	45	3	graphics	graphic	NOUN
app01-4651	45	4	,	,	PUNCT
app01-4651	45	5	for	for	ADP
app01-4651	45	6	example	example	NOUN
app01-4651	45	7	,	,	PUNCT
app01-4651	45	8	it	it	PRON
app01-4651	45	9	is	be	AUX
app01-4651	45	10	essential	essential	ADJ
app01-4651	45	11	to	to	PART
app01-4651	45	12	generate	generate	VERB
app01-4651	45	13	visually	visually	ADV
app01-4651	45	14	appealing	appealing	ADJ
app01-4651	45	15	patterns	pattern	NOUN
app01-4651	45	16	quickly	quickly	ADV
app01-4651	45	17	,	,	PUNCT
app01-4651	45	18	which	which	PRON
app01-4651	45	19	is	be	AUX
app01-4651	45	20	best	well	ADV
app01-4651	45	21	achieved	achieve	VERB
app01-4651	45	22	with	with	ADP
app01-4651	45	23	stochastic	stochastic	ADJ
app01-4651	45	24	tile	tile	NOUN
app01-4651	45	25	sets	set	NOUN
app01-4651	45	26	.	.	PUNCT
app01-4651	46	1	tiling	tile	VERB
app01-4651	46	2	a	a	DET
app01-4651	46	3	finite	finite	ADJ
app01-4651	46	4	area	area	NOUN
app01-4651	46	5	has	have	VERB
app01-4651	46	6	then	then	ADV
app01-4651	46	7	a	a	DET
app01-4651	46	8	o(n	o(n	NOUN
app01-4651	46	9	)	)	PUNCT
app01-4651	46	10	complexity	complexity	NOUN
app01-4651	46	11	,	,	PUNCT
app01-4651	46	12	adopting	adopt	VERB
app01-4651	46	13	,	,	PUNCT
app01-4651	46	14	e.g.	e.g.	ADV
app01-4651	46	15	,	,	PUNCT
app01-4651	46	16	the	the	DET
app01-4651	46	17	stochastic	stochastic	ADJ
app01-4651	46	18	tiling	tiling	NOUN
app01-4651	46	19	[	[	X
app01-4651	46	20	21	21	NUM
app01-4651	46	21	]	]	PUNCT
app01-4651	46	22	,	,	PUNCT
app01-4651	46	23	or	or	CCONJ
app01-4651	46	24	the	the	DET
app01-4651	46	25	hash	hash	NOUN
app01-4651	46	26	-	-	PUNCT
app01-4651	46	27	based	base	VERB
app01-4651	46	28	direct	direct	ADJ
app01-4651	46	29	stochastic	stochastic	NOUN
app01-4651	46	30	tiling	tiling	NOUN
app01-4651	46	31	[	[	X
app01-4651	46	32	27	27	NUM
app01-4651	46	33	]	]	PUNCT
app01-4651	46	34	algorithms	algorithm	NOUN
app01-4651	46	35	.	.	PUNCT
app01-4651	47	1	the	the	DET
app01-4651	47	2	latter	latter	ADJ
app01-4651	47	3	algorithm	algorithm	NOUN
app01-4651	47	4	allows	allow	VERB
app01-4651	47	5	straightforward	straightforward	ADJ
app01-4651	47	6	definition	definition	NOUN
app01-4651	47	7	of	of	ADP
app01-4651	47	8	boundary	boundary	ADJ
app01-4651	47	9	conditions	condition	NOUN
app01-4651	47	10	.	.	PUNCT
app01-4651	48	1	in	in	ADP
app01-4651	48	2	the	the	DET
app01-4651	48	3	case	case	NOUN
app01-4651	48	4	of	of	ADP
app01-4651	48	5	mathematical	mathematical	ADJ
app01-4651	48	6	logic	logic	NOUN
app01-4651	48	7	,	,	PUNCT
app01-4651	48	8	it	it	PRON
app01-4651	48	9	is	be	AUX
app01-4651	48	10	crucial	crucial	ADJ
app01-4651	48	11	to	to	PART
app01-4651	48	12	prove	prove	VERB
app01-4651	48	13	that	that	SCONJ
app01-4651	48	14	an	an	DET
app01-4651	48	15	investigated	investigated	ADJ
app01-4651	48	16	tile	tile	NOUN
app01-4651	48	17	set	set	NOUN
app01-4651	48	18	can	can	AUX
app01-4651	48	19	tile	tile	VERB
app01-4651	48	20	the	the	DET
app01-4651	48	21	whole	whole	ADJ
app01-4651	48	22	infinite	infinite	ADJ
app01-4651	48	23	plane	plane	NOUN
app01-4651	48	24	,	,	PUNCT
app01-4651	48	25	and	and	CCONJ
app01-4651	48	26	does	do	VERB
app01-4651	48	27	so	so	ADV
app01-4651	48	28	only	only	ADV
app01-4651	48	29	aperiodically	aperiodically	ADV
app01-4651	48	30	.	.	PUNCT
app01-4651	49	1	as	as	SCONJ
app01-4651	49	2	the	the	DET
app01-4651	49	3	problem	problem	NOUN
app01-4651	49	4	is	be	AUX
app01-4651	49	5	undecidable	undecidable	ADJ
app01-4651	49	6	,	,	PUNCT
app01-4651	49	7	no	no	DET
app01-4651	49	8	general	general	ADJ
app01-4651	49	9	algorithm	algorithm	NOUN
app01-4651	49	10	exists	exist	VERB
app01-4651	49	11	,	,	PUNCT
app01-4651	49	12	and	and	CCONJ
app01-4651	49	13	thus	thus	ADV
app01-4651	49	14	all	all	DET
app01-4651	49	15	the	the	DET
app01-4651	49	16	algorithms	algorithm	NOUN
app01-4651	49	17	need	need	VERB
app01-4651	49	18	to	to	PART
app01-4651	49	19	exploit	exploit	VERB
app01-4651	49	20	the	the	DET
app01-4651	49	21	specific	specific	ADJ
app01-4651	49	22	structure	structure	NOUN
app01-4651	49	23	of	of	ADP
app01-4651	49	24	each	each	DET
app01-4651	49	25	individual	individual	NOUN
app01-4651	49	26	(	(	PUNCT
app01-4651	49	27	family	family	NOUN
app01-4651	49	28	of	of	ADP
app01-4651	49	29	)	)	PUNCT
app01-4651	49	30	tile	tile	NOUN
app01-4651	49	31	sets	set	NOUN
app01-4651	49	32	.	.	PUNCT
app01-4651	50	1	although	although	SCONJ
app01-4651	50	2	the	the	DET
app01-4651	50	3	algorithms	algorithm	NOUN
app01-4651	50	4	are	be	AUX
app01-4651	50	5	fast	fast	ADJ
app01-4651	50	6	,	,	PUNCT
app01-4651	50	7	they	they	PRON
app01-4651	50	8	remain	remain	VERB
app01-4651	50	9	tile	tile	NOUN
app01-4651	50	10	set	set	VERB
app01-4651	50	11	dependent	dependent	ADJ
app01-4651	50	12	.	.	PUNCT
app01-4651	51	1	all	all	DET
app01-4651	51	2	tilings	tiling	NOUN
app01-4651	51	3	of	of	ADP
app01-4651	51	4	finite	finite	ADJ
app01-4651	51	5	-	-	ADJ
app01-4651	51	6	sized	sized	ADJ
app01-4651	51	7	areas	area	NOUN
app01-4651	51	8	are	be	AUX
app01-4651	51	9	restricted	restrict	VERB
app01-4651	51	10	to	to	PART
app01-4651	51	11	be	be	AUX
app01-4651	51	12	subsets	subset	NOUN
app01-4651	51	13	of	of	ADP
app01-4651	51	14	the	the	DET
app01-4651	51	15	infinite	infinite	ADJ
app01-4651	51	16	plane	plane	NOUN
app01-4651	51	17	,	,	PUNCT
app01-4651	51	18	which	which	PRON
app01-4651	51	19	is	be	AUX
app01-4651	51	20	not	not	PART
app01-4651	51	21	required	require	VERB
app01-4651	51	22	in	in	ADP
app01-4651	51	23	the	the	DET
app01-4651	51	24	finite	finite	ADJ
app01-4651	51	25	domain	domain	NOUN
app01-4651	51	26	,	,	PUNCT
app01-4651	51	27	and	and	CCONJ
app01-4651	51	28	it	it	PRON
app01-4651	51	29	is	be	AUX
app01-4651	51	30	almost	almost	ADV
app01-4651	51	31	impossible	impossible	ADJ
app01-4651	51	32	to	to	PART
app01-4651	51	33	introduce	introduce	VERB
app01-4651	51	34	boundary	boundary	ADJ
app01-4651	51	35	conditions	condition	NOUN
app01-4651	51	36	.	.	PUNCT
app01-4651	52	1	on	on	ADP
app01-4651	52	2	top	top	NOUN
app01-4651	52	3	of	of	ADP
app01-4651	52	4	that	that	PRON
app01-4651	52	5	,	,	PUNCT
app01-4651	52	6	there	there	PRON
app01-4651	52	7	provably	provably	ADV
app01-4651	52	8	exist	exist	VERB
app01-4651	52	9	aperiodic	aperiodic	ADJ
app01-4651	52	10	tile	tile	NOUN
app01-4651	52	11	sets	set	NOUN
app01-4651	52	12	that	that	PRON
app01-4651	52	13	admit	admit	VERB
app01-4651	52	14	only	only	ADV
app01-4651	52	15	non	non	ADJ
app01-4651	52	16	-	-	ADJ
app01-4651	52	17	recursive	recursive	ADJ
app01-4651	52	18	tiling	tiling	NOUN
app01-4651	52	19	[	[	X
app01-4651	52	20	28	28	NUM
app01-4651	52	21	,	,	PUNCT
app01-4651	52	22	29	29	NUM
app01-4651	52	23	]	]	PUNCT
app01-4651	52	24	,	,	PUNCT
app01-4651	52	25	forbidding	forbid	VERB
app01-4651	52	26	design	design	NOUN
app01-4651	52	27	of	of	ADP
app01-4651	52	28	any	any	DET
app01-4651	52	29	problem	problem	NOUN
app01-4651	52	30	-	-	PUNCT
app01-4651	52	31	specific	specific	ADJ
app01-4651	52	32	algorithm	algorithm	NOUN
app01-4651	52	33	to	to	PART
app01-4651	52	34	tile	tile	VERB
app01-4651	52	35	the	the	DET
app01-4651	52	36	infinite	infinite	ADJ
app01-4651	52	37	plane	plane	NOUN
app01-4651	52	38	.	.	PUNCT
app01-4651	53	1	to	to	ADP
app01-4651	53	2	the	the	DET
app01-4651	53	3	authors	author	NOUN
app01-4651	53	4	’	’	PART
app01-4651	53	5	knowledge	knowledge	NOUN
app01-4651	53	6	,	,	PUNCT
app01-4651	53	7	the	the	DET
app01-4651	53	8	only	only	ADJ
app01-4651	53	9	method	method	NOUN
app01-4651	53	10	that	that	PRON
app01-4651	53	11	has	have	AUX
app01-4651	53	12	been	be	AUX
app01-4651	53	13	used	use	VERB
app01-4651	53	14	for	for	ADP
app01-4651	53	15	tiling	tile	VERB
app01-4651	53	16	of	of	ADP
app01-4651	53	17	finite	finite	ADJ
app01-4651	53	18	-	-	ADJ
app01-4651	53	19	sized	sized	ADJ
app01-4651	53	20	areas	area	NOUN
app01-4651	53	21	by	by	ADP
app01-4651	53	22	arbitrary	arbitrary	ADJ
app01-4651	53	23	tile	tile	NOUN
app01-4651	53	24	sets	set	NOUN
app01-4651	53	25	is	be	AUX
app01-4651	53	26	the	the	DET
app01-4651	53	27	backtracking	backtrack	VERB
app01-4651	53	28	algorithm	algorithm	NOUN
app01-4651	53	29	,	,	PUNCT
app01-4651	53	30	see	see	VERB
app01-4651	53	31	[	[	X
app01-4651	53	32	30	30	NUM
app01-4651	53	33	]	]	PUNCT
app01-4651	53	34	.	.	PUNCT
app01-4651	54	1	although	although	SCONJ
app01-4651	54	2	the	the	DET
app01-4651	54	3	algorithm	algorithm	NOUN
app01-4651	54	4	is	be	AUX
app01-4651	54	5	general	general	ADJ
app01-4651	54	6	,	,	PUNCT
app01-4651	54	7	it	it	PRON
app01-4651	54	8	is	be	AUX
app01-4651	54	9	generally	generally	ADV
app01-4651	54	10	inefficient	inefficient	ADJ
app01-4651	54	11	,	,	PUNCT
app01-4651	54	12	as	as	SCONJ
app01-4651	54	13	it	it	PRON
app01-4651	54	14	commonly	commonly	ADV
app01-4651	54	15	creates	create	VERB
app01-4651	54	16	impossible	impossible	ADJ
app01-4651	54	17	assemblies	assembly	NOUN
app01-4651	54	18	too	too	ADV
app01-4651	54	19	early	early	ADV
app01-4651	54	20	.	.	PUNCT
app01-4651	55	1	moreover	moreover	ADV
app01-4651	55	2	,	,	PUNCT
app01-4651	55	3	distant	distant	ADJ
app01-4651	55	4	boundary	boundary	ADJ
app01-4651	55	5	conditions	condition	NOUN
app01-4651	55	6	make	make	VERB
app01-4651	55	7	the	the	DET
app01-4651	55	8	problem	problem	NOUN
app01-4651	55	9	more	more	ADV
app01-4651	55	10	difficult	difficult	ADJ
app01-4651	55	11	to	to	PART
app01-4651	55	12	solve	solve	VERB
app01-4651	55	13	.	.	PUNCT
app01-4651	56	1	1.4	1.4	NUM
app01-4651	56	2	.	.	PUNCT
app01-4651	56	3	contributions	contribution	NOUN
app01-4651	56	4	this	this	DET
app01-4651	56	5	paper	paper	NOUN
app01-4651	56	6	aims	aim	VERB
app01-4651	56	7	to	to	PART
app01-4651	56	8	overcome	overcome	VERB
app01-4651	56	9	the	the	DET
app01-4651	56	10	shortcomings	shortcoming	NOUN
app01-4651	56	11	of	of	ADP
app01-4651	56	12	the	the	DET
app01-4651	56	13	methods	method	NOUN
app01-4651	56	14	outlined	outline	VERB
app01-4651	56	15	in	in	ADP
app01-4651	56	16	the	the	DET
app01-4651	56	17	previous	previous	ADJ
app01-4651	56	18	section	section	NOUN
app01-4651	56	19	,	,	PUNCT
app01-4651	56	20	and	and	CCONJ
app01-4651	56	21	to	to	PART
app01-4651	56	22	develop	develop	VERB
app01-4651	56	23	an	an	DET
app01-4651	56	24	approach	approach	NOUN
app01-4651	56	25	that	that	PRON
app01-4651	56	26	handles	handle	VERB
app01-4651	56	27	tiling	tile	VERB
app01-4651	56	28	of	of	ADP
app01-4651	56	29	finitesized	finitesize	VERB
app01-4651	56	30	areas	area	NOUN
app01-4651	56	31	using	use	VERB
app01-4651	56	32	arbitrary	arbitrary	ADJ
app01-4651	56	33	tile	tile	NOUN
app01-4651	56	34	sets	set	NOUN
app01-4651	56	35	,	,	PUNCT
app01-4651	56	36	together	together	ADV
app01-4651	56	37	with	with	ADP
app01-4651	56	38	a	a	DET
app01-4651	56	39	straightforward	straightforward	ADJ
app01-4651	56	40	approach	approach	NOUN
app01-4651	56	41	to	to	PART
app01-4651	56	42	define	define	VERB
app01-4651	56	43	edgeor	edgeor	NOUN
app01-4651	56	44	tilebased	tilebase	VERB
app01-4651	56	45	boundary	boundary	ADJ
app01-4651	56	46	conditions	condition	NOUN
app01-4651	56	47	.	.	PUNCT
app01-4651	57	1	our	our	PRON
app01-4651	57	2	exposition	exposition	NOUN
app01-4651	57	3	is	be	AUX
app01-4651	57	4	structured	structure	VERB
app01-4651	57	5	as	as	SCONJ
app01-4651	57	6	follows	follow	VERB
app01-4651	57	7	.	.	PUNCT
app01-4651	58	1	in	in	ADP
app01-4651	58	2	section	section	NOUN
app01-4651	58	3	2	2	NUM
app01-4651	58	4	,	,	PUNCT
app01-4651	58	5	we	we	PRON
app01-4651	58	6	develop	develop	VERB
app01-4651	58	7	a	a	DET
app01-4651	58	8	binary	binary	ADJ
app01-4651	58	9	linear	linear	NOUN
app01-4651	58	10	programming	programming	NOUN
app01-4651	58	11	representation	representation	NOUN
app01-4651	58	12	of	of	ADP
app01-4651	58	13	the	the	DET
app01-4651	58	14	tiling	tile	VERB
app01-4651	58	15	generation	generation	NOUN
app01-4651	58	16	problem	problem	NOUN
app01-4651	58	17	.	.	PUNCT
app01-4651	59	1	the	the	DET
app01-4651	59	2	formulation	formulation	NOUN
app01-4651	59	3	is	be	AUX
app01-4651	59	4	relaxed	relax	VERB
app01-4651	59	5	,	,	PUNCT
app01-4651	59	6	and	and	CCONJ
app01-4651	59	7	its	its	PRON
app01-4651	59	8	linear	linear	ADJ
app01-4651	59	9	and	and	CCONJ
app01-4651	59	10	semidefinite	semidefinite	ADJ
app01-4651	59	11	approximations	approximation	NOUN
app01-4651	59	12	are	be	AUX
app01-4651	59	13	presented	present	VERB
app01-4651	59	14	.	.	PUNCT
app01-4651	60	1	in	in	ADP
app01-4651	60	2	order	order	NOUN
app01-4651	60	3	to	to	PART
app01-4651	60	4	show	show	VERB
app01-4651	60	5	generality	generality	NOUN
app01-4651	60	6	of	of	ADP
app01-4651	60	7	the	the	DET
app01-4651	60	8	formulations	formulation	NOUN
app01-4651	60	9	,	,	PUNCT
app01-4651	60	10	we	we	PRON
app01-4651	60	11	introduce	introduce	VERB
app01-4651	60	12	their	their	PRON
app01-4651	60	13	extensions	extension	NOUN
app01-4651	60	14	to	to	PART
app01-4651	60	15	solve	solve	VERB
app01-4651	60	16	the	the	DET
app01-4651	60	17	tile	tile	NOUN
app01-4651	60	18	-	-	PUNCT
app01-4651	60	19	packing	pack	VERB
app01-4651	60	20	problem	problem	NOUN
app01-4651	60	21	,	,	PUNCT
app01-4651	60	22	to	to	PART
app01-4651	60	23	prove	prove	VERB
app01-4651	60	24	that	that	SCONJ
app01-4651	60	25	a	a	DET
app01-4651	60	26	tile	tile	NOUN
app01-4651	60	27	set	set	NOUN
app01-4651	60	28	can	can	AUX
app01-4651	60	29	not	not	PART
app01-4651	60	30	tile	tile	VERB
app01-4651	60	31	the	the	DET
app01-4651	60	32	plane	plane	NOUN
app01-4651	60	33	,	,	PUNCT
app01-4651	60	34	and	and	CCONJ
app01-4651	60	35	to	to	PART
app01-4651	60	36	prove	prove	VERB
app01-4651	60	37	that	that	SCONJ
app01-4651	60	38	a	a	DET
app01-4651	60	39	tile	tile	NOUN
app01-4651	60	40	set	set	NOUN
app01-4651	60	41	admits	admit	VERB
app01-4651	60	42	periodic	periodic	ADJ
app01-4651	60	43	tiling	tiling	NOUN
app01-4651	60	44	.	.	PUNCT
app01-4651	61	1	the	the	DET
app01-4651	61	2	relaxations	relaxation	NOUN
app01-4651	61	3	are	be	AUX
app01-4651	61	4	finally	finally	ADV
app01-4651	61	5	employed	employ	VERB
app01-4651	61	6	in	in	ADP
app01-4651	61	7	a	a	DET
app01-4651	61	8	branch	branch	NOUN
app01-4651	61	9	and	and	CCONJ
app01-4651	61	10	bound	bind	VERB
app01-4651	61	11	method	method	NOUN
app01-4651	61	12	in	in	ADP
app01-4651	61	13	section	section	NOUN
app01-4651	61	14	3	3	NUM
app01-4651	61	15	and	and	CCONJ
app01-4651	61	16	their	their	PRON
app01-4651	61	17	performance	performance	NOUN
app01-4651	61	18	is	be	AUX
app01-4651	61	19	assessed	assess	VERB
app01-4651	61	20	in	in	ADP
app01-4651	61	21	section	section	NOUN
app01-4651	61	22	4	4	NUM
app01-4651	61	23	.	.	NOUN
app01-4651	61	24	2	2	NUM
app01-4651	61	25	.	.	X
app01-4651	61	26	optimization	optimization	NOUN
app01-4651	61	27	problem	problem	NOUN
app01-4651	61	28	formulation	formulation	NOUN
app01-4651	61	29	2.1	2.1	NUM
app01-4651	61	30	.	.	PUNCT
app01-4651	62	1	valid	valid	ADJ
app01-4651	62	2	tiling	tiling	NOUN
app01-4651	62	3	consider	consider	VERB
app01-4651	62	4	a	a	DET
app01-4651	62	5	finite	finite	ADJ
app01-4651	62	6	rectangular	rectangular	ADJ
app01-4651	62	7	area	area	NOUN
app01-4651	62	8	a	a	PRON
app01-4651	62	9	of	of	ADP
app01-4651	62	10	the	the	DET
app01-4651	62	11	size	size	NOUN
app01-4651	62	12	nt	not	PART
app01-4651	62	13	,	,	PUNCT
app01-4651	62	14	h×	h×	AUX
app01-4651	62	15	nt	not	PART
app01-4651	62	16	,	,	PUNCT
app01-4651	62	17	w	w	PROPN
app01-4651	62	18	,	,	PUNCT
app01-4651	62	19	with	with	ADP
app01-4651	62	20	nt	not	PART
app01-4651	62	21	,	,	PUNCT
app01-4651	62	22	h	h	NOUN
app01-4651	62	23	and	and	CCONJ
app01-4651	62	24	nt	not	PART
app01-4651	62	25	,	,	PUNCT
app01-4651	62	26	w	w	ADP
app01-4651	62	27	denoting	denote	VERB
app01-4651	62	28	its	its	PRON
app01-4651	62	29	height	height	NOUN
app01-4651	62	30	and	and	CCONJ
app01-4651	62	31	width	width	ADJ
app01-4651	62	32	,	,	PUNCT
app01-4651	62	33	respectively	respectively	ADV
app01-4651	62	34	.	.	PUNCT
app01-4651	63	1	placing	place	VERB
app01-4651	63	2	wang	wang	PROPN
app01-4651	63	3	tiles	tile	NOUN
app01-4651	63	4	(	(	PUNCT
app01-4651	63	5	of	of	ADP
app01-4651	63	6	a	a	DET
app01-4651	63	7	unit	unit	NOUN
app01-4651	63	8	size	size	NOUN
app01-4651	63	9	)	)	PUNCT
app01-4651	63	10	from	from	ADP
app01-4651	63	11	the	the	DET
app01-4651	63	12	tile	tile	NOUN
app01-4651	63	13	set	set	VERB
app01-4651	63	14	t	t	PROPN
app01-4651	63	15	,	,	PUNCT
app01-4651	63	16	such	such	ADJ
app01-4651	63	17	that	that	SCONJ
app01-4651	63	18	their	their	PRON
app01-4651	63	19	vertices	vertex	NOUN
app01-4651	63	20	lie	lie	VERB
app01-4651	63	21	at	at	ADP
app01-4651	63	22	the	the	DET
app01-4651	63	23	integer	integer	NOUN
app01-4651	63	24	lattice	lattice	PROPN
app01-4651	63	25	points	point	NOUN
app01-4651	63	26	of	of	ADP
app01-4651	63	27	a	a	PRON
app01-4651	63	28	,	,	PUNCT
app01-4651	63	29	we	we	PRON
app01-4651	63	30	obtain	obtain	VERB
app01-4651	63	31	a	a	DET
app01-4651	63	32	tiling	tiling	NOUN
app01-4651	63	33	with	with	ADP
app01-4651	63	34	nt	not	PART
app01-4651	63	35	,	,	PUNCT
app01-4651	63	36	h	h	NOUN
app01-4651	63	37	rows	row	NOUN
app01-4651	63	38	and	and	CCONJ
app01-4651	63	39	nt	not	PART
app01-4651	63	40	,	,	PUNCT
app01-4651	63	41	w	w	ADJ
app01-4651	63	42	columns	column	NOUN
app01-4651	63	43	of	of	ADP
app01-4651	63	44	tiles	tile	NOUN
app01-4651	63	45	.	.	PUNCT
app01-4651	64	1	each	each	DET
app01-4651	64	2	tile	tile	NOUN
app01-4651	64	3	k	k	PROPN
app01-4651	64	4	∈	∈	PROPN
app01-4651	64	5	{	{	PUNCT
app01-4651	64	6	1	1	NUM
app01-4651	64	7	,	,	PUNCT
app01-4651	64	8	..	..	PUNCT
app01-4651	64	9	,	,	PUNCT
app01-4651	64	10	nt	not	PART
app01-4651	64	11	}	}	PUNCT
app01-4651	64	12	from	from	ADP
app01-4651	64	13	the	the	DET
app01-4651	64	14	tile	tile	NOUN
app01-4651	64	15	set	set	VERB
app01-4651	64	16	t	t	PROPN
app01-4651	64	17	,	,	PUNCT
app01-4651	64	18	with	with	ADP
app01-4651	64	19	nt	not	PART
app01-4651	64	20	denoting	denote	VERB
app01-4651	64	21	the	the	DET
app01-4651	64	22	number	number	NOUN
app01-4651	64	23	of	of	ADP
app01-4651	64	24	tiles	tile	NOUN
app01-4651	64	25	,	,	PUNCT
app01-4651	64	26	is	be	AUX
app01-4651	64	27	described	describe	VERB
app01-4651	64	28	by	by	ADP
app01-4651	64	29	the	the	DET
app01-4651	64	30	4	4	NUM
app01-4651	64	31	-	-	PUNCT
app01-4651	64	32	tuple	tuple	NOUN
app01-4651	64	33	(	(	PUNCT
app01-4651	64	34	nk	nk	PROPN
app01-4651	64	35	,	,	PUNCT
app01-4651	64	36	wk	wk	PROPN
app01-4651	64	37	,	,	PUNCT
app01-4651	64	38	sk	sk	PROPN
app01-4651	64	39	,	,	PUNCT
app01-4651	64	40	ek	ek	NOUN
app01-4651	64	41	)	)	PUNCT
app01-4651	64	42	,	,	PUNCT
app01-4651	64	43	assigning	assign	VERB
app01-4651	64	44	color	color	NOUN
app01-4651	64	45	codes	code	NOUN
app01-4651	64	46	c	c	NOUN
app01-4651	64	47	to	to	ADP
app01-4651	64	48	the	the	DET
app01-4651	64	49	north	north	NOUN
app01-4651	64	50	,	,	PUNCT
app01-4651	64	51	west	west	NOUN
app01-4651	64	52	,	,	PUNCT
app01-4651	64	53	south	south	ADJ
app01-4651	64	54	,	,	PUNCT
app01-4651	64	55	and	and	CCONJ
app01-4651	64	56	east	east	ADJ
app01-4651	64	57	edge	edge	NOUN
app01-4651	64	58	of	of	ADP
app01-4651	64	59	the	the	DET
app01-4651	64	60	tile	tile	NOUN
app01-4651	64	61	,	,	PUNCT
app01-4651	64	62	respectively	respectively	ADV
app01-4651	64	63	.	.	PUNCT
app01-4651	65	1	in	in	ADP
app01-4651	65	2	any	any	DET
app01-4651	65	3	valid	valid	ADJ
app01-4651	65	4	tiling	tiling	NOUN
app01-4651	65	5	,	,	PUNCT
app01-4651	65	6	for	for	SCONJ
app01-4651	65	7	any	any	DET
app01-4651	65	8	two	two	NUM
app01-4651	65	9	adjacent	adjacent	ADJ
app01-4651	65	10	tiles	tile	NOUN
app01-4651	65	11	k	k	PROPN
app01-4651	65	12	and	and	CCONJ
app01-4651	65	13	`	`	PUNCT
app01-4651	65	14	,	,	PUNCT
app01-4651	65	15	with	with	ADP
app01-4651	65	16	the	the	DET
app01-4651	65	17	tile	tile	NOUN
app01-4651	65	18	`	`	PUNCT
app01-4651	65	19	being	be	AUX
app01-4651	65	20	placed	place	VERB
app01-4651	65	21	in	in	ADP
app01-4651	65	22	the	the	DET
app01-4651	65	23	east	east	NOUN
app01-4651	65	24	of	of	ADP
app01-4651	65	25	k	k	PROPN
app01-4651	65	26	,	,	PUNCT
app01-4651	65	27	it	it	PRON
app01-4651	65	28	holds	hold	VERB
app01-4651	65	29	that	that	SCONJ
app01-4651	65	30	ek	ek	PROPN
app01-4651	65	31	=	=	SYM
app01-4651	65	32	w	w	PROPN
app01-4651	65	33	`	`	PUNCT
app01-4651	65	34	.	.	PUNCT
app01-4651	66	1	(	(	PUNCT
app01-4651	66	2	1	1	X
app01-4651	66	3	)	)	PUNCT
app01-4651	66	4	similarly	similarly	ADV
app01-4651	66	5	,	,	PUNCT
app01-4651	66	6	for	for	ADP
app01-4651	66	7	any	any	DET
app01-4651	66	8	two	two	NUM
app01-4651	66	9	vertically	vertically	ADV
app01-4651	66	10	adjacent	adjacent	ADJ
app01-4651	66	11	tiles	tile	NOUN
app01-4651	66	12	k	k	PROPN
app01-4651	66	13	and	and	CCONJ
app01-4651	66	14	m	m	PROPN
app01-4651	66	15	,	,	PUNCT
app01-4651	66	16	with	with	SCONJ
app01-4651	66	17	the	the	DET
app01-4651	66	18	tile	tile	NOUN
app01-4651	66	19	m	m	AUX
app01-4651	66	20	being	be	AUX
app01-4651	66	21	placed	place	VERB
app01-4651	66	22	in	in	ADP
app01-4651	66	23	the	the	DET
app01-4651	66	24	south	south	NOUN
app01-4651	66	25	of	of	ADP
app01-4651	66	26	k	k	PROPN
app01-4651	66	27	,	,	PUNCT
app01-4651	66	28	it	it	PRON
app01-4651	66	29	stands	stand	VERB
app01-4651	66	30	that	that	SCONJ
app01-4651	66	31	sk	sk	PROPN
app01-4651	66	32	=	=	PROPN
app01-4651	66	33	nm	nm	PROPN
app01-4651	66	34	.	.	PUNCT
app01-4651	67	1	(	(	PUNCT
app01-4651	67	2	2	2	X
app01-4651	67	3	)	)	PUNCT
app01-4651	67	4	both	both	CCONJ
app01-4651	67	5	the	the	DET
app01-4651	67	6	cases	case	NOUN
app01-4651	67	7	are	be	AUX
app01-4651	67	8	illustrated	illustrate	VERB
app01-4651	67	9	in	in	ADP
app01-4651	67	10	fig	fig	NOUN
app01-4651	67	11	.	.	PUNCT
app01-4651	68	1	2	2	NUM
app01-4651	68	2	.	.	NOUN
app01-4651	68	3	136	136	NUM
app01-4651	68	4	vol	vol	NOUN
app01-4651	68	5	.	.	PUNCT
app01-4651	69	1	13/2017	13/2017	NUM
app01-4651	69	2	optimization	optimization	NOUN
app01-4651	69	3	approach	approach	NOUN
app01-4651	69	4	to	to	ADP
app01-4651	69	5	tiling	tile	VERB
app01-4651	69	6	of	of	ADP
app01-4651	69	7	finite	finite	ADJ
app01-4651	69	8	areas	area	NOUN
app01-4651	69	9	with	with	ADP
app01-4651	69	10	wang	wang	PROPN
app01-4651	69	11	tiles	tiles	PROPN
app01-4651	69	12	sm	sm	PROPN
app01-4651	69	13	nm	nm	ADV
app01-4651	69	14	wm	wm	ADP
app01-4651	69	15	em	em	PRON
app01-4651	69	16	s	s	NOUN
app01-4651	69	17	`	`	PUNCT
app01-4651	69	18	n	n	CCONJ
app01-4651	69	19	`	`	PUNCT
app01-4651	69	20	w	w	PROPN
app01-4651	69	21	`	`	PUNCT
app01-4651	69	22	e	e	NOUN
app01-4651	69	23	`	`	PUNCT
app01-4651	69	24	sk	sk	INTJ
app01-4651	69	25	nk	nk	PROPN
app01-4651	69	26	wk	wk	INTJ
app01-4651	69	27	ek	ek	PROPN
app01-4651	69	28	figure	figure	NOUN
app01-4651	69	29	2	2	NUM
app01-4651	69	30	.	.	PUNCT
app01-4651	69	31	horizontal	horizontal	ADJ
app01-4651	69	32	,	,	PUNCT
app01-4651	69	33	and	and	CCONJ
app01-4651	69	34	vertical	vertical	ADJ
app01-4651	69	35	connectivity	connectivity	NOUN
app01-4651	69	36	among	among	ADP
app01-4651	69	37	tiles	tile	NOUN
app01-4651	69	38	k-	k-	X
app01-4651	70	1	`	`	PUNCT
app01-4651	70	2	,	,	PUNCT
app01-4651	70	3	and	and	CCONJ
app01-4651	70	4	k	k	X
app01-4651	70	5	-	-	PUNCT
app01-4651	70	6	m	m	PROPN
app01-4651	70	7	,	,	PUNCT
app01-4651	70	8	respectively	respectively	ADV
app01-4651	70	9	.	.	PUNCT
app01-4651	71	1	2.2	2.2	NUM
app01-4651	71	2	.	.	PUNCT
app01-4651	71	3	binary	binary	PROPN
app01-4651	71	4	linear	linear	PROPN
app01-4651	71	5	programming	programming	NOUN
app01-4651	71	6	formulation	formulation	NOUN
app01-4651	71	7	let	let	VERB
app01-4651	71	8	x	x	PRON
app01-4651	71	9	∈	∈	PROPN
app01-4651	71	10	{	{	PUNCT
app01-4651	71	11	0	0	NUM
app01-4651	71	12	,	,	PUNCT
app01-4651	71	13	1}nt	1}nt	ADJ
app01-4651	71	14	,	,	PUNCT
app01-4651	71	15	h·nt	h·nt	NOUN
app01-4651	71	16	,	,	PUNCT
app01-4651	71	17	w·nt	w·nt	PROPN
app01-4651	71	18	denote	denote	VERB
app01-4651	71	19	a	a	DET
app01-4651	71	20	binary	binary	ADJ
app01-4651	71	21	vector	vector	NOUN
app01-4651	71	22	describing	describe	VERB
app01-4651	71	23	the	the	DET
app01-4651	71	24	placement	placement	NOUN
app01-4651	71	25	of	of	ADP
app01-4651	71	26	individual	individual	ADJ
app01-4651	71	27	tiles	tile	NOUN
app01-4651	71	28	within	within	ADP
app01-4651	71	29	a.	a.	NOUN
app01-4651	71	30	the	the	DET
app01-4651	71	31	vector	vector	NOUN
app01-4651	71	32	consists	consist	VERB
app01-4651	71	33	of	of	ADP
app01-4651	71	34	all	all	DET
app01-4651	71	35	the	the	DET
app01-4651	71	36	xi	xi	PROPN
app01-4651	71	37	,	,	PUNCT
app01-4651	71	38	j	j	PROPN
app01-4651	71	39	,	,	PUNCT
app01-4651	71	40	k	k	PROPN
app01-4651	71	41	variables	variable	NOUN
app01-4651	71	42	,	,	PUNCT
app01-4651	71	43	where	where	SCONJ
app01-4651	71	44	i	i	PRON
app01-4651	71	45	∈	∈	PROPN
app01-4651	71	46	{	{	PUNCT
app01-4651	71	47	1	1	NUM
app01-4651	71	48	,	,	PUNCT
app01-4651	71	49	..	..	PUNCT
app01-4651	71	50	,	,	PUNCT
app01-4651	71	51	nt	not	PART
app01-4651	71	52	,	,	PUNCT
app01-4651	71	53	h	h	NOUN
app01-4651	71	54	}	}	PUNCT
app01-4651	71	55	and	and	CCONJ
app01-4651	71	56	j	j	PROPN
app01-4651	71	57	∈	∈	PROPN
app01-4651	71	58	{	{	PUNCT
app01-4651	71	59	1	1	NUM
app01-4651	71	60	,	,	PUNCT
app01-4651	71	61	..	..	PUNCT
app01-4651	71	62	,	,	PUNCT
app01-4651	71	63	nt	not	PART
app01-4651	71	64	,	,	PUNCT
app01-4651	71	65	w	w	NOUN
app01-4651	71	66	}	}	PUNCT
app01-4651	71	67	are	be	AUX
app01-4651	71	68	the	the	DET
app01-4651	71	69	row	row	NOUN
app01-4651	71	70	and	and	CCONJ
app01-4651	71	71	column	column	NOUN
app01-4651	71	72	iterators	iterator	NOUN
app01-4651	71	73	,	,	PUNCT
app01-4651	71	74	respectively	respectively	ADV
app01-4651	71	75	.	.	PUNCT
app01-4651	72	1	let	let	VERB
app01-4651	72	2	us	we	PRON
app01-4651	72	3	also	also	ADV
app01-4651	72	4	define	define	VERB
app01-4651	72	5	xi	xi	PROPN
app01-4651	72	6	,	,	PUNCT
app01-4651	72	7	j	j	PROPN
app01-4651	72	8	,	,	PUNCT
app01-4651	72	9	k	k	PROPN
app01-4651	73	1	=	=	X
app01-4651	73	2	{	{	PUNCT
app01-4651	73	3	0	0	NUM
app01-4651	73	4	if	if	SCONJ
app01-4651	73	5	the	the	DET
app01-4651	73	6	tile	tile	NOUN
app01-4651	73	7	k	k	PROPN
app01-4651	73	8	is	be	AUX
app01-4651	73	9	not	not	PART
app01-4651	73	10	at	at	ADP
app01-4651	73	11	(	(	PUNCT
app01-4651	73	12	i	i	PROPN
app01-4651	73	13	,	,	PUNCT
app01-4651	73	14	j	j	PROPN
app01-4651	73	15	)	)	PUNCT
app01-4651	73	16	,	,	PUNCT
app01-4651	73	17	1	1	NUM
app01-4651	73	18	if	if	SCONJ
app01-4651	73	19	the	the	DET
app01-4651	73	20	tile	tile	NOUN
app01-4651	73	21	k	k	PROPN
app01-4651	73	22	is	be	AUX
app01-4651	73	23	at	at	ADP
app01-4651	73	24	(	(	PUNCT
app01-4651	73	25	i	i	PROPN
app01-4651	73	26	,	,	PUNCT
app01-4651	73	27	j	j	PROPN
app01-4651	73	28	)	)	PUNCT
app01-4651	73	29	.	.	PUNCT
app01-4651	74	1	(	(	PUNCT
app01-4651	74	2	3	3	X
app01-4651	74	3	)	)	PUNCT
app01-4651	74	4	because	because	SCONJ
app01-4651	74	5	each	each	DET
app01-4651	74	6	position	position	NOUN
app01-4651	74	7	is	be	AUX
app01-4651	74	8	occupied	occupy	VERB
app01-4651	74	9	by	by	ADP
app01-4651	74	10	a	a	DET
app01-4651	74	11	single	single	ADJ
app01-4651	74	12	tile	tile	NOUN
app01-4651	74	13	,	,	PUNCT
app01-4651	74	14	we	we	PRON
app01-4651	74	15	have	have	VERB
app01-4651	74	16	∑	∑	PROPN
app01-4651	74	17	k∈t	k∈t	NOUN
app01-4651	74	18	xi	xi	PROPN
app01-4651	74	19	,	,	PUNCT
app01-4651	74	20	j	j	PROPN
app01-4651	74	21	,	,	PUNCT
app01-4651	74	22	k	k	PROPN
app01-4651	74	23	=	=	SYM
app01-4651	74	24	1	1	NUM
app01-4651	74	25	,	,	PUNCT
app01-4651	74	26	∀i	∀i	NOUN
app01-4651	74	27	∈	∈	NOUN
app01-4651	74	28	h,∀j	h,∀j	PUNCT
app01-4651	74	29	∈	∈	PROPN
app01-4651	74	30	w.	w.	NOUN
app01-4651	74	31	(	(	PUNCT
app01-4651	74	32	4	4	X
app01-4651	74	33	)	)	PUNCT
app01-4651	74	34	the	the	DET
app01-4651	74	35	compatibility	compatibility	NOUN
app01-4651	74	36	constraint	constraint	NOUN
app01-4651	74	37	(	(	PUNCT
app01-4651	74	38	1	1	X
app01-4651	74	39	)	)	PUNCT
app01-4651	74	40	can	can	AUX
app01-4651	74	41	be	be	AUX
app01-4651	74	42	written	write	VERB
app01-4651	74	43	in	in	ADP
app01-4651	74	44	terms	term	NOUN
app01-4651	74	45	of	of	ADP
app01-4651	74	46	x	x	PUNCT
app01-4651	74	47	after	after	ADP
app01-4651	74	48	realizing	realize	VERB
app01-4651	74	49	that	that	SCONJ
app01-4651	74	50	the	the	DET
app01-4651	74	51	number	number	NOUN
app01-4651	74	52	of	of	ADP
app01-4651	74	53	tiles	tile	NOUN
app01-4651	74	54	at	at	ADP
app01-4651	74	55	(	(	PUNCT
app01-4651	74	56	i	i	PROPN
app01-4651	74	57	,	,	PUNCT
app01-4651	74	58	j	j	PROPN
app01-4651	74	59	)	)	PUNCT
app01-4651	74	60	that	that	PRON
app01-4651	74	61	have	have	VERB
app01-4651	74	62	east	east	ADJ
app01-4651	74	63	edge	edge	NOUN
app01-4651	74	64	colored	color	VERB
app01-4651	74	65	by	by	ADP
app01-4651	74	66	c	c	PROPN
app01-4651	74	67	∈	∈	PROPN
app01-4651	74	68	c	c	NOUN
app01-4651	74	69	has	have	VERB
app01-4651	74	70	to	to	PART
app01-4651	74	71	be	be	AUX
app01-4651	74	72	equal	equal	ADJ
app01-4651	74	73	to	to	ADP
app01-4651	74	74	the	the	DET
app01-4651	74	75	number	number	NOUN
app01-4651	74	76	of	of	ADP
app01-4651	74	77	tiles	tile	NOUN
app01-4651	74	78	at	at	ADP
app01-4651	74	79	(	(	PUNCT
app01-4651	74	80	i	i	PROPN
app01-4651	74	81	,	,	PUNCT
app01-4651	74	82	j	j	PROPN
app01-4651	74	83	+	+	PROPN
app01-4651	74	84	1	1	NUM
app01-4651	74	85	)	)	PUNCT
app01-4651	74	86	with	with	ADP
app01-4651	74	87	west	west	ADJ
app01-4651	74	88	edge	edge	NOUN
app01-4651	74	89	colored	color	VERB
app01-4651	74	90	also	also	ADV
app01-4651	74	91	by	by	ADP
app01-4651	74	92	c.	c.	PROPN
app01-4651	74	93	consequently	consequently	ADV
app01-4651	74	94	,	,	PUNCT
app01-4651	74	95	we	we	PRON
app01-4651	74	96	have∑	have∑	VERB
app01-4651	74	97	k∈t	k∈t	NOUN
app01-4651	74	98	xi	xi	PROPN
app01-4651	74	99	,	,	PUNCT
app01-4651	74	100	j	j	PROPN
app01-4651	74	101	,	,	PUNCT
app01-4651	74	102	k[ek	k[ek	NOUN
app01-4651	74	103	=	=	SYM
app01-4651	75	1	c]−	c]−	VERB
app01-4651	75	2	∑	∑	PROPN
app01-4651	75	3	k∈t	k∈t	NOUN
app01-4651	75	4	xi	xi	PROPN
app01-4651	75	5	,	,	PUNCT
app01-4651	75	6	j+1,k[wk	j+1,k[wk	PROPN
app01-4651	76	1	=	=	SYM
app01-4651	76	2	c	c	X
app01-4651	76	3	]	]	X
app01-4651	76	4	=	=	SYM
app01-4651	76	5	0	0	X
app01-4651	76	6	.	.	PUNCT
app01-4651	77	1	(	(	PUNCT
app01-4651	77	2	5	5	NUM
app01-4651	77	3	)	)	PUNCT
app01-4651	77	4	as	as	ADP
app01-4651	77	5	the	the	DET
app01-4651	77	6	sums	sum	NOUN
app01-4651	77	7	in	in	ADP
app01-4651	77	8	eq	eq	ADP
app01-4651	77	9	.	.	PUNCT
app01-4651	78	1	(	(	PUNCT
app01-4651	78	2	5	5	X
app01-4651	78	3	)	)	PUNCT
app01-4651	78	4	are	be	AUX
app01-4651	78	5	either	either	ADV
app01-4651	78	6	equal	equal	ADJ
app01-4651	78	7	to	to	ADP
app01-4651	78	8	0	0	NUM
app01-4651	78	9	or	or	CCONJ
app01-4651	78	10	1	1	NUM
app01-4651	78	11	,	,	PUNCT
app01-4651	78	12	resulting	result	VERB
app01-4651	78	13	from	from	ADP
app01-4651	78	14	eq	eq	ADP
app01-4651	78	15	.	.	PUNCT
app01-4651	79	1	(	(	PUNCT
app01-4651	79	2	4	4	NUM
app01-4651	79	3	)	)	PUNCT
app01-4651	79	4	,	,	PUNCT
app01-4651	79	5	only	only	ADV
app01-4651	79	6	two	two	NUM
app01-4651	79	7	options	option	NOUN
app01-4651	79	8	are	be	AUX
app01-4651	79	9	possible	possible	ADJ
app01-4651	79	10	:	:	PUNCT
app01-4651	79	11	if	if	SCONJ
app01-4651	79	12	the	the	DET
app01-4651	79	13	edge	edge	NOUN
app01-4651	79	14	is	be	AUX
app01-4651	79	15	colored	color	VERB
app01-4651	79	16	by	by	ADP
app01-4651	79	17	c	c	PROPN
app01-4651	79	18	,	,	PUNCT
app01-4651	79	19	the	the	DET
app01-4651	79	20	relation	relation	NOUN
app01-4651	79	21	simplifies	simplifie	NOUN
app01-4651	79	22	to	to	ADP
app01-4651	79	23	1−	1−	NUM
app01-4651	79	24	1	1	NUM
app01-4651	79	25	=	=	SYM
app01-4651	79	26	0	0	NUM
app01-4651	79	27	,	,	PUNCT
app01-4651	79	28	(	(	PUNCT
app01-4651	79	29	6	6	NUM
app01-4651	79	30	)	)	PUNCT
app01-4651	79	31	otherwise	otherwise	ADV
app01-4651	79	32	,	,	PUNCT
app01-4651	79	33	it	it	PRON
app01-4651	79	34	equals	equal	VERB
app01-4651	79	35	to	to	ADP
app01-4651	79	36	0−	0−	NUM
app01-4651	79	37	0	0	NUM
app01-4651	80	1	=	=	SYM
app01-4651	80	2	0	0	NUM
app01-4651	80	3	,	,	PUNCT
app01-4651	80	4	(	(	PUNCT
app01-4651	80	5	7	7	X
app01-4651	80	6	)	)	PUNCT
app01-4651	80	7	showing	show	VERB
app01-4651	80	8	that	that	SCONJ
app01-4651	80	9	(	(	PUNCT
app01-4651	80	10	5	5	X
app01-4651	80	11	)	)	PUNCT
app01-4651	80	12	remains	remain	VERB
app01-4651	80	13	valid	valid	ADJ
app01-4651	80	14	in	in	ADP
app01-4651	80	15	both	both	DET
app01-4651	80	16	cases	case	NOUN
app01-4651	80	17	.	.	PUNCT
app01-4651	81	1	after	after	ADP
app01-4651	81	2	applying	apply	VERB
app01-4651	81	3	the	the	DET
app01-4651	81	4	same	same	ADJ
app01-4651	81	5	approach	approach	NOUN
app01-4651	81	6	to	to	ADP
app01-4651	81	7	eq	eq	PROPN
app01-4651	81	8	.	.	PUNCT
app01-4651	82	1	(	(	PUNCT
app01-4651	82	2	2	2	NUM
app01-4651	82	3	)	)	PUNCT
app01-4651	83	1	and	and	CCONJ
app01-4651	83	2	writing	write	VERB
app01-4651	83	3	constraints	constraint	NOUN
app01-4651	83	4	through	through	ADP
app01-4651	83	5	the	the	DET
app01-4651	83	6	entire	entire	ADJ
app01-4651	83	7	area	area	NOUN
app01-4651	83	8	a	a	PRON
app01-4651	83	9	,	,	PUNCT
app01-4651	83	10	we	we	PRON
app01-4651	83	11	obtain	obtain	VERB
app01-4651	83	12	the	the	DET
app01-4651	83	13	following	follow	VERB
app01-4651	83	14	binary	binary	PROPN
app01-4651	83	15	linear	linear	PROPN
app01-4651	83	16	program	program	NOUN
app01-4651	83	17	:	:	PUNCT
app01-4651	84	1	min	min	NOUN
app01-4651	84	2	x	x	SYM
app01-4651	84	3	0	0	NUM
app01-4651	84	4	(	(	PUNCT
app01-4651	84	5	8a	8a	NUM
app01-4651	84	6	)	)	PUNCT
app01-4651	84	7	s.t	s.t	PROPN
app01-4651	84	8	.	.	PUNCT
app01-4651	84	9	∑	∑	PROPN
app01-4651	84	10	k∈t	k∈t	PROPN
app01-4651	84	11	xi	xi	PROPN
app01-4651	84	12	,	,	PUNCT
app01-4651	84	13	j	j	PROPN
app01-4651	84	14	,	,	PUNCT
app01-4651	84	15	k[ek	k[ek	NOUN
app01-4651	84	16	=	=	SYM
app01-4651	84	17	c]−	c]−	VERB
app01-4651	84	18	∑	∑	PROPN
app01-4651	84	19	k∈t	k∈t	NOUN
app01-4651	84	20	xi	xi	PROPN
app01-4651	84	21	,	,	PUNCT
app01-4651	84	22	j+1,k[wk	j+1,k[wk	PROPN
app01-4651	84	23	=	=	SYM
app01-4651	84	24	c	c	X
app01-4651	84	25	]	]	X
app01-4651	84	26	=	=	SYM
app01-4651	84	27	0	0	NUM
app01-4651	84	28	,	,	PUNCT
app01-4651	84	29	∀c	∀c	VERB
app01-4651	84	30	∈	∈	PROPN
app01-4651	84	31	c,∀i	c,∀i	ADP
app01-4651	84	32	∈	∈	PROPN
app01-4651	84	33	h,∀j	h,∀j	PUNCT
app01-4651	84	34	∈	∈	PROPN
app01-4651	84	35	w	w	PROPN
app01-4651	84	36	\	\	PROPN
app01-4651	84	37	{	{	PUNCT
app01-4651	84	38	nt	nt	INTJ
app01-4651	84	39	,	,	PUNCT
app01-4651	84	40	w	w	NOUN
app01-4651	84	41	}	}	PUNCT
app01-4651	84	42	,	,	PUNCT
app01-4651	84	43	(	(	PUNCT
app01-4651	84	44	8b	8b	NUM
app01-4651	84	45	)	)	PUNCT
app01-4651	84	46	∑	∑	PROPN
app01-4651	84	47	k∈t	k∈t	PROPN
app01-4651	84	48	xi	xi	PROPN
app01-4651	84	49	,	,	PUNCT
app01-4651	84	50	j	j	PROPN
app01-4651	84	51	,	,	PUNCT
app01-4651	84	52	k[sk	k[sk	NOUN
app01-4651	84	53	=	=	SYM
app01-4651	84	54	c]−	c]−	VERB
app01-4651	84	55	∑	∑	PROPN
app01-4651	84	56	k∈t	k∈t	NOUN
app01-4651	84	57	xi+1,j	xi+1,j	PROPN
app01-4651	84	58	,	,	PUNCT
app01-4651	84	59	k[nk	k[nk	PROPN
app01-4651	84	60	=	=	SYM
app01-4651	84	61	c	c	X
app01-4651	84	62	]	]	X
app01-4651	84	63	=	=	SYM
app01-4651	84	64	0	0	NUM
app01-4651	84	65	,	,	PUNCT
app01-4651	84	66	∀c	∀c	X
app01-4651	84	67	∈	∈	PROPN
app01-4651	84	68	c,∀j	c,∀j	X
app01-4651	84	69	∈	∈	PROPN
app01-4651	84	70	w,∀i	w,∀i	PROPN
app01-4651	84	71	∈	∈	PROPN
app01-4651	84	72	h	h	NOUN
app01-4651	84	73	\	\	PUNCT
app01-4651	84	74	{	{	PUNCT
app01-4651	84	75	nt	nt	INTJ
app01-4651	84	76	,	,	PUNCT
app01-4651	84	77	h	h	NOUN
app01-4651	84	78	}	}	PUNCT
app01-4651	84	79	,	,	PUNCT
app01-4651	84	80	(	(	PUNCT
app01-4651	84	81	8c	8c	X
app01-4651	84	82	)	)	PUNCT
app01-4651	84	83	∑	∑	PUNCT
app01-4651	84	84	k∈t	k∈t	NOUN
app01-4651	84	85	xi	xi	PROPN
app01-4651	84	86	,	,	PUNCT
app01-4651	84	87	j	j	PROPN
app01-4651	84	88	,	,	PUNCT
app01-4651	84	89	k	k	PROPN
app01-4651	84	90	=	=	SYM
app01-4651	84	91	1	1	NUM
app01-4651	84	92	,	,	PUNCT
app01-4651	84	93	∀i	∀i	NOUN
app01-4651	84	94	∈	∈	NOUN
app01-4651	84	95	h,∀j	h,∀j	PUNCT
app01-4651	84	96	∈	∈	PROPN
app01-4651	84	97	w	w	PROPN
app01-4651	84	98	,	,	PUNCT
app01-4651	84	99	(	(	PUNCT
app01-4651	84	100	8d	8d	NUM
app01-4651	84	101	)	)	PUNCT
app01-4651	84	102	xi	xi	PROPN
app01-4651	84	103	,	,	PUNCT
app01-4651	84	104	j	j	PROPN
app01-4651	84	105	,	,	PUNCT
app01-4651	84	106	k	k	PROPN
app01-4651	84	107	∈	∈	PROPN
app01-4651	84	108	{	{	PUNCT
app01-4651	84	109	0	0	NUM
app01-4651	84	110	,	,	PUNCT
app01-4651	84	111	1	1	NUM
app01-4651	84	112	}	}	PUNCT
app01-4651	84	113	,	,	PUNCT
app01-4651	84	114	∀i	∀i	NOUN
app01-4651	84	115	∈	∈	NOUN
app01-4651	84	116	h,∀j	h,∀j	PUNCT
app01-4651	84	117	∈	∈	PROPN
app01-4651	84	118	w,∀k	w,∀k	PROPN
app01-4651	84	119	∈	∈	PROPN
app01-4651	84	120	t	t	PROPN
app01-4651	84	121	.	.	PUNCT
app01-4651	85	1	(	(	PUNCT
app01-4651	85	2	8e	8e	NUM
app01-4651	85	3	)	)	PUNCT
app01-4651	85	4	despite	despite	SCONJ
app01-4651	85	5	the	the	DET
app01-4651	85	6	program	program	NOUN
app01-4651	85	7	(	(	PUNCT
app01-4651	85	8	8)	8)	NUM
app01-4651	85	9	being	be	AUX
app01-4651	85	10	formulated	formulate	VERB
app01-4651	85	11	straightforwardly	straightforwardly	ADV
app01-4651	85	12	,	,	PUNCT
app01-4651	85	13	it	it	PRON
app01-4651	85	14	is	be	AUX
app01-4651	85	15	hard	hard	ADJ
app01-4651	85	16	to	to	PART
app01-4651	85	17	solve	solve	VERB
app01-4651	85	18	in	in	ADP
app01-4651	85	19	this	this	DET
app01-4651	85	20	original	original	ADJ
app01-4651	85	21	form	form	NOUN
app01-4651	85	22	due	due	ADP
app01-4651	85	23	to	to	ADP
app01-4651	85	24	the	the	DET
app01-4651	85	25	(	(	PUNCT
app01-4651	85	26	non	non	ADJ
app01-4651	85	27	-	-	ADJ
app01-4651	85	28	convex	convex	ADJ
app01-4651	85	29	)	)	PUNCT
app01-4651	85	30	integrality	integrality	NOUN
app01-4651	85	31	constraint	constraint	NOUN
app01-4651	85	32	(	(	PUNCT
app01-4651	85	33	8e	8e	NUM
app01-4651	85	34	)	)	PUNCT
app01-4651	85	35	.	.	PUNCT
app01-4651	86	1	note	note	VERB
app01-4651	86	2	that	that	SCONJ
app01-4651	86	3	the	the	DET
app01-4651	86	4	problem	problem	NOUN
app01-4651	86	5	is	be	AUX
app01-4651	86	6	np	np	INTJ
app01-4651	86	7	-	-	PUNCT
app01-4651	86	8	complete	complete	ADJ
app01-4651	86	9	because	because	SCONJ
app01-4651	86	10	of	of	ADP
app01-4651	86	11	its	its	PRON
app01-4651	86	12	combinatorial	combinatorial	ADJ
app01-4651	86	13	nature	nature	NOUN
app01-4651	87	1	[	[	X
app01-4651	87	2	31	31	NUM
app01-4651	87	3	]	]	PUNCT
app01-4651	87	4	.	.	PUNCT
app01-4651	88	1	2.3	2.3	NUM
app01-4651	88	2	.	.	PUNCT
app01-4651	89	1	linear	linear	ADJ
app01-4651	89	2	programming	programming	NOUN
app01-4651	89	3	relaxation	relaxation	NOUN
app01-4651	89	4	in	in	ADP
app01-4651	89	5	order	order	NOUN
app01-4651	89	6	to	to	PART
app01-4651	89	7	make	make	VERB
app01-4651	89	8	the	the	DET
app01-4651	89	9	problem	problem	NOUN
app01-4651	89	10	(	(	PUNCT
app01-4651	89	11	8)	8)	NOUN
app01-4651	89	12	easier	easy	ADJ
app01-4651	89	13	to	to	PART
app01-4651	89	14	solve	solve	VERB
app01-4651	89	15	,	,	PUNCT
app01-4651	89	16	let	let	VERB
app01-4651	89	17	us	we	PRON
app01-4651	89	18	relax	relax	VERB
app01-4651	89	19	the	the	DET
app01-4651	89	20	integrality	integrality	NOUN
app01-4651	89	21	constraint	constraint	NOUN
app01-4651	89	22	(	(	PUNCT
app01-4651	89	23	8e	8e	NUM
app01-4651	89	24	)	)	PUNCT
app01-4651	89	25	into	into	ADP
app01-4651	89	26	a	a	DET
app01-4651	89	27	linear	linear	ADJ
app01-4651	89	28	form	form	NOUN
app01-4651	89	29	0	0	NUM
app01-4651	89	30	≤	≤	NUM
app01-4651	89	31	xi	xi	PROPN
app01-4651	89	32	,	,	PUNCT
app01-4651	89	33	j	j	PROPN
app01-4651	89	34	,	,	PUNCT
app01-4651	89	35	k	k	PROPN
app01-4651	89	36	≤	≤	PROPN
app01-4651	89	37	1	1	NUM
app01-4651	89	38	,	,	PUNCT
app01-4651	89	39	∀i	∀i	NOUN
app01-4651	89	40	∈	∈	NOUN
app01-4651	89	41	h,∀j	h,∀j	PUNCT
app01-4651	89	42	∈	∈	PROPN
app01-4651	89	43	w,∀k	w,∀k	PROPN
app01-4651	89	44	∈	∈	PROPN
app01-4651	89	45	t	t	PROPN
app01-4651	89	46	.	.	PUNCT
app01-4651	90	1	(	(	PUNCT
app01-4651	90	2	9	9	X
app01-4651	90	3	)	)	PUNCT
app01-4651	90	4	clearly	clearly	ADV
app01-4651	90	5	,	,	PUNCT
app01-4651	90	6	eq	eq	ADJ
app01-4651	90	7	.	.	PUNCT
app01-4651	91	1	(	(	PUNCT
app01-4651	91	2	9	9	X
app01-4651	91	3	)	)	PUNCT
app01-4651	91	4	allows	allow	VERB
app01-4651	91	5	for	for	ADP
app01-4651	91	6	all	all	DET
app01-4651	91	7	configurations	configuration	NOUN
app01-4651	91	8	of	of	ADP
app01-4651	91	9	(	(	PUNCT
app01-4651	91	10	8e	8e	NUM
app01-4651	91	11	)	)	PUNCT
app01-4651	91	12	,	,	PUNCT
app01-4651	91	13	but	but	CCONJ
app01-4651	91	14	additionally	additionally	ADV
app01-4651	91	15	also	also	ADV
app01-4651	91	16	intermediate	intermediate	ADJ
app01-4651	91	17	non	non	ADJ
app01-4651	91	18	-	-	ADJ
app01-4651	91	19	binary	binary	ADJ
app01-4651	91	20	values	value	NOUN
app01-4651	91	21	.	.	PUNCT
app01-4651	92	1	in	in	ADP
app01-4651	92	2	addition	addition	NOUN
app01-4651	92	3	,	,	PUNCT
app01-4651	92	4	because	because	SCONJ
app01-4651	92	5	the	the	DET
app01-4651	92	6	constraints	constraint	NOUN
app01-4651	92	7	in	in	ADP
app01-4651	92	8	(	(	PUNCT
app01-4651	92	9	8)	8)	NUM
app01-4651	92	10	are	be	AUX
app01-4651	92	11	linear	linear	ADJ
app01-4651	92	12	,	,	PUNCT
app01-4651	92	13	the	the	DET
app01-4651	92	14	resulting	result	VERB
app01-4651	92	15	approximation	approximation	NOUN
app01-4651	92	16	is	be	AUX
app01-4651	92	17	convex	convex	ADJ
app01-4651	92	18	and	and	CCONJ
app01-4651	92	19	reads	read	VERB
app01-4651	92	20	as	as	ADP
app01-4651	92	21	min	min	NOUN
app01-4651	92	22	x	x	SYM
app01-4651	92	23	0	0	NUM
app01-4651	92	24	(	(	PUNCT
app01-4651	92	25	10a	10a	NUM
app01-4651	92	26	)	)	PUNCT
app01-4651	92	27	s.t	s.t	PROPN
app01-4651	92	28	.	.	PUNCT
app01-4651	92	29	∑	∑	PROPN
app01-4651	92	30	k∈t	k∈t	PROPN
app01-4651	92	31	xi	xi	PROPN
app01-4651	92	32	,	,	PUNCT
app01-4651	92	33	j	j	PROPN
app01-4651	92	34	,	,	PUNCT
app01-4651	92	35	k[ek	k[ek	NOUN
app01-4651	92	36	=	=	SYM
app01-4651	92	37	c]−	c]−	VERB
app01-4651	92	38	∑	∑	PROPN
app01-4651	92	39	k∈t	k∈t	NOUN
app01-4651	92	40	xi	xi	PROPN
app01-4651	92	41	,	,	PUNCT
app01-4651	92	42	j+1,k[wk	j+1,k[wk	PROPN
app01-4651	93	1	=	=	SYM
app01-4651	93	2	c	c	X
app01-4651	93	3	]	]	X
app01-4651	93	4	=	=	SYM
app01-4651	93	5	0	0	NUM
app01-4651	93	6	,	,	PUNCT
app01-4651	93	7	∀c	∀c	VERB
app01-4651	93	8	∈	∈	PROPN
app01-4651	93	9	c,∀i	c,∀i	ADP
app01-4651	93	10	∈	∈	PROPN
app01-4651	93	11	h,∀j	h,∀j	PUNCT
app01-4651	93	12	∈	∈	PROPN
app01-4651	93	13	w	w	PROPN
app01-4651	93	14	\	\	PROPN
app01-4651	93	15	{	{	PUNCT
app01-4651	93	16	nt	nt	INTJ
app01-4651	93	17	,	,	PUNCT
app01-4651	93	18	w	w	NOUN
app01-4651	93	19	}	}	PUNCT
app01-4651	93	20	,	,	PUNCT
app01-4651	93	21	(	(	PUNCT
app01-4651	93	22	10b	10b	NOUN
app01-4651	93	23	)	)	PUNCT
app01-4651	93	24	∑	∑	PUNCT
app01-4651	93	25	k∈t	k∈t	NOUN
app01-4651	93	26	xi	xi	PROPN
app01-4651	93	27	,	,	PUNCT
app01-4651	93	28	j	j	PROPN
app01-4651	93	29	,	,	PUNCT
app01-4651	93	30	k[sk	k[sk	NOUN
app01-4651	93	31	=	=	SYM
app01-4651	93	32	c]−	c]−	VERB
app01-4651	93	33	∑	∑	PROPN
app01-4651	93	34	k∈t	k∈t	NOUN
app01-4651	93	35	xi+1,j	xi+1,j	PROPN
app01-4651	93	36	,	,	PUNCT
app01-4651	93	37	k[nk	k[nk	PROPN
app01-4651	93	38	=	=	SYM
app01-4651	93	39	c	c	X
app01-4651	93	40	]	]	X
app01-4651	93	41	=	=	SYM
app01-4651	93	42	0	0	NUM
app01-4651	93	43	,	,	PUNCT
app01-4651	93	44	∀c	∀c	X
app01-4651	93	45	∈	∈	PROPN
app01-4651	93	46	c,∀j	c,∀j	X
app01-4651	93	47	∈	∈	PROPN
app01-4651	93	48	w,∀i	w,∀i	PROPN
app01-4651	93	49	∈	∈	PROPN
app01-4651	93	50	h	h	NOUN
app01-4651	93	51	\	\	PUNCT
app01-4651	93	52	{	{	PUNCT
app01-4651	93	53	nt	nt	INTJ
app01-4651	93	54	,	,	PUNCT
app01-4651	93	55	h	h	NOUN
app01-4651	93	56	}	}	PUNCT
app01-4651	93	57	,	,	PUNCT
app01-4651	93	58	(	(	PUNCT
app01-4651	93	59	10c	10c	NOUN
app01-4651	93	60	)	)	PUNCT
app01-4651	93	61	∑	∑	PUNCT
app01-4651	93	62	k∈t	k∈t	NOUN
app01-4651	93	63	xi	xi	PROPN
app01-4651	93	64	,	,	PUNCT
app01-4651	93	65	j	j	PROPN
app01-4651	93	66	,	,	PUNCT
app01-4651	93	67	k	k	PROPN
app01-4651	93	68	=	=	SYM
app01-4651	93	69	1	1	NUM
app01-4651	93	70	,	,	PUNCT
app01-4651	93	71	∀i	∀i	NOUN
app01-4651	93	72	∈	∈	NOUN
app01-4651	93	73	h,∀j	h,∀j	PUNCT
app01-4651	93	74	∈	∈	PROPN
app01-4651	93	75	w	w	PROPN
app01-4651	93	76	,	,	PUNCT
app01-4651	93	77	(	(	PUNCT
app01-4651	93	78	10d	10d	NUM
app01-4651	93	79	)	)	PUNCT
app01-4651	93	80	0	0	NUM
app01-4651	94	1	≤	≤	NUM
app01-4651	94	2	xi	xi	PROPN
app01-4651	94	3	,	,	PUNCT
app01-4651	94	4	j	j	PROPN
app01-4651	94	5	,	,	PUNCT
app01-4651	94	6	k	k	PROPN
app01-4651	94	7	≤	≤	PROPN
app01-4651	94	8	1	1	NUM
app01-4651	94	9	,	,	PUNCT
app01-4651	94	10	∀i	∀i	NOUN
app01-4651	94	11	∈	∈	NOUN
app01-4651	94	12	h,∀j	h,∀j	PUNCT
app01-4651	94	13	∈	∈	PROPN
app01-4651	94	14	w,∀k	w,∀k	PROPN
app01-4651	94	15	∈	∈	PROPN
app01-4651	94	16	t	t	PROPN
app01-4651	94	17	.	.	PUNCT
app01-4651	95	1	(	(	PUNCT
app01-4651	95	2	10e	10e	NOUN
app01-4651	95	3	)	)	PUNCT
app01-4651	95	4	2.4	2.4	NUM
app01-4651	95	5	.	.	PUNCT
app01-4651	96	1	semidefinite	semidefinite	PROPN
app01-4651	96	2	programming	programming	PROPN
app01-4651	96	3	relaxation	relaxation	NOUN
app01-4651	96	4	the	the	DET
app01-4651	96	5	integrality	integrality	NOUN
app01-4651	96	6	constraint	constraint	NOUN
app01-4651	96	7	(	(	PUNCT
app01-4651	96	8	8e	8e	NUM
app01-4651	96	9	)	)	PUNCT
app01-4651	96	10	can	can	AUX
app01-4651	96	11	be	be	AUX
app01-4651	96	12	rewritten	rewrite	VERB
app01-4651	96	13	using	use	VERB
app01-4651	96	14	the	the	DET
app01-4651	96	15	non	non	ADJ
app01-4651	96	16	-	-	ADJ
app01-4651	96	17	convex	convex	ADJ
app01-4651	96	18	quadratic	quadratic	ADJ
app01-4651	96	19	constraint	constraint	NOUN
app01-4651	97	1	x2	x2	INTJ
app01-4651	97	2	i	i	PROPN
app01-4651	97	3	,	,	PUNCT
app01-4651	97	4	j	j	PROPN
app01-4651	97	5	,	,	PUNCT
app01-4651	97	6	k	k	PROPN
app01-4651	97	7	−	−	PROPN
app01-4651	98	1	xi	xi	PROPN
app01-4651	98	2	,	,	PUNCT
app01-4651	98	3	j	j	PROPN
app01-4651	98	4	,	,	PUNCT
app01-4651	98	5	k	k	PROPN
app01-4651	98	6	=	=	SYM
app01-4651	98	7	0	0	NUM
app01-4651	98	8	,	,	PUNCT
app01-4651	98	9	∀i	∀i	X
app01-4651	98	10	∈	∈	NOUN
app01-4651	98	11	h,∀j	h,∀j	PUNCT
app01-4651	98	12	∈	∈	PROPN
app01-4651	98	13	w,∀k	w,∀k	PROPN
app01-4651	98	14	∈	∈	PROPN
app01-4651	98	15	t	t	PROPN
app01-4651	98	16	,	,	PUNCT
app01-4651	98	17	(	(	PUNCT
app01-4651	98	18	11	11	NUM
app01-4651	98	19	)	)	PUNCT
app01-4651	98	20	which	which	PRON
app01-4651	98	21	is	be	AUX
app01-4651	98	22	satisfied	satisfied	ADJ
app01-4651	98	23	only	only	ADV
app01-4651	98	24	if	if	SCONJ
app01-4651	98	25	xi	xi	PROPN
app01-4651	98	26	,	,	PUNCT
app01-4651	98	27	j	j	PROPN
app01-4651	98	28	,	,	PUNCT
app01-4651	98	29	k	k	PROPN
app01-4651	98	30	=	=	X
app01-4651	98	31	{	{	PUNCT
app01-4651	98	32	0	0	NUM
app01-4651	98	33	,	,	PUNCT
app01-4651	98	34	1	1	NUM
app01-4651	98	35	}	}	PUNCT
app01-4651	98	36	,	,	PUNCT
app01-4651	98	37	being	be	AUX
app01-4651	98	38	thus	thus	ADV
app01-4651	98	39	equivalent	equivalent	ADJ
app01-4651	98	40	to	to	ADP
app01-4651	98	41	(	(	PUNCT
app01-4651	98	42	8e	8e	NUM
app01-4651	98	43	)	)	PUNCT
app01-4651	98	44	.	.	PUNCT
app01-4651	99	1	this	this	DET
app01-4651	99	2	quadratic	quadratic	ADJ
app01-4651	99	3	form	form	NOUN
app01-4651	99	4	does	do	AUX
app01-4651	99	5	not	not	PART
app01-4651	99	6	simplify	simplify	VERB
app01-4651	99	7	the	the	DET
app01-4651	99	8	solution	solution	NOUN
app01-4651	99	9	,	,	PUNCT
app01-4651	99	10	because	because	SCONJ
app01-4651	99	11	the	the	DET
app01-4651	99	12	problem	problem	NOUN
app01-4651	99	13	is	be	AUX
app01-4651	99	14	still	still	ADV
app01-4651	99	15	np	np	NOUN
app01-4651	99	16	-	-	NOUN
app01-4651	99	17	complete	complete	ADJ
app01-4651	99	18	,	,	PUNCT
app01-4651	99	19	but	but	CCONJ
app01-4651	99	20	we	we	PRON
app01-4651	99	21	will	will	AUX
app01-4651	99	22	use	use	VERB
app01-4651	99	23	it	it	PRON
app01-4651	99	24	for	for	ADP
app01-4651	99	25	the	the	DET
app01-4651	99	26	derivation	derivation	NOUN
app01-4651	99	27	of	of	ADP
app01-4651	99	28	a	a	DET
app01-4651	99	29	semidefinite	semidefinite	NOUN
app01-4651	99	30	programming	programming	NOUN
app01-4651	99	31	relaxation	relaxation	NOUN
app01-4651	99	32	.	.	PUNCT
app01-4651	100	1	let	let	VERB
app01-4651	100	2	us	we	PRON
app01-4651	100	3	now	now	ADV
app01-4651	100	4	substitute	substitute	VERB
app01-4651	100	5	the	the	DET
app01-4651	100	6	binary	binary	ADJ
app01-4651	100	7	variables	variable	NOUN
app01-4651	100	8	x	x	PUNCT
app01-4651	100	9	∈	∈	NOUN
app01-4651	100	10	{	{	PUNCT
app01-4651	100	11	0	0	NUM
app01-4651	100	12	,	,	PUNCT
app01-4651	100	13	1	1	NUM
app01-4651	100	14	}	}	PUNCT
app01-4651	100	15	with	with	ADP
app01-4651	100	16	y	y	PROPN
app01-4651	100	17	∈	∈	PROPN
app01-4651	100	18	{	{	PUNCT
app01-4651	100	19	−1	−1	NOUN
app01-4651	100	20	,	,	PUNCT
app01-4651	100	21	1	1	NUM
app01-4651	100	22	}	}	PUNCT
app01-4651	100	23	,	,	PUNCT
app01-4651	100	24	which	which	PRON
app01-4651	100	25	requires	require	VERB
app01-4651	100	26	x	x	X
app01-4651	100	27	=	=	SYM
app01-4651	100	28	1	1	NUM
app01-4651	100	29	2(y	2(y	NUM
app01-4651	100	30	+	+	CCONJ
app01-4651	100	31	1	1	NUM
app01-4651	100	32	)	)	PUNCT
app01-4651	100	33	.	.	PUNCT
app01-4651	101	1	(	(	PUNCT
app01-4651	101	2	12	12	X
app01-4651	101	3	)	)	PUNCT
app01-4651	101	4	inserting	insert	VERB
app01-4651	101	5	this	this	PRON
app01-4651	101	6	into	into	ADP
app01-4651	101	7	eq	eq	NOUN
app01-4651	101	8	.	.	PUNCT
app01-4651	102	1	(	(	PUNCT
app01-4651	102	2	3	3	X
app01-4651	102	3	)	)	PUNCT
app01-4651	102	4	yields	yield	VERB
app01-4651	102	5	yi	yi	PROPN
app01-4651	102	6	,	,	PUNCT
app01-4651	102	7	j	j	PROPN
app01-4651	102	8	,	,	PUNCT
app01-4651	102	9	k	k	PROPN
app01-4651	103	1	=	=	PRON
app01-4651	104	1	{	{	PUNCT
app01-4651	104	2	−1	−1	NOUN
app01-4651	104	3	if	if	SCONJ
app01-4651	104	4	the	the	DET
app01-4651	104	5	tile	tile	NOUN
app01-4651	104	6	k	k	PROPN
app01-4651	104	7	is	be	AUX
app01-4651	104	8	not	not	PART
app01-4651	104	9	at	at	ADP
app01-4651	104	10	(	(	PUNCT
app01-4651	104	11	i	i	PROPN
app01-4651	104	12	,	,	PUNCT
app01-4651	104	13	j	j	PROPN
app01-4651	104	14	)	)	PUNCT
app01-4651	104	15	,	,	PUNCT
app01-4651	104	16	1	1	NUM
app01-4651	104	17	if	if	SCONJ
app01-4651	104	18	the	the	DET
app01-4651	104	19	tile	tile	NOUN
app01-4651	104	20	k	k	PROPN
app01-4651	104	21	is	be	AUX
app01-4651	104	22	at	at	ADP
app01-4651	104	23	(	(	PUNCT
app01-4651	104	24	i	i	PROPN
app01-4651	104	25	,	,	PUNCT
app01-4651	104	26	j	j	PROPN
app01-4651	104	27	)	)	PUNCT
app01-4651	104	28	.	.	PUNCT
app01-4651	105	1	(	(	PUNCT
app01-4651	105	2	13	13	NUM
app01-4651	105	3	)	)	PUNCT
app01-4651	105	4	consequently	consequently	ADV
app01-4651	105	5	,	,	PUNCT
app01-4651	105	6	we	we	PRON
app01-4651	105	7	can	can	AUX
app01-4651	105	8	write	write	VERB
app01-4651	105	9	a	a	DET
app01-4651	105	10	non	non	ADJ
app01-4651	105	11	-	-	ADJ
app01-4651	105	12	convex	convex	ADJ
app01-4651	105	13	quadratically	quadratically	ADV
app01-4651	105	14	-	-	PUNCT
app01-4651	105	15	constrained	constrain	VERB
app01-4651	105	16	optimization	optimization	NOUN
app01-4651	105	17	program	program	NOUN
app01-4651	105	18	in	in	ADP
app01-4651	105	19	terms	term	NOUN
app01-4651	105	20	of	of	ADP
app01-4651	105	21	y	y	PROPN
app01-4651	105	22	137	137	NUM
app01-4651	105	23	marek	marek	PROPN
app01-4651	105	24	tyburec	tyburec	NOUN
app01-4651	105	25	,	,	PUNCT
app01-4651	105	26	jan	jan	PROPN
app01-4651	105	27	zeman	zeman	PROPN
app01-4651	105	28	acta	acta	PROPN
app01-4651	105	29	polytechnica	polytechnica	PROPN
app01-4651	105	30	ctu	ctu	PROPN
app01-4651	105	31	proceedings	proceeding	NOUN
app01-4651	105	32	min	min	VERB
app01-4651	106	1	y	y	PROPN
app01-4651	106	2	0	0	NUM
app01-4651	106	3	(	(	PUNCT
app01-4651	106	4	14a	14a	NOUN
app01-4651	106	5	)	)	PUNCT
app01-4651	106	6	s.t	s.t	PROPN
app01-4651	106	7	.	.	PROPN
app01-4651	106	8	∑	∑	PROPN
app01-4651	106	9	k∈t	k∈t	NOUN
app01-4651	106	10	(	(	PUNCT
app01-4651	106	11	yi	yi	PROPN
app01-4651	106	12	,	,	PUNCT
app01-4651	106	13	j	j	PROPN
app01-4651	106	14	,	,	PUNCT
app01-4651	106	15	k	k	PROPN
app01-4651	106	16	+	+	PROPN
app01-4651	106	17	1)[ek	1)[ek	NUM
app01-4651	106	18	=	=	SYM
app01-4651	106	19	c	c	X
app01-4651	106	20	]	]	X
app01-4651	106	21	−	−	PROPN
app01-4651	106	22	∑	∑	PROPN
app01-4651	106	23	k∈t	k∈t	NOUN
app01-4651	106	24	(	(	PUNCT
app01-4651	106	25	yi	yi	PROPN
app01-4651	106	26	,	,	PUNCT
app01-4651	106	27	j+1,k	j+1,k	PROPN
app01-4651	106	28	+	+	CCONJ
app01-4651	106	29	1)[wk	1)[wk	NUM
app01-4651	106	30	=	=	SYM
app01-4651	106	31	c	c	X
app01-4651	106	32	]	]	X
app01-4651	106	33	=	=	SYM
app01-4651	106	34	0	0	NUM
app01-4651	106	35	,	,	PUNCT
app01-4651	106	36	∀c	∀c	VERB
app01-4651	106	37	∈	∈	PROPN
app01-4651	106	38	c,∀i	c,∀i	ADP
app01-4651	106	39	∈	∈	PROPN
app01-4651	106	40	h,∀j	h,∀j	PUNCT
app01-4651	106	41	∈	∈	PROPN
app01-4651	106	42	w	w	PROPN
app01-4651	106	43	\	\	PROPN
app01-4651	106	44	{	{	PUNCT
app01-4651	106	45	nt	nt	INTJ
app01-4651	106	46	,	,	PUNCT
app01-4651	106	47	w	w	NOUN
app01-4651	106	48	}	}	PUNCT
app01-4651	106	49	,	,	PUNCT
app01-4651	106	50	(	(	PUNCT
app01-4651	106	51	14b	14b	NUM
app01-4651	106	52	)	)	PUNCT
app01-4651	106	53	∑	∑	PUNCT
app01-4651	106	54	k∈t	k∈t	NOUN
app01-4651	106	55	(	(	PUNCT
app01-4651	106	56	yi	yi	PROPN
app01-4651	106	57	,	,	PUNCT
app01-4651	106	58	j	j	PROPN
app01-4651	106	59	,	,	PUNCT
app01-4651	106	60	k	k	PROPN
app01-4651	107	1	+	+	PROPN
app01-4651	107	2	1)[sk	1)[sk	NUM
app01-4651	107	3	=	=	SYM
app01-4651	107	4	c	c	X
app01-4651	107	5	]	]	X
app01-4651	107	6	−	−	PROPN
app01-4651	107	7	∑	∑	PROPN
app01-4651	107	8	k∈t	k∈t	NOUN
app01-4651	107	9	(	(	PUNCT
app01-4651	107	10	yi+1,j	yi+1,j	PROPN
app01-4651	107	11	,	,	PUNCT
app01-4651	107	12	k	k	PROPN
app01-4651	107	13	+	+	PROPN
app01-4651	107	14	1)[nk	1)[nk	NUM
app01-4651	107	15	=	=	SYM
app01-4651	107	16	c	c	NOUN
app01-4651	107	17	]	]	X
app01-4651	107	18	=	=	SYM
app01-4651	107	19	0	0	NUM
app01-4651	107	20	,	,	PUNCT
app01-4651	107	21	∀c	∀c	X
app01-4651	107	22	∈	∈	PROPN
app01-4651	107	23	c,∀j	c,∀j	X
app01-4651	107	24	∈	∈	PROPN
app01-4651	107	25	w,∀i	w,∀i	PROPN
app01-4651	107	26	∈	∈	PROPN
app01-4651	107	27	h	h	NOUN
app01-4651	107	28	\	\	PUNCT
app01-4651	107	29	{	{	PUNCT
app01-4651	107	30	nt	nt	INTJ
app01-4651	107	31	,	,	PUNCT
app01-4651	107	32	h	h	NOUN
app01-4651	107	33	}	}	PUNCT
app01-4651	107	34	,	,	PUNCT
app01-4651	107	35	(	(	PUNCT
app01-4651	107	36	14c	14c	NUM
app01-4651	107	37	)	)	PUNCT
app01-4651	107	38	∑	∑	PROPN
app01-4651	107	39	k∈t	k∈t	PROPN
app01-4651	107	40	yi	yi	PROPN
app01-4651	107	41	,	,	PUNCT
app01-4651	107	42	j	j	PROPN
app01-4651	107	43	,	,	PUNCT
app01-4651	107	44	k	k	PROPN
app01-4651	107	45	=	=	PUNCT
app01-4651	107	46	2−	2−	NUM
app01-4651	107	47	nt	not	PART
app01-4651	107	48	,	,	PUNCT
app01-4651	107	49	∀i	∀i	NOUN
app01-4651	107	50	∈	∈	NOUN
app01-4651	107	51	h,∀j	h,∀j	PUNCT
app01-4651	107	52	∈	∈	PROPN
app01-4651	107	53	w	w	PROPN
app01-4651	107	54	,	,	PUNCT
app01-4651	107	55	(	(	PUNCT
app01-4651	107	56	14d	14d	NOUN
app01-4651	107	57	)	)	PUNCT
app01-4651	108	1	y2	y2	PROPN
app01-4651	109	1	i	i	PROPN
app01-4651	109	2	,	,	PUNCT
app01-4651	109	3	j	j	PROPN
app01-4651	109	4	,	,	PUNCT
app01-4651	109	5	k	k	PROPN
app01-4651	109	6	=	=	SYM
app01-4651	109	7	1	1	NUM
app01-4651	109	8	,	,	PUNCT
app01-4651	109	9	∀i	∀i	NOUN
app01-4651	109	10	∈	∈	NOUN
app01-4651	109	11	h,∀j	h,∀j	PUNCT
app01-4651	109	12	∈	∈	PROPN
app01-4651	109	13	w,∀k	w,∀k	PROPN
app01-4651	109	14	∈	∈	PROPN
app01-4651	109	15	t	t	PROPN
app01-4651	109	16	.	.	PUNCT
app01-4651	110	1	(	(	PUNCT
app01-4651	110	2	14e	14e	NOUN
app01-4651	110	3	)	)	PUNCT
app01-4651	110	4	let	let	VERB
app01-4651	110	5	us	we	PRON
app01-4651	110	6	further	far	ADV
app01-4651	110	7	introduce	introduce	VERB
app01-4651	110	8	a	a	DET
app01-4651	110	9	symmetric	symmetric	ADJ
app01-4651	110	10	matrix	matrix	NOUN
app01-4651	110	11	y	y	PROPN
app01-4651	110	12	∈	∈	PROPN
app01-4651	110	13	snt	snt	PROPN
app01-4651	110	14	,	,	PUNCT
app01-4651	110	15	y·nt	y·nt	NOUN
app01-4651	110	16	,	,	PUNCT
app01-4651	110	17	x·nt	x·nt	NUM
app01-4651	110	18	defined	define	VERB
app01-4651	110	19	as	as	ADP
app01-4651	110	20	y	y	PROPN
app01-4651	110	21	=	=	PROPN
app01-4651	110	22	yyt	yyt	PROPN
app01-4651	110	23	.	.	PUNCT
app01-4651	111	1	(	(	PUNCT
app01-4651	111	2	15	15	NUM
app01-4651	111	3	)	)	PUNCT
app01-4651	111	4	the	the	DET
app01-4651	111	5	definition	definition	NOUN
app01-4651	111	6	directly	directly	ADV
app01-4651	111	7	implies	imply	VERB
app01-4651	111	8	that	that	SCONJ
app01-4651	111	9	any	any	DET
app01-4651	111	10	solution	solution	NOUN
app01-4651	111	11	to	to	ADP
app01-4651	111	12	the	the	DET
app01-4651	111	13	quadratically	quadratically	ADV
app01-4651	111	14	-	-	PUNCT
app01-4651	111	15	constrained	constrain	VERB
app01-4651	111	16	optimization	optimization	NOUN
app01-4651	111	17	problem	problem	NOUN
app01-4651	111	18	(	(	PUNCT
app01-4651	111	19	14	14	NUM
app01-4651	111	20	)	)	PUNCT
app01-4651	111	21	renders	render	VERB
app01-4651	111	22	the	the	DET
app01-4651	111	23	matrix	matrix	NOUN
app01-4651	111	24	y	y	PROPN
app01-4651	111	25	positive	positive	ADJ
app01-4651	111	26	semidefinite	semidefinite	NOUN
app01-4651	111	27	,	,	PUNCT
app01-4651	111	28	in	in	ADP
app01-4651	111	29	our	our	PRON
app01-4651	111	30	notation	notation	NOUN
app01-4651	111	31	y	y	PROPN
app01-4651	111	32	�	�	PROPN
app01-4651	111	33	0	0	NUM
app01-4651	111	34	,	,	PUNCT
app01-4651	111	35	and	and	CCONJ
app01-4651	111	36	the	the	DET
app01-4651	111	37	rank	rank	NOUN
app01-4651	111	38	of	of	ADP
app01-4651	111	39	the	the	DET
app01-4651	111	40	matrix	matrix	NOUN
app01-4651	111	41	y	y	PRON
app01-4651	111	42	equal	equal	ADJ
app01-4651	111	43	to	to	ADP
app01-4651	111	44	1	1	NUM
app01-4651	111	45	.	.	PUNCT
app01-4651	112	1	moreover	moreover	ADV
app01-4651	112	2	,	,	PUNCT
app01-4651	112	3	the	the	DET
app01-4651	112	4	definition	definition	NOUN
app01-4651	112	5	of	of	ADP
app01-4651	112	6	y	y	PROPN
app01-4651	112	7	constrains	constrain	VERB
app01-4651	112	8	all	all	DET
app01-4651	112	9	the	the	DET
app01-4651	112	10	elements	element	NOUN
app01-4651	112	11	in	in	ADP
app01-4651	112	12	the	the	DET
app01-4651	112	13	main	main	ADJ
app01-4651	112	14	diagonal	diagonal	NOUN
app01-4651	112	15	of	of	ADP
app01-4651	112	16	y	y	PROPN
app01-4651	112	17	equal	equal	ADJ
app01-4651	112	18	to	to	ADP
app01-4651	112	19	1	1	NUM
app01-4651	112	20	.	.	PUNCT
app01-4651	113	1	consequently	consequently	ADV
app01-4651	113	2	,	,	PUNCT
app01-4651	113	3	another	another	DET
app01-4651	113	4	equivalent	equivalent	ADJ
app01-4651	113	5	formulation	formulation	NOUN
app01-4651	113	6	to	to	ADP
app01-4651	113	7	the	the	DET
app01-4651	113	8	problem	problem	NOUN
app01-4651	113	9	(	(	PUNCT
app01-4651	113	10	8)	8)	NUM
app01-4651	113	11	reads	read	NOUN
app01-4651	113	12	as	as	ADP
app01-4651	113	13	min	min	PROPN
app01-4651	113	14	y	y	PROPN
app01-4651	113	15	,	,	PUNCT
app01-4651	113	16	y	y	PROPN
app01-4651	113	17	0	0	NUM
app01-4651	113	18	(	(	PUNCT
app01-4651	113	19	16a	16a	NOUN
app01-4651	113	20	)	)	PUNCT
app01-4651	113	21	s.t	s.t	PROPN
app01-4651	113	22	.	.	PROPN
app01-4651	113	23	∑	∑	PROPN
app01-4651	113	24	k∈t	k∈t	NOUN
app01-4651	113	25	(	(	PUNCT
app01-4651	113	26	yi	yi	PROPN
app01-4651	113	27	,	,	PUNCT
app01-4651	113	28	j	j	PROPN
app01-4651	113	29	,	,	PUNCT
app01-4651	113	30	k	k	PROPN
app01-4651	113	31	+	+	PROPN
app01-4651	113	32	1)[ek	1)[ek	NUM
app01-4651	113	33	=	=	SYM
app01-4651	113	34	c	c	X
app01-4651	113	35	]	]	X
app01-4651	113	36	−	−	PROPN
app01-4651	113	37	∑	∑	PROPN
app01-4651	113	38	k∈t	k∈t	NOUN
app01-4651	113	39	(	(	PUNCT
app01-4651	113	40	yi	yi	PROPN
app01-4651	113	41	,	,	PUNCT
app01-4651	113	42	j+1,k	j+1,k	PROPN
app01-4651	113	43	+	+	CCONJ
app01-4651	113	44	1)[wk	1)[wk	NUM
app01-4651	113	45	=	=	SYM
app01-4651	113	46	c	c	X
app01-4651	113	47	]	]	X
app01-4651	113	48	=	=	SYM
app01-4651	113	49	0	0	NUM
app01-4651	113	50	,	,	PUNCT
app01-4651	113	51	∀c	∀c	VERB
app01-4651	113	52	∈	∈	PROPN
app01-4651	113	53	c,∀i	c,∀i	ADP
app01-4651	113	54	∈	∈	PROPN
app01-4651	113	55	h,∀j	h,∀j	PUNCT
app01-4651	113	56	∈	∈	PROPN
app01-4651	113	57	w	w	PROPN
app01-4651	113	58	\	\	PROPN
app01-4651	113	59	{	{	PUNCT
app01-4651	113	60	nt	nt	INTJ
app01-4651	113	61	,	,	PUNCT
app01-4651	113	62	w	w	NOUN
app01-4651	113	63	}	}	PUNCT
app01-4651	113	64	,	,	PUNCT
app01-4651	113	65	(	(	PUNCT
app01-4651	113	66	16b	16b	X
app01-4651	113	67	)	)	PUNCT
app01-4651	113	68	∑	∑	PUNCT
app01-4651	113	69	k∈t	k∈t	NOUN
app01-4651	113	70	(	(	PUNCT
app01-4651	113	71	yi	yi	PROPN
app01-4651	113	72	,	,	PUNCT
app01-4651	113	73	j	j	PROPN
app01-4651	113	74	,	,	PUNCT
app01-4651	113	75	k	k	PROPN
app01-4651	114	1	+	+	PROPN
app01-4651	114	2	1)[sk	1)[sk	NUM
app01-4651	114	3	=	=	SYM
app01-4651	114	4	c	c	X
app01-4651	114	5	]	]	X
app01-4651	114	6	−	−	PROPN
app01-4651	114	7	∑	∑	PROPN
app01-4651	114	8	k∈t	k∈t	NOUN
app01-4651	114	9	(	(	PUNCT
app01-4651	114	10	yi+1,j	yi+1,j	PROPN
app01-4651	114	11	,	,	PUNCT
app01-4651	114	12	k	k	PROPN
app01-4651	114	13	+	+	PROPN
app01-4651	114	14	1)[nk	1)[nk	NUM
app01-4651	114	15	=	=	SYM
app01-4651	114	16	c	c	NOUN
app01-4651	114	17	]	]	X
app01-4651	114	18	=	=	SYM
app01-4651	114	19	0	0	NUM
app01-4651	114	20	,	,	PUNCT
app01-4651	114	21	∀c	∀c	X
app01-4651	114	22	∈	∈	PROPN
app01-4651	114	23	c,∀j	c,∀j	X
app01-4651	114	24	∈	∈	PROPN
app01-4651	114	25	w,∀i	w,∀i	PROPN
app01-4651	114	26	∈	∈	PROPN
app01-4651	114	27	h	h	NOUN
app01-4651	114	28	\	\	PUNCT
app01-4651	114	29	{	{	PUNCT
app01-4651	114	30	nt	nt	INTJ
app01-4651	114	31	,	,	PUNCT
app01-4651	114	32	h	h	NOUN
app01-4651	114	33	}	}	PUNCT
app01-4651	114	34	,	,	PUNCT
app01-4651	114	35	(	(	PUNCT
app01-4651	114	36	16c	16c	NOUN
app01-4651	114	37	)	)	PUNCT
app01-4651	114	38	∑	∑	PROPN
app01-4651	114	39	k∈t	k∈t	PROPN
app01-4651	114	40	yi	yi	PROPN
app01-4651	114	41	,	,	PUNCT
app01-4651	114	42	j	j	PROPN
app01-4651	114	43	,	,	PUNCT
app01-4651	114	44	k	k	PROPN
app01-4651	114	45	=	=	PUNCT
app01-4651	114	46	2−	2−	NUM
app01-4651	114	47	nt	not	PART
app01-4651	114	48	,	,	PUNCT
app01-4651	114	49	∀i	∀i	NOUN
app01-4651	114	50	∈	∈	NOUN
app01-4651	114	51	h,∀j	h,∀j	PUNCT
app01-4651	114	52	∈	∈	PROPN
app01-4651	114	53	w	w	PROPN
app01-4651	114	54	,	,	PUNCT
app01-4651	114	55	(	(	PUNCT
app01-4651	114	56	16d	16d	NOUN
app01-4651	114	57	)	)	PUNCT
app01-4651	114	58	diag(y	diag(y	NOUN
app01-4651	114	59	)	)	PUNCT
app01-4651	114	60	=	=	SYM
app01-4651	114	61	1	1	NUM
app01-4651	114	62	,	,	PUNCT
app01-4651	114	63	(	(	PUNCT
app01-4651	114	64	16e	16e	NUM
app01-4651	114	65	)	)	PUNCT
app01-4651	114	66	y−	y−	NOUN
app01-4651	114	67	yyt	yyt	NOUN
app01-4651	114	68	=	=	NOUN
app01-4651	114	69	0	0	PROPN
app01-4651	114	70	.	.	PUNCT
app01-4651	114	71	(	(	PUNCT
app01-4651	114	72	16f	16f	NUM
app01-4651	114	73	)	)	PUNCT
app01-4651	114	74	the	the	DET
app01-4651	114	75	only	only	ADJ
app01-4651	114	76	non	non	ADJ
app01-4651	114	77	-	-	ADJ
app01-4651	114	78	convex	convex	ADJ
app01-4651	114	79	constraint	constraint	NOUN
app01-4651	114	80	(	(	PUNCT
app01-4651	114	81	16f	16f	NUM
app01-4651	114	82	)	)	PUNCT
app01-4651	114	83	can	can	AUX
app01-4651	114	84	be	be	AUX
app01-4651	114	85	relaxed	relax	VERB
app01-4651	114	86	,	,	PUNCT
app01-4651	114	87	see	see	VERB
app01-4651	114	88	,	,	PUNCT
app01-4651	114	89	e.g.	e.g.	ADV
app01-4651	114	90	,	,	PUNCT
app01-4651	114	91	[	[	X
app01-4651	114	92	32	32	NUM
app01-4651	114	93	]	]	PUNCT
app01-4651	114	94	,	,	PUNCT
app01-4651	114	95	into	into	ADP
app01-4651	114	96	a	a	DET
app01-4651	114	97	convex	convex	NOUN
app01-4651	114	98	form	form	NOUN
app01-4651	114	99	y−	y−	NOUN
app01-4651	114	100	yyt	yyt	PROPN
app01-4651	114	101	�	�	PROPN
app01-4651	114	102	0	0	NUM
app01-4651	114	103	,	,	PUNCT
app01-4651	114	104	(	(	PUNCT
app01-4651	114	105	17	17	NUM
app01-4651	114	106	)	)	PUNCT
app01-4651	114	107	and	and	CCONJ
app01-4651	114	108	based	base	VERB
app01-4651	114	109	on	on	ADP
app01-4651	114	110	the	the	DET
app01-4651	114	111	schur	schur	PROPN
app01-4651	114	112	complement	complement	PROPN
app01-4651	114	113	lemma	lemma	PROPN
app01-4651	114	114	equivalently	equivalently	ADV
app01-4651	114	115	rewritten	rewrite	VERB
app01-4651	114	116	to	to	ADP
app01-4651	114	117	(	(	PUNCT
app01-4651	114	118	1	1	NUM
app01-4651	114	119	yt	yt	VERB
app01-4651	114	120	y	y	PROPN
app01-4651	114	121	y	y	PROPN
app01-4651	114	122	)	)	PUNCT
app01-4651	114	123	�	�	PROPN
app01-4651	114	124	0	0	NUM
app01-4651	114	125	.	.	PUNCT
app01-4651	115	1	(	(	PUNCT
app01-4651	115	2	18	18	NUM
app01-4651	115	3	)	)	PUNCT
app01-4651	115	4	finally	finally	ADV
app01-4651	115	5	,	,	PUNCT
app01-4651	115	6	the	the	DET
app01-4651	115	7	semidefinite	semidefinite	NOUN
app01-4651	115	8	programming	programming	NOUN
app01-4651	115	9	relaxation	relaxation	NOUN
app01-4651	115	10	of	of	ADP
app01-4651	115	11	the	the	DET
app01-4651	115	12	binary	binary	PROPN
app01-4651	115	13	linear	linear	PROPN
app01-4651	115	14	program	program	NOUN
app01-4651	115	15	(	(	PUNCT
app01-4651	115	16	8)	8)	NUM
app01-4651	115	17	reads	read	NOUN
app01-4651	115	18	as	as	ADP
app01-4651	115	19	min	min	PROPN
app01-4651	115	20	y	y	PROPN
app01-4651	115	21	,	,	PUNCT
app01-4651	115	22	y	y	PROPN
app01-4651	115	23	0	0	NUM
app01-4651	115	24	(	(	PUNCT
app01-4651	115	25	19a	19a	NUM
app01-4651	115	26	)	)	PUNCT
app01-4651	115	27	s.t	s.t	PROPN
app01-4651	115	28	.	.	PROPN
app01-4651	115	29	∑	∑	PROPN
app01-4651	115	30	k∈t	k∈t	NOUN
app01-4651	115	31	(	(	PUNCT
app01-4651	115	32	yi	yi	PROPN
app01-4651	115	33	,	,	PUNCT
app01-4651	115	34	j	j	PROPN
app01-4651	115	35	,	,	PUNCT
app01-4651	115	36	k	k	PROPN
app01-4651	115	37	+	+	PROPN
app01-4651	115	38	1)[ek	1)[ek	NUM
app01-4651	116	1	=	=	SYM
app01-4651	116	2	c	c	X
app01-4651	116	3	]	]	X
app01-4651	116	4	−	−	PROPN
app01-4651	116	5	∑	∑	PROPN
app01-4651	116	6	k∈t	k∈t	NOUN
app01-4651	116	7	(	(	PUNCT
app01-4651	116	8	yi	yi	PROPN
app01-4651	116	9	,	,	PUNCT
app01-4651	116	10	j+1,k	j+1,k	PROPN
app01-4651	116	11	+	+	CCONJ
app01-4651	116	12	1)[wk	1)[wk	NUM
app01-4651	116	13	=	=	SYM
app01-4651	116	14	c	c	X
app01-4651	116	15	]	]	X
app01-4651	116	16	=	=	SYM
app01-4651	116	17	0	0	NUM
app01-4651	116	18	,	,	PUNCT
app01-4651	116	19	∀c	∀c	VERB
app01-4651	116	20	∈	∈	PROPN
app01-4651	116	21	c,∀i	c,∀i	ADP
app01-4651	116	22	∈	∈	PROPN
app01-4651	116	23	h,∀j	h,∀j	PUNCT
app01-4651	116	24	∈	∈	PROPN
app01-4651	116	25	w	w	PROPN
app01-4651	116	26	\	\	PROPN
app01-4651	116	27	{	{	PUNCT
app01-4651	116	28	nt	nt	INTJ
app01-4651	116	29	,	,	PUNCT
app01-4651	116	30	w	w	NOUN
app01-4651	116	31	}	}	PUNCT
app01-4651	116	32	,	,	PUNCT
app01-4651	116	33	(	(	PUNCT
app01-4651	116	34	19b	19b	NOUN
app01-4651	116	35	)	)	PUNCT
app01-4651	116	36	∑	∑	PUNCT
app01-4651	116	37	k∈t	k∈t	NOUN
app01-4651	116	38	(	(	PUNCT
app01-4651	116	39	yi	yi	PROPN
app01-4651	116	40	,	,	PUNCT
app01-4651	116	41	j	j	PROPN
app01-4651	116	42	,	,	PUNCT
app01-4651	116	43	k	k	PROPN
app01-4651	116	44	+	+	PROPN
app01-4651	116	45	1)[sk	1)[sk	NUM
app01-4651	116	46	=	=	SYM
app01-4651	116	47	c	c	X
app01-4651	116	48	]	]	X
app01-4651	116	49	−	−	PROPN
app01-4651	116	50	∑	∑	PROPN
app01-4651	116	51	k∈t	k∈t	NOUN
app01-4651	116	52	(	(	PUNCT
app01-4651	116	53	yi+1,j	yi+1,j	PROPN
app01-4651	116	54	,	,	PUNCT
app01-4651	116	55	k	k	PROPN
app01-4651	116	56	+	+	PROPN
app01-4651	116	57	1)[nk	1)[nk	NUM
app01-4651	116	58	=	=	SYM
app01-4651	116	59	c	c	NOUN
app01-4651	116	60	]	]	X
app01-4651	116	61	=	=	SYM
app01-4651	116	62	0	0	NUM
app01-4651	116	63	,	,	PUNCT
app01-4651	116	64	∀c	∀c	X
app01-4651	116	65	∈	∈	PROPN
app01-4651	116	66	c,∀j	c,∀j	X
app01-4651	116	67	∈	∈	PROPN
app01-4651	116	68	w,∀i	w,∀i	PROPN
app01-4651	116	69	∈	∈	PROPN
app01-4651	116	70	h	h	NOUN
app01-4651	116	71	\	\	PUNCT
app01-4651	116	72	{	{	PUNCT
app01-4651	116	73	nt	nt	INTJ
app01-4651	116	74	,	,	PUNCT
app01-4651	116	75	h	h	NOUN
app01-4651	116	76	}	}	PUNCT
app01-4651	116	77	,	,	PUNCT
app01-4651	116	78	(	(	PUNCT
app01-4651	116	79	19c	19c	NUM
app01-4651	116	80	)	)	PUNCT
app01-4651	116	81	∑	∑	PROPN
app01-4651	116	82	k∈t	k∈t	PROPN
app01-4651	116	83	yi	yi	PROPN
app01-4651	116	84	,	,	PUNCT
app01-4651	116	85	j	j	PROPN
app01-4651	116	86	,	,	PUNCT
app01-4651	116	87	k	k	PROPN
app01-4651	116	88	=	=	PUNCT
app01-4651	116	89	2−	2−	NUM
app01-4651	116	90	nt	not	PART
app01-4651	116	91	,	,	PUNCT
app01-4651	116	92	∀i	∀i	NOUN
app01-4651	116	93	∈	∈	NOUN
app01-4651	116	94	h,∀j	h,∀j	PUNCT
app01-4651	116	95	∈	∈	PROPN
app01-4651	116	96	w	w	PROPN
app01-4651	116	97	,	,	PUNCT
app01-4651	116	98	(	(	PUNCT
app01-4651	116	99	19d	19d	NOUN
app01-4651	116	100	)	)	PUNCT
app01-4651	116	101	diag(y	diag(y	NOUN
app01-4651	116	102	)	)	PUNCT
app01-4651	116	103	=	=	SYM
app01-4651	116	104	1	1	NUM
app01-4651	116	105	,	,	PUNCT
app01-4651	116	106	(	(	PUNCT
app01-4651	116	107	19e	19e	NOUN
app01-4651	116	108	)	)	PUNCT
app01-4651	116	109	(	(	PUNCT
app01-4651	116	110	1	1	NUM
app01-4651	116	111	yt	yt	VERB
app01-4651	116	112	y	y	PROPN
app01-4651	116	113	y	y	PROPN
app01-4651	116	114	)	)	PUNCT
app01-4651	116	115	�	�	PROPN
app01-4651	116	116	0	0	NUM
app01-4651	116	117	,	,	PUNCT
app01-4651	116	118	(	(	PUNCT
app01-4651	116	119	19f	19f	NUM
app01-4651	116	120	)	)	PUNCT
app01-4651	116	121	−	−	PROPN
app01-4651	116	122	1	1	NUM
app01-4651	116	123	≤	≤	NUM
app01-4651	116	124	y	y	PROPN
app01-4651	116	125	≤	≤	NUM
app01-4651	116	126	1	1	NUM
app01-4651	116	127	.	.	PUNCT
app01-4651	116	128	(	(	PUNCT
app01-4651	116	129	19	19	NUM
app01-4651	116	130	g	g	NOUN
app01-4651	116	131	)	)	PUNCT
app01-4651	116	132	2.5	2.5	NUM
app01-4651	116	133	.	.	PUNCT
app01-4651	116	134	extensions	extension	NOUN
app01-4651	116	135	introduced	introduce	VERB
app01-4651	116	136	formulations	formulation	NOUN
app01-4651	116	137	can	can	AUX
app01-4651	116	138	include	include	VERB
app01-4651	116	139	additional	additional	ADJ
app01-4651	116	140	requirements	requirement	NOUN
app01-4651	116	141	for	for	ADP
app01-4651	116	142	generated	generate	VERB
app01-4651	116	143	tilings	tiling	NOUN
app01-4651	116	144	.	.	PUNCT
app01-4651	117	1	we	we	PRON
app01-4651	117	2	list	list	VERB
app01-4651	117	3	some	some	PRON
app01-4651	117	4	of	of	ADP
app01-4651	117	5	them	they	PRON
app01-4651	117	6	below	below	ADV
app01-4651	117	7	,	,	PUNCT
app01-4651	117	8	but	but	CCONJ
app01-4651	117	9	only	only	ADV
app01-4651	117	10	in	in	ADP
app01-4651	117	11	terms	term	NOUN
app01-4651	117	12	of	of	ADP
app01-4651	117	13	x	x	X
app01-4651	117	14	,	,	PUNCT
app01-4651	117	15	as	as	ADP
app01-4651	117	16	substitution	substitution	NOUN
app01-4651	117	17	of	of	ADP
app01-4651	117	18	eq	eq	PROPN
app01-4651	117	19	.	.	PUNCT
app01-4651	118	1	(	(	PUNCT
app01-4651	118	2	12	12	NUM
app01-4651	118	3	)	)	PUNCT
app01-4651	118	4	into	into	ADP
app01-4651	118	5	developed	developed	ADJ
app01-4651	118	6	equations	equation	NOUN
app01-4651	118	7	is	be	AUX
app01-4651	118	8	obvious	obvious	ADJ
app01-4651	118	9	.	.	PUNCT
app01-4651	119	1	2.5.1	2.5.1	NUM
app01-4651	119	2	.	.	PUNCT
app01-4651	120	1	tile	tile	NOUN
app01-4651	120	2	-	-	PUNCT
app01-4651	120	3	based	base	VERB
app01-4651	120	4	boundary	boundary	ADJ
app01-4651	120	5	conditions	condition	NOUN
app01-4651	120	6	there	there	PRON
app01-4651	120	7	are	be	VERB
app01-4651	120	8	four	four	NUM
app01-4651	120	9	types	type	NOUN
app01-4651	120	10	of	of	ADP
app01-4651	120	11	tile	tile	NOUN
app01-4651	120	12	-	-	PUNCT
app01-4651	120	13	based	base	VERB
app01-4651	120	14	boundary	boundary	ADJ
app01-4651	120	15	conditions	condition	NOUN
app01-4651	120	16	.	.	PUNCT
app01-4651	121	1	first	first	ADV
app01-4651	121	2	,	,	PUNCT
app01-4651	121	3	we	we	PRON
app01-4651	121	4	can	can	AUX
app01-4651	121	5	enforce	enforce	VERB
app01-4651	121	6	placement	placement	NOUN
app01-4651	121	7	of	of	ADP
app01-4651	121	8	the	the	DET
app01-4651	121	9	tile	tile	NOUN
app01-4651	121	10	k	k	PROPN
app01-4651	121	11	∈	∈	PROPN
app01-4651	121	12	t	t	PROPN
app01-4651	121	13	at	at	ADP
app01-4651	121	14	position	position	NOUN
app01-4651	121	15	(	(	PUNCT
app01-4651	121	16	i	i	PROPN
app01-4651	121	17	,	,	PUNCT
app01-4651	121	18	j	j	PROPN
app01-4651	121	19	):	):	PUNCT
app01-4651	121	20	xi	xi	PROPN
app01-4651	121	21	,	,	PUNCT
app01-4651	121	22	j	j	PROPN
app01-4651	121	23	,	,	PUNCT
app01-4651	121	24	k	k	PROPN
app01-4651	121	25	=	=	SYM
app01-4651	121	26	1	1	NUM
app01-4651	121	27	,	,	PUNCT
app01-4651	121	28	i	i	PRON
app01-4651	121	29	∈	∈	PROPN
app01-4651	121	30	h	h	NOUN
app01-4651	121	31	,	,	PUNCT
app01-4651	121	32	j	j	PROPN
app01-4651	121	33	∈	∈	PROPN
app01-4651	121	34	w	w	PROPN
app01-4651	121	35	,	,	PUNCT
app01-4651	121	36	k	k	PROPN
app01-4651	121	37	∈	∈	PROPN
app01-4651	121	38	t	t	PROPN
app01-4651	121	39	.	.	PUNCT
app01-4651	122	1	(	(	PUNCT
app01-4651	122	2	20	20	NUM
app01-4651	122	3	)	)	PUNCT
app01-4651	122	4	conversely	conversely	ADV
app01-4651	122	5	,	,	PUNCT
app01-4651	122	6	avoiding	avoid	VERB
app01-4651	122	7	the	the	DET
app01-4651	122	8	tile	tile	NOUN
app01-4651	122	9	k	k	PROPN
app01-4651	123	1	at	at	ADP
app01-4651	123	2	(	(	PUNCT
app01-4651	123	3	i	i	PROPN
app01-4651	123	4	,	,	PUNCT
app01-4651	123	5	j	j	PROPN
app01-4651	123	6	)	)	PUNCT
app01-4651	123	7	requires	require	VERB
app01-4651	123	8	xi	xi	PROPN
app01-4651	123	9	,	,	PUNCT
app01-4651	123	10	j	j	PROPN
app01-4651	123	11	,	,	PUNCT
app01-4651	123	12	k	k	PROPN
app01-4651	123	13	=	=	SYM
app01-4651	123	14	0	0	NUM
app01-4651	123	15	,	,	PUNCT
app01-4651	123	16	i	i	PRON
app01-4651	123	17	∈	∈	PROPN
app01-4651	123	18	h	h	NOUN
app01-4651	123	19	,	,	PUNCT
app01-4651	123	20	j	j	PROPN
app01-4651	123	21	∈	∈	PROPN
app01-4651	123	22	w	w	PROPN
app01-4651	123	23	,	,	PUNCT
app01-4651	123	24	k	k	PROPN
app01-4651	123	25	∈	∈	PROPN
app01-4651	123	26	t	t	PROPN
app01-4651	123	27	.	.	PUNCT
app01-4651	124	1	(	(	PUNCT
app01-4651	124	2	21	21	NUM
app01-4651	124	3	)	)	PUNCT
app01-4651	124	4	the	the	DET
app01-4651	124	5	requirement	requirement	NOUN
app01-4651	124	6	that	that	SCONJ
app01-4651	124	7	the	the	DET
app01-4651	124	8	same	same	ADJ
app01-4651	124	9	tile	tile	NOUN
app01-4651	124	10	is	be	AUX
app01-4651	124	11	placed	place	VERB
app01-4651	124	12	at	at	ADP
app01-4651	124	13	both	both	PRON
app01-4651	124	14	(	(	PUNCT
app01-4651	124	15	i	i	PROPN
app01-4651	124	16	,	,	PUNCT
app01-4651	124	17	j	j	PROPN
app01-4651	124	18	)	)	PUNCT
app01-4651	124	19	and	and	CCONJ
app01-4651	124	20	(	(	PUNCT
app01-4651	124	21	p	p	X
app01-4651	124	22	,	,	PUNCT
app01-4651	124	23	q	q	NOUN
app01-4651	124	24	)	)	PUNCT
app01-4651	124	25	can	can	AUX
app01-4651	124	26	be	be	AUX
app01-4651	124	27	written	write	VERB
app01-4651	124	28	as	as	ADP
app01-4651	124	29	xi	xi	PROPN
app01-4651	124	30	,	,	PUNCT
app01-4651	124	31	j	j	PROPN
app01-4651	124	32	,	,	PUNCT
app01-4651	124	33	k	k	PROPN
app01-4651	124	34	−	−	PROPN
app01-4651	124	35	xp	xp	PROPN
app01-4651	124	36	,	,	PUNCT
app01-4651	124	37	q	q	X
app01-4651	124	38	,	,	PUNCT
app01-4651	124	39	k	k	NOUN
app01-4651	124	40	=	=	SYM
app01-4651	124	41	0	0	PROPN
app01-4651	124	42	,	,	PUNCT
app01-4651	124	43	{	{	PUNCT
app01-4651	124	44	i	i	PRON
app01-4651	124	45	,	,	PUNCT
app01-4651	124	46	p	p	NOUN
app01-4651	124	47	}	}	PUNCT
app01-4651	124	48	∈	∈	PROPN
app01-4651	124	49	h	h	NOUN
app01-4651	124	50	,	,	PUNCT
app01-4651	124	51	{	{	PUNCT
app01-4651	124	52	j	j	NOUN
app01-4651	124	53	,	,	PUNCT
app01-4651	124	54	q	q	ADJ
app01-4651	124	55	}	}	PUNCT
app01-4651	124	56	∈	∈	PROPN
app01-4651	124	57	w,∀k	w,∀k	SYM
app01-4651	124	58	∈	∈	PROPN
app01-4651	124	59	t	t	PROPN
app01-4651	124	60	.	.	PUNCT
app01-4651	125	1	(	(	PUNCT
app01-4651	125	2	22	22	X
app01-4651	125	3	)	)	PUNCT
app01-4651	125	4	enforcing	enforce	VERB
app01-4651	125	5	different	different	ADJ
app01-4651	125	6	tiles	tile	NOUN
app01-4651	125	7	at	at	ADP
app01-4651	125	8	(	(	PUNCT
app01-4651	125	9	i	i	PROPN
app01-4651	125	10	,	,	PUNCT
app01-4651	125	11	j	j	PROPN
app01-4651	125	12	)	)	PUNCT
app01-4651	125	13	and	and	CCONJ
app01-4651	125	14	(	(	PUNCT
app01-4651	125	15	p	p	X
app01-4651	125	16	,	,	PUNCT
app01-4651	125	17	q	q	NOUN
app01-4651	125	18	)	)	PUNCT
app01-4651	125	19	requires	require	VERB
app01-4651	125	20	xi	xi	PROPN
app01-4651	125	21	,	,	PUNCT
app01-4651	125	22	j	j	PROPN
app01-4651	125	23	,	,	PUNCT
app01-4651	125	24	k+xp	k+xp	PROPN
app01-4651	125	25	,	,	PUNCT
app01-4651	125	26	q	q	X
app01-4651	125	27	,	,	PUNCT
app01-4651	125	28	k	k	PROPN
app01-4651	125	29	≤	≤	ADJ
app01-4651	125	30	1	1	NUM
app01-4651	125	31	,	,	PUNCT
app01-4651	125	32	{	{	PUNCT
app01-4651	125	33	i	i	PRON
app01-4651	125	34	,	,	PUNCT
app01-4651	125	35	p	p	NOUN
app01-4651	125	36	}	}	PUNCT
app01-4651	125	37	∈	∈	PROPN
app01-4651	125	38	h	h	NOUN
app01-4651	125	39	,	,	PUNCT
app01-4651	125	40	{	{	PUNCT
app01-4651	125	41	j	j	NOUN
app01-4651	125	42	,	,	PUNCT
app01-4651	125	43	q	q	ADJ
app01-4651	125	44	}	}	PUNCT
app01-4651	125	45	∈	∈	PROPN
app01-4651	125	46	w,∀k	w,∀k	SYM
app01-4651	125	47	∈	∈	PROPN
app01-4651	125	48	t	t	PROPN
app01-4651	125	49	.	.	PUNCT
app01-4651	126	1	(	(	PUNCT
app01-4651	126	2	23	23	NUM
app01-4651	126	3	)	)	PUNCT
app01-4651	126	4	2.5.2	2.5.2	NUM
app01-4651	126	5	.	.	PUNCT
app01-4651	126	6	edge	edge	NOUN
app01-4651	126	7	-	-	PUNCT
app01-4651	126	8	based	base	VERB
app01-4651	126	9	boundary	boundary	ADJ
app01-4651	126	10	conditions	condition	NOUN
app01-4651	126	11	starting	start	VERB
app01-4651	126	12	from	from	ADP
app01-4651	126	13	eq	eq	PROPN
app01-4651	126	14	.	.	PUNCT
app01-4651	127	1	(	(	PUNCT
app01-4651	127	2	5	5	NUM
app01-4651	127	3	)	)	PUNCT
app01-4651	127	4	,	,	PUNCT
app01-4651	127	5	we	we	PRON
app01-4651	127	6	can	can	AUX
app01-4651	127	7	also	also	ADV
app01-4651	127	8	easily	easily	ADV
app01-4651	127	9	formulate	formulate	VERB
app01-4651	127	10	edge	edge	NOUN
app01-4651	127	11	-	-	PUNCT
app01-4651	127	12	based	base	VERB
app01-4651	127	13	boundary	boundary	ADJ
app01-4651	127	14	conditions	condition	NOUN
app01-4651	127	15	.	.	PUNCT
app01-4651	128	1	to	to	PART
app01-4651	128	2	constrain	constrain	VERB
app01-4651	128	3	the	the	DET
app01-4651	128	4	north	north	NOUN
app01-4651	128	5	edge	edge	NOUN
app01-4651	128	6	at	at	ADP
app01-4651	128	7	(	(	PUNCT
app01-4651	128	8	i	i	PROPN
app01-4651	128	9	,	,	PUNCT
app01-4651	128	10	j	j	PROPN
app01-4651	128	11	)	)	PUNCT
app01-4651	128	12	to	to	ADP
app01-4651	128	13	the	the	DET
app01-4651	128	14	color	color	NOUN
app01-4651	129	1	c	c	NOUN
app01-4651	129	2	∈	∈	PROPN
app01-4651	129	3	c	c	X
app01-4651	129	4	,	,	PUNCT
app01-4651	129	5	we	we	PRON
app01-4651	129	6	write∑	write∑	VERB
app01-4651	129	7	k∈t	k∈t	NOUN
app01-4651	129	8	xi	xi	PROPN
app01-4651	129	9	,	,	PUNCT
app01-4651	129	10	j	j	PROPN
app01-4651	129	11	,	,	PUNCT
app01-4651	129	12	k[nk	k[nk	PROPN
app01-4651	129	13	=	=	SYM
app01-4651	130	1	c	c	X
app01-4651	130	2	]	]	X
app01-4651	130	3	=	=	SYM
app01-4651	130	4	1	1	NUM
app01-4651	130	5	,	,	PUNCT
app01-4651	130	6	i	i	PRON
app01-4651	130	7	∈	∈	PROPN
app01-4651	130	8	h	h	NOUN
app01-4651	130	9	,	,	PUNCT
app01-4651	130	10	j	j	PROPN
app01-4651	130	11	∈	∈	PROPN
app01-4651	130	12	w	w	PROPN
app01-4651	130	13	,	,	PUNCT
app01-4651	130	14	c	c	PROPN
app01-4651	130	15	∈	∈	PROPN
app01-4651	130	16	c.	c.	NOUN
app01-4651	130	17	(	(	PUNCT
app01-4651	130	18	24	24	NUM
app01-4651	130	19	)	)	PUNCT
app01-4651	130	20	if	if	SCONJ
app01-4651	130	21	the	the	DET
app01-4651	130	22	north	north	NOUN
app01-4651	130	23	edge	edge	NOUN
app01-4651	130	24	at	at	ADP
app01-4651	130	25	(	(	PUNCT
app01-4651	130	26	i	i	PROPN
app01-4651	130	27	,	,	PUNCT
app01-4651	130	28	j	j	PROPN
app01-4651	130	29	)	)	PUNCT
app01-4651	130	30	has	have	VERB
app01-4651	130	31	to	to	PART
app01-4651	130	32	differ	differ	VERB
app01-4651	130	33	from	from	ADP
app01-4651	130	34	c	c	PROPN
app01-4651	130	35	,	,	PUNCT
app01-4651	130	36	it	it	PRON
app01-4651	130	37	holds	hold	VERB
app01-4651	130	38	that∑	that∑	NOUN
app01-4651	130	39	k∈t	k∈t	NOUN
app01-4651	130	40	xi	xi	PROPN
app01-4651	130	41	,	,	PUNCT
app01-4651	130	42	j	j	PROPN
app01-4651	130	43	,	,	PUNCT
app01-4651	130	44	k[nk	k[nk	PROPN
app01-4651	131	1	=	=	SYM
app01-4651	131	2	c	c	X
app01-4651	131	3	]	]	X
app01-4651	131	4	=	=	SYM
app01-4651	131	5	0	0	NUM
app01-4651	131	6	,	,	PUNCT
app01-4651	131	7	i	i	PRON
app01-4651	131	8	∈	∈	PROPN
app01-4651	131	9	h	h	NOUN
app01-4651	131	10	,	,	PUNCT
app01-4651	131	11	j	j	PROPN
app01-4651	131	12	∈	∈	PROPN
app01-4651	131	13	w	w	PROPN
app01-4651	131	14	,	,	PUNCT
app01-4651	131	15	c	c	PROPN
app01-4651	131	16	∈	∈	PROPN
app01-4651	131	17	c.	c.	NOUN
app01-4651	131	18	(	(	PUNCT
app01-4651	131	19	25	25	NUM
app01-4651	131	20	)	)	PUNCT
app01-4651	131	21	138	138	NUM
app01-4651	131	22	vol	vol	NOUN
app01-4651	131	23	.	.	PUNCT
app01-4651	132	1	13/2017	13/2017	NUM
app01-4651	132	2	optimization	optimization	NOUN
app01-4651	132	3	approach	approach	NOUN
app01-4651	132	4	to	to	ADP
app01-4651	132	5	tiling	tile	VERB
app01-4651	132	6	of	of	ADP
app01-4651	132	7	finite	finite	ADJ
app01-4651	132	8	areas	area	NOUN
app01-4651	132	9	with	with	ADP
app01-4651	132	10	wang	wang	PROPN
app01-4651	132	11	tiles	tiles	PROPN
app01-4651	132	12	equal	equal	ADJ
app01-4651	132	13	color	color	NOUN
app01-4651	132	14	c	c	NOUN
app01-4651	132	15	of	of	ADP
app01-4651	132	16	two	two	NUM
app01-4651	132	17	edges	edge	NOUN
app01-4651	132	18	,	,	PUNCT
app01-4651	132	19	e.g.	e.g.	ADV
app01-4651	132	20	,	,	PUNCT
app01-4651	132	21	of	of	ADP
app01-4651	132	22	the	the	DET
app01-4651	132	23	north	north	NOUN
app01-4651	132	24	edge	edge	NOUN
app01-4651	132	25	at	at	ADP
app01-4651	132	26	(	(	PUNCT
app01-4651	132	27	i	i	PROPN
app01-4651	132	28	,	,	PUNCT
app01-4651	132	29	j	j	PROPN
app01-4651	132	30	)	)	PUNCT
app01-4651	132	31	and	and	CCONJ
app01-4651	132	32	of	of	ADP
app01-4651	132	33	the	the	DET
app01-4651	132	34	west	west	PROPN
app01-4651	132	35	edge	edge	NOUN
app01-4651	132	36	at	at	ADP
app01-4651	132	37	(	(	PUNCT
app01-4651	132	38	p	p	X
app01-4651	132	39	,	,	PUNCT
app01-4651	132	40	q	q	NOUN
app01-4651	132	41	)	)	PUNCT
app01-4651	132	42	,	,	PUNCT
app01-4651	132	43	is	be	AUX
app01-4651	132	44	provided	provide	VERB
app01-4651	132	45	by∑	by∑	ADJ
app01-4651	132	46	k∈t	k∈t	NOUN
app01-4651	132	47	xi	xi	PROPN
app01-4651	132	48	,	,	PUNCT
app01-4651	132	49	j	j	PROPN
app01-4651	132	50	,	,	PUNCT
app01-4651	132	51	k[nk	k[nk	PROPN
app01-4651	132	52	=	=	SYM
app01-4651	132	53	c]−	c]−	PROPN
app01-4651	132	54	∑	∑	PROPN
app01-4651	132	55	k∈t	k∈t	NOUN
app01-4651	132	56	xp	xp	PROPN
app01-4651	132	57	,	,	PUNCT
app01-4651	132	58	q	q	ADJ
app01-4651	132	59	,	,	PUNCT
app01-4651	132	60	k[wk	k[wk	NOUN
app01-4651	132	61	=	=	PUNCT
app01-4651	133	1	c	c	X
app01-4651	133	2	]	]	X
app01-4651	133	3	=	=	SYM
app01-4651	133	4	0	0	NUM
app01-4651	133	5	,	,	PUNCT
app01-4651	133	6	{	{	PUNCT
app01-4651	133	7	i	i	PRON
app01-4651	133	8	,	,	PUNCT
app01-4651	133	9	p	p	NOUN
app01-4651	133	10	}	}	PUNCT
app01-4651	133	11	∈	∈	PROPN
app01-4651	133	12	h	h	NOUN
app01-4651	133	13	,	,	PUNCT
app01-4651	133	14	{	{	PUNCT
app01-4651	133	15	j	j	NOUN
app01-4651	133	16	,	,	PUNCT
app01-4651	133	17	q	q	ADJ
app01-4651	133	18	}	}	PUNCT
app01-4651	133	19	∈	∈	PROPN
app01-4651	133	20	w,∀c	w,∀c	PROPN
app01-4651	133	21	∈	∈	PROPN
app01-4651	133	22	c.	c.	NOUN
app01-4651	133	23	(	(	PUNCT
app01-4651	133	24	26	26	NUM
app01-4651	133	25	)	)	PUNCT
app01-4651	133	26	finally	finally	ADV
app01-4651	133	27	,	,	PUNCT
app01-4651	133	28	different	different	ADJ
app01-4651	133	29	coloring	coloring	NOUN
app01-4651	133	30	of	of	ADP
app01-4651	133	31	the	the	DET
app01-4651	133	32	north	north	NOUN
app01-4651	133	33	edge	edge	NOUN
app01-4651	133	34	at	at	ADP
app01-4651	133	35	(	(	PUNCT
app01-4651	133	36	i	i	PROPN
app01-4651	133	37	,	,	PUNCT
app01-4651	133	38	j	j	PROPN
app01-4651	133	39	)	)	PUNCT
app01-4651	133	40	and	and	CCONJ
app01-4651	133	41	the	the	DET
app01-4651	133	42	west	west	PROPN
app01-4651	133	43	edge	edge	NOUN
app01-4651	133	44	at	at	ADP
app01-4651	133	45	(	(	PUNCT
app01-4651	133	46	p	p	X
app01-4651	133	47	,	,	PUNCT
app01-4651	133	48	q	q	NOUN
app01-4651	133	49	)	)	PUNCT
app01-4651	133	50	is	be	AUX
app01-4651	133	51	guaranteed	guarantee	VERB
app01-4651	133	52	through∑	through∑	PRON
app01-4651	133	53	k∈t	k∈t	NOUN
app01-4651	133	54	xi	xi	PROPN
app01-4651	133	55	,	,	PUNCT
app01-4651	133	56	j	j	PROPN
app01-4651	133	57	,	,	PUNCT
app01-4651	133	58	k[nk	k[nk	PROPN
app01-4651	133	59	=	=	SYM
app01-4651	134	1	c	c	X
app01-4651	134	2	]	]	X
app01-4651	134	3	+	+	CCONJ
app01-4651	134	4	∑	∑	PROPN
app01-4651	134	5	k∈t	k∈t	NOUN
app01-4651	134	6	xp	xp	PROPN
app01-4651	134	7	,	,	PUNCT
app01-4651	134	8	q	q	ADJ
app01-4651	134	9	,	,	PUNCT
app01-4651	134	10	k[wk	k[wk	NOUN
app01-4651	134	11	=	=	SYM
app01-4651	135	1	c	c	X
app01-4651	135	2	]	]	PUNCT
app01-4651	135	3	≤	≤	NUM
app01-4651	135	4	1	1	NUM
app01-4651	135	5	,	,	PUNCT
app01-4651	135	6	{	{	PUNCT
app01-4651	135	7	i	i	PRON
app01-4651	135	8	,	,	PUNCT
app01-4651	135	9	p	p	NOUN
app01-4651	135	10	}	}	PUNCT
app01-4651	135	11	∈	∈	PROPN
app01-4651	135	12	h	h	NOUN
app01-4651	135	13	,	,	PUNCT
app01-4651	135	14	{	{	PUNCT
app01-4651	135	15	j	j	NOUN
app01-4651	135	16	,	,	PUNCT
app01-4651	135	17	q	q	ADJ
app01-4651	135	18	}	}	PUNCT
app01-4651	135	19	∈	∈	PROPN
app01-4651	135	20	w,∀c	w,∀c	PROPN
app01-4651	135	21	∈	∈	PROPN
app01-4651	135	22	c.	c.	NOUN
app01-4651	135	23	(	(	PUNCT
app01-4651	135	24	27	27	NUM
app01-4651	135	25	)	)	PUNCT
app01-4651	135	26	2.5.3	2.5.3	NUM
app01-4651	135	27	.	.	PUNCT
app01-4651	135	28	periodic	periodic	ADJ
app01-4651	135	29	tiling	tile	VERB
app01-4651	135	30	periodic	periodic	ADJ
app01-4651	135	31	tiling	tiling	NOUN
app01-4651	135	32	is	be	AUX
app01-4651	135	33	a	a	DET
app01-4651	135	34	tiling	tiling	NOUN
app01-4651	135	35	with	with	ADP
app01-4651	135	36	equally	equally	ADV
app01-4651	135	37	colored	color	VERB
app01-4651	135	38	both	both	CCONJ
app01-4651	135	39	horizontal	horizontal	ADJ
app01-4651	135	40	and	and	CCONJ
app01-4651	135	41	also	also	ADV
app01-4651	135	42	both	both	CCONJ
app01-4651	135	43	vertical	vertical	ADJ
app01-4651	135	44	edges	edge	NOUN
app01-4651	135	45	.	.	PUNCT
app01-4651	136	1	thus	thus	ADV
app01-4651	136	2	,	,	PUNCT
app01-4651	136	3	periodic	periodic	ADJ
app01-4651	136	4	tiling	tiling	NOUN
app01-4651	136	5	secures	secure	VERB
app01-4651	136	6	tilability	tilability	NOUN
app01-4651	136	7	of	of	ADP
app01-4651	136	8	the	the	DET
app01-4651	136	9	infinite	infinite	ADJ
app01-4651	136	10	plane	plane	NOUN
app01-4651	136	11	.	.	PUNCT
app01-4651	137	1	building	build	VERB
app01-4651	137	2	on	on	ADP
app01-4651	137	3	the	the	DET
app01-4651	137	4	edge	edge	NOUN
app01-4651	137	5	-	-	PUNCT
app01-4651	137	6	based	base	VERB
app01-4651	137	7	boundary	boundary	ADJ
app01-4651	137	8	conditions	condition	NOUN
app01-4651	137	9	,	,	PUNCT
app01-4651	137	10	a	a	DET
app01-4651	137	11	periodic	periodic	ADJ
app01-4651	137	12	tiling	tiling	NOUN
app01-4651	137	13	can	can	AUX
app01-4651	137	14	be	be	AUX
app01-4651	137	15	enforced	enforce	VERB
app01-4651	137	16	by∑	by∑	ADJ
app01-4651	137	17	k∈t	k∈t	NOUN
app01-4651	137	18	x1,j	x1,j	PROPN
app01-4651	137	19	,	,	PUNCT
app01-4651	137	20	k[nk	k[nk	PROPN
app01-4651	137	21	=	=	PUNCT
app01-4651	137	22	c]−	c]−	VERB
app01-4651	137	23	∑	∑	PROPN
app01-4651	137	24	k∈t	k∈t	NOUN
app01-4651	137	25	xnt	xnt	PROPN
app01-4651	137	26	,	,	PUNCT
app01-4651	137	27	h	h	NOUN
app01-4651	137	28	,	,	PUNCT
app01-4651	137	29	j	j	PROPN
app01-4651	137	30	,	,	PUNCT
app01-4651	137	31	k[sk	k[sk	PROPN
app01-4651	137	32	=	=	PUNCT
app01-4651	137	33	c	c	X
app01-4651	137	34	]	]	X
app01-4651	137	35	=	=	SYM
app01-4651	137	36	0	0	NUM
app01-4651	137	37	,	,	PUNCT
app01-4651	137	38	∀j	∀j	PROPN
app01-4651	137	39	∈	∈	PROPN
app01-4651	137	40	w,∀c	w,∀c	PROPN
app01-4651	137	41	∈	∈	PROPN
app01-4651	137	42	c	c	PROPN
app01-4651	137	43	,	,	PUNCT
app01-4651	137	44	(	(	PUNCT
app01-4651	137	45	28a	28a	NOUN
app01-4651	137	46	)	)	PUNCT
app01-4651	137	47	∑	∑	PUNCT
app01-4651	137	48	k∈t	k∈t	NOUN
app01-4651	137	49	xi,1,k[wk	xi,1,k[wk	PUNCT
app01-4651	138	1	=	=	PUNCT
app01-4651	138	2	c]−	c]−	VERB
app01-4651	138	3	∑	∑	PROPN
app01-4651	138	4	k∈t	k∈t	NOUN
app01-4651	138	5	xi	xi	PROPN
app01-4651	138	6	,	,	PUNCT
app01-4651	138	7	nt	not	PART
app01-4651	138	8	,	,	PUNCT
app01-4651	138	9	w	w	NOUN
app01-4651	138	10	,	,	PUNCT
app01-4651	138	11	k[ek	k[ek	NOUN
app01-4651	138	12	=	=	SYM
app01-4651	138	13	c	c	X
app01-4651	138	14	]	]	X
app01-4651	138	15	=	=	SYM
app01-4651	138	16	0	0	NUM
app01-4651	138	17	,	,	PUNCT
app01-4651	138	18	∀i	∀i	X
app01-4651	138	19	∈	∈	PROPN
app01-4651	138	20	h,∀c	h,∀c	PROPN
app01-4651	138	21	∈	∈	PROPN
app01-4651	138	22	c.	c.	PROPN
app01-4651	138	23	(	(	PUNCT
app01-4651	138	24	28b	28b	NUM
app01-4651	138	25	)	)	PUNCT
app01-4651	138	26	2.5.4	2.5.4	NUM
app01-4651	138	27	.	.	PUNCT
app01-4651	139	1	tile	tile	NOUN
app01-4651	139	2	packing	packing	NOUN
app01-4651	139	3	problem	problem	NOUN
app01-4651	139	4	the	the	DET
app01-4651	139	5	tile	tile	NOUN
app01-4651	139	6	packing	packing	NOUN
app01-4651	139	7	problem	problem	NOUN
app01-4651	139	8	,	,	PUNCT
app01-4651	139	9	see	see	VERB
app01-4651	139	10	,	,	PUNCT
app01-4651	139	11	e.g.	e.g.	ADV
app01-4651	139	12	,	,	PUNCT
app01-4651	139	13	[	[	X
app01-4651	139	14	30	30	NUM
app01-4651	139	15	]	]	PUNCT
app01-4651	139	16	,	,	PUNCT
app01-4651	139	17	consists	consist	VERB
app01-4651	139	18	in	in	ADP
app01-4651	139	19	generation	generation	NOUN
app01-4651	139	20	of	of	ADP
app01-4651	139	21	a	a	DET
app01-4651	139	22	tiling	tiling	NOUN
app01-4651	139	23	with	with	ADP
app01-4651	139	24	periodic	periodic	ADJ
app01-4651	139	25	boundary	boundary	ADJ
app01-4651	139	26	conditions	condition	NOUN
app01-4651	139	27	,	,	PUNCT
app01-4651	139	28	and	and	CCONJ
app01-4651	139	29	each	each	DET
app01-4651	139	30	tile	tile	NOUN
app01-4651	139	31	has	have	VERB
app01-4651	139	32	to	to	PART
app01-4651	139	33	be	be	AUX
app01-4651	139	34	placed	place	VERB
app01-4651	139	35	exactly	exactly	ADV
app01-4651	139	36	once	once	ADV
app01-4651	139	37	.	.	PUNCT
app01-4651	140	1	in	in	ADP
app01-4651	140	2	order	order	NOUN
app01-4651	140	3	to	to	PART
app01-4651	140	4	describe	describe	VERB
app01-4651	140	5	the	the	DET
app01-4651	140	6	problem	problem	NOUN
app01-4651	140	7	in	in	ADP
app01-4651	140	8	our	our	PRON
app01-4651	140	9	framework	framework	NOUN
app01-4651	140	10	,	,	PUNCT
app01-4651	140	11	we	we	PRON
app01-4651	140	12	just	just	ADV
app01-4651	140	13	need	need	VERB
app01-4651	140	14	to	to	PART
app01-4651	140	15	use	use	VERB
app01-4651	140	16	eq	eq	ADP
app01-4651	140	17	.	.	PUNCT
app01-4651	141	1	(	(	PUNCT
app01-4651	141	2	28	28	NUM
app01-4651	141	3	)	)	PUNCT
app01-4651	141	4	together	together	ADV
app01-4651	141	5	with∑	with∑	PROPN
app01-4651	141	6	i∈h	i∈h	NOUN
app01-4651	141	7	∑	∑	PROPN
app01-4651	141	8	j∈w	j∈w	PROPN
app01-4651	141	9	xi	xi	PROPN
app01-4651	141	10	,	,	PUNCT
app01-4651	141	11	j	j	PROPN
app01-4651	141	12	,	,	PUNCT
app01-4651	141	13	k	k	PROPN
app01-4651	141	14	=	=	SYM
app01-4651	141	15	1	1	NUM
app01-4651	141	16	,	,	PUNCT
app01-4651	141	17	∀k	∀k	NOUN
app01-4651	141	18	∈	∈	PROPN
app01-4651	141	19	t	t	PROPN
app01-4651	141	20	.	.	PUNCT
app01-4651	142	1	(	(	PUNCT
app01-4651	142	2	29	29	NUM
app01-4651	142	3	)	)	PUNCT
app01-4651	142	4	2.5.5	2.5.5	NUM
app01-4651	142	5	.	.	PUNCT
app01-4651	142	6	objective	objective	ADJ
app01-4651	142	7	function	function	NOUN
app01-4651	142	8	obviously	obviously	ADV
app01-4651	142	9	,	,	PUNCT
app01-4651	142	10	the	the	DET
app01-4651	142	11	developed	develop	VERB
app01-4651	142	12	formulations	formulation	NOUN
app01-4651	142	13	can	can	AUX
app01-4651	142	14	contain	contain	VERB
app01-4651	142	15	arbitrary	arbitrary	ADJ
app01-4651	142	16	convex	convex	ADJ
app01-4651	142	17	objective	objective	ADJ
app01-4651	142	18	function	function	NOUN
app01-4651	142	19	.	.	PUNCT
app01-4651	143	1	for	for	ADP
app01-4651	143	2	instance	instance	NOUN
app01-4651	143	3	,	,	PUNCT
app01-4651	143	4	we	we	PRON
app01-4651	143	5	can	can	AUX
app01-4651	143	6	minimize	minimize	VERB
app01-4651	143	7	the	the	DET
app01-4651	143	8	maximum	maximum	ADJ
app01-4651	143	9	occurrences	occurrence	NOUN
app01-4651	143	10	of	of	ADP
app01-4651	143	11	tiles	tile	NOUN
app01-4651	143	12	,	,	PUNCT
app01-4651	143	13	compose	compose	VERB
app01-4651	143	14	the	the	DET
app01-4651	143	15	tiling	tiling	NOUN
app01-4651	143	16	such	such	ADJ
app01-4651	143	17	that	that	SCONJ
app01-4651	143	18	it	it	PRON
app01-4651	143	19	fits	fit	VERB
app01-4651	143	20	some	some	DET
app01-4651	143	21	pattern	pattern	NOUN
app01-4651	143	22	,	,	PUNCT
app01-4651	143	23	etc	etc	X
app01-4651	143	24	.	.	X
app01-4651	144	1	3	3	X
app01-4651	144	2	.	.	X
app01-4651	144	3	the	the	DET
app01-4651	144	4	branch	branch	NOUN
app01-4651	144	5	and	and	CCONJ
app01-4651	144	6	bound	bind	VERB
app01-4651	144	7	method	method	NOUN
app01-4651	144	8	the	the	DET
app01-4651	144	9	whole	whole	ADJ
app01-4651	144	10	integer	integer	NOUN
app01-4651	144	11	design	design	NOUN
app01-4651	144	12	space	space	NOUN
app01-4651	144	13	,	,	PUNCT
app01-4651	144	14	i.e.	i.e.	X
app01-4651	144	15	,	,	PUNCT
app01-4651	144	16	{	{	PUNCT
app01-4651	144	17	0	0	NUM
app01-4651	144	18	,	,	PUNCT
app01-4651	144	19	1	1	NUM
app01-4651	144	20	}	}	PUNCT
app01-4651	144	21	for	for	ADP
app01-4651	144	22	the	the	DET
app01-4651	144	23	linear	linear	NOUN
app01-4651	144	24	(	(	PUNCT
app01-4651	144	25	10	10	NUM
app01-4651	144	26	)	)	PUNCT
app01-4651	144	27	and	and	CCONJ
app01-4651	144	28	{	{	PUNCT
app01-4651	144	29	−1	−1	NOUN
app01-4651	144	30	,	,	PUNCT
app01-4651	144	31	1	1	NUM
app01-4651	144	32	}	}	PUNCT
app01-4651	144	33	for	for	ADP
app01-4651	144	34	the	the	DET
app01-4651	144	35	semidefinite	semidefinite	NOUN
app01-4651	144	36	(	(	PUNCT
app01-4651	144	37	19	19	NUM
app01-4651	144	38	)	)	PUNCT
app01-4651	144	39	approximation	approximation	NOUN
app01-4651	144	40	,	,	PUNCT
app01-4651	144	41	can	can	AUX
app01-4651	144	42	be	be	AUX
app01-4651	144	43	described	describe	VERB
app01-4651	144	44	using	use	VERB
app01-4651	144	45	a	a	DET
app01-4651	144	46	tree	tree	NOUN
app01-4651	144	47	data	datum	NOUN
app01-4651	144	48	structure	structure	NOUN
app01-4651	144	49	,	,	PUNCT
app01-4651	144	50	with	with	ADP
app01-4651	144	51	each	each	DET
app01-4651	144	52	node	node	NOUN
app01-4651	144	53	corresponding	correspond	VERB
app01-4651	144	54	to	to	ADP
app01-4651	144	55	variables	variable	NOUN
app01-4651	144	56	x	x	PRON
app01-4651	144	57	,	,	PUNCT
app01-4651	144	58	or	or	CCONJ
app01-4651	144	59	y.	y.	NOUN
app01-4651	144	60	however	however	ADV
app01-4651	144	61	,	,	PUNCT
app01-4651	144	62	as	as	SCONJ
app01-4651	144	63	there	there	PRON
app01-4651	144	64	is	be	VERB
app01-4651	144	65	exactly	exactly	ADV
app01-4651	144	66	one	one	NUM
app01-4651	144	67	tile	tile	NOUN
app01-4651	144	68	per	per	ADP
app01-4651	144	69	position	position	NOUN
app01-4651	144	70	,	,	PUNCT
app01-4651	144	71	it	it	PRON
app01-4651	144	72	is	be	AUX
app01-4651	144	73	advantageous	advantageous	ADJ
app01-4651	144	74	to	to	PART
app01-4651	144	75	use	use	VERB
app01-4651	144	76	the	the	DET
app01-4651	144	77	nt	not	PART
app01-4651	144	78	-	-	PUNCT
app01-4651	144	79	ary	ary	ADJ
app01-4651	144	80	tree	tree	NOUN
app01-4651	144	81	representation	representation	NOUN
app01-4651	144	82	instead	instead	ADV
app01-4651	144	83	of	of	ADP
app01-4651	144	84	the	the	DET
app01-4651	144	85	binary	binary	ADJ
app01-4651	144	86	one	one	NUM
app01-4651	144	87	,	,	PUNCT
app01-4651	144	88	so	so	SCONJ
app01-4651	144	89	that	that	SCONJ
app01-4651	144	90	the	the	DET
app01-4651	144	91	nodes	node	NOUN
app01-4651	144	92	correspond	correspond	VERB
app01-4651	144	93	to	to	ADP
app01-4651	144	94	the	the	DET
app01-4651	144	95	positions	position	NOUN
app01-4651	144	96	and	and	CCONJ
app01-4651	144	97	branch	branch	NOUN
app01-4651	144	98	into	into	ADP
app01-4651	144	99	nt	not	PART
app01-4651	144	100	children	child	NOUN
app01-4651	144	101	,	,	PUNCT
app01-4651	144	102	avoiding	avoid	VERB
app01-4651	144	103	solution	solution	NOUN
app01-4651	144	104	to	to	PART
app01-4651	144	105	infeasible	infeasible	VERB
app01-4651	144	106	programs	program	NOUN
app01-4651	144	107	placing	place	VERB
app01-4651	144	108	multiple	multiple	ADJ
app01-4651	144	109	tiles	tile	NOUN
app01-4651	144	110	at	at	ADP
app01-4651	144	111	the	the	DET
app01-4651	144	112	same	same	ADJ
app01-4651	144	113	position	position	NOUN
app01-4651	144	114	.	.	PUNCT
app01-4651	145	1	solution	solution	NOUN
app01-4651	145	2	to	to	ADP
app01-4651	145	3	the	the	DET
app01-4651	145	4	developed	develop	VERB
app01-4651	145	5	approximations	approximation	NOUN
app01-4651	145	6	,	,	PUNCT
app01-4651	145	7	(	(	PUNCT
app01-4651	145	8	10	10	NUM
app01-4651	145	9	)	)	PUNCT
app01-4651	145	10	or	or	CCONJ
app01-4651	145	11	(	(	PUNCT
app01-4651	145	12	19	19	NUM
app01-4651	145	13	)	)	PUNCT
app01-4651	145	14	,	,	PUNCT
app01-4651	145	15	corresponds	correspond	VERB
app01-4651	145	16	to	to	ADP
app01-4651	145	17	exploring	explore	VERB
app01-4651	145	18	the	the	DET
app01-4651	145	19	root	root	NOUN
app01-4651	145	20	node	node	NOUN
app01-4651	145	21	of	of	ADP
app01-4651	145	22	the	the	DET
app01-4651	145	23	tree	tree	NOUN
app01-4651	145	24	.	.	PUNCT
app01-4651	146	1	unfortunately	unfortunately	ADV
app01-4651	146	2	,	,	PUNCT
app01-4651	146	3	because	because	SCONJ
app01-4651	146	4	the	the	DET
app01-4651	146	5	approximations	approximation	NOUN
app01-4651	146	6	widen	widen	VERB
app01-4651	146	7	the	the	DET
app01-4651	146	8	feasible	feasible	ADJ
app01-4651	146	9	design	design	NOUN
app01-4651	146	10	space	space	NOUN
app01-4651	146	11	,	,	PUNCT
app01-4651	146	12	their	their	PRON
app01-4651	146	13	solution	solution	NOUN
app01-4651	146	14	does	do	AUX
app01-4651	146	15	not	not	PART
app01-4651	146	16	assure	assure	VERB
app01-4651	146	17	to	to	PART
app01-4651	146	18	solve	solve	VERB
app01-4651	146	19	the	the	DET
app01-4651	146	20	original	original	ADJ
app01-4651	146	21	problem	problem	NOUN
app01-4651	146	22	(	(	PUNCT
app01-4651	146	23	8)	8)	NUM
app01-4651	146	24	due	due	ADP
app01-4651	146	25	to	to	ADP
app01-4651	146	26	the	the	DET
app01-4651	146	27	design	design	NOUN
app01-4651	146	28	variables	variable	NOUN
app01-4651	146	29	being	be	AUX
app01-4651	146	30	allowed	allow	VERB
app01-4651	146	31	to	to	PART
app01-4651	146	32	take	take	VERB
app01-4651	146	33	non	non	ADJ
app01-4651	146	34	-	-	ADJ
app01-4651	146	35	integer	integer	ADJ
app01-4651	146	36	values	value	NOUN
app01-4651	146	37	.	.	PUNCT
app01-4651	147	1	in	in	ADP
app01-4651	147	2	order	order	NOUN
app01-4651	147	3	to	to	PART
app01-4651	147	4	overcome	overcome	VERB
app01-4651	147	5	that	that	SCONJ
app01-4651	147	6	,	,	PUNCT
app01-4651	147	7	we	we	PRON
app01-4651	147	8	branch	branch	VERB
app01-4651	147	9	some	some	DET
app01-4651	147	10	nodes	node	NOUN
app01-4651	147	11	of	of	ADP
app01-4651	147	12	the	the	DET
app01-4651	147	13	tree	tree	NOUN
app01-4651	147	14	,	,	PUNCT
app01-4651	147	15	i.e.	i.e.	X
app01-4651	147	16	,	,	PUNCT
app01-4651	147	17	gradually	gradually	ADV
app01-4651	147	18	fix	fix	VERB
app01-4651	147	19	all	all	DET
app01-4651	147	20	variables	variable	NOUN
app01-4651	147	21	that	that	PRON
app01-4651	147	22	correspond	correspond	VERB
app01-4651	147	23	to	to	ADP
app01-4651	147	24	the	the	DET
app01-4651	147	25	specific	specific	ADJ
app01-4651	147	26	tile	tile	NOUN
app01-4651	147	27	position	position	NOUN
app01-4651	147	28	to	to	ADP
app01-4651	147	29	all	all	DET
app01-4651	147	30	possible	possible	ADJ
app01-4651	147	31	combinations	combination	NOUN
app01-4651	147	32	of	of	ADP
app01-4651	147	33	integer	integer	NOUN
app01-4651	147	34	values	value	NOUN
app01-4651	147	35	,	,	PUNCT
app01-4651	147	36	nt	not	PART
app01-4651	147	37	in	in	ADP
app01-4651	147	38	our	our	PRON
app01-4651	147	39	case	case	NOUN
app01-4651	147	40	.	.	PUNCT
app01-4651	148	1	the	the	DET
app01-4651	148	2	relaxation	relaxation	NOUN
app01-4651	148	3	is	be	AUX
app01-4651	148	4	solved	solve	VERB
app01-4651	148	5	in	in	ADP
app01-4651	148	6	each	each	DET
app01-4651	148	7	node	node	NOUN
app01-4651	148	8	,	,	PUNCT
app01-4651	148	9	bounding	bound	VERB
app01-4651	148	10	the	the	DET
app01-4651	148	11	problem1	problem1	NOUN
app01-4651	148	12	,	,	PUNCT
app01-4651	148	13	hence	hence	ADV
app01-4651	148	14	the	the	DET
app01-4651	148	15	name	name	NOUN
app01-4651	148	16	of	of	ADP
app01-4651	148	17	the	the	DET
app01-4651	148	18	method	method	NOUN
app01-4651	148	19	branch	branch	NOUN
app01-4651	148	20	and	and	CCONJ
app01-4651	148	21	bound	bind	VERB
app01-4651	148	22	[	[	PUNCT
app01-4651	148	23	33	33	NUM
app01-4651	148	24	]	]	PUNCT
app01-4651	148	25	.	.	PUNCT
app01-4651	149	1	the	the	DET
app01-4651	149	2	branching	branching	NOUN
app01-4651	149	3	and	and	CCONJ
app01-4651	149	4	bounding	bounding	NOUN
app01-4651	149	5	continues	continue	VERB
app01-4651	149	6	until	until	SCONJ
app01-4651	149	7	the	the	DET
app01-4651	149	8	optimal	optimal	ADJ
app01-4651	149	9	(	(	PUNCT
app01-4651	149	10	feasible	feasible	ADJ
app01-4651	149	11	)	)	PUNCT
app01-4651	149	12	solution	solution	NOUN
app01-4651	149	13	to	to	ADP
app01-4651	149	14	(	(	PUNCT
app01-4651	149	15	8)	8)	NUM
app01-4651	149	16	is	be	AUX
app01-4651	149	17	found	find	VERB
app01-4651	149	18	.	.	PUNCT
app01-4651	150	1	if	if	SCONJ
app01-4651	150	2	no	no	DET
app01-4651	150	3	such	such	ADJ
app01-4651	150	4	solution	solution	NOUN
app01-4651	150	5	exists	exist	VERB
app01-4651	150	6	,	,	PUNCT
app01-4651	150	7	the	the	DET
app01-4651	150	8	solution	solution	NOUN
app01-4651	150	9	space	space	NOUN
app01-4651	150	10	is	be	AUX
app01-4651	150	11	proven	prove	VERB
app01-4651	150	12	to	to	PART
app01-4651	150	13	be	be	AUX
app01-4651	150	14	empty	empty	ADJ
app01-4651	150	15	and	and	CCONJ
app01-4651	150	16	the	the	DET
app01-4651	150	17	tiling	tile	VERB
app01-4651	150	18	generation	generation	NOUN
app01-4651	150	19	problem	problem	NOUN
app01-4651	150	20	infeasible	infeasible	ADJ
app01-4651	150	21	.	.	PUNCT
app01-4651	151	1	without	without	ADP
app01-4651	151	2	boundary	boundary	ADJ
app01-4651	151	3	conditions	condition	NOUN
app01-4651	151	4	,	,	PUNCT
app01-4651	151	5	infeasibility	infeasibility	NOUN
app01-4651	151	6	proves	prove	VERB
app01-4651	151	7	the	the	DET
app01-4651	151	8	tile	tile	NOUN
app01-4651	151	9	set	set	NOUN
app01-4651	151	10	does	do	AUX
app01-4651	151	11	not	not	PART
app01-4651	151	12	tile	tile	VERB
app01-4651	151	13	infinite	infinite	ADJ
app01-4651	151	14	plane	plane	NOUN
app01-4651	151	15	.	.	PUNCT
app01-4651	152	1	3.1	3.1	NUM
app01-4651	152	2	.	.	X
app01-4651	153	1	branching	branch	VERB
app01-4651	153	2	rule	rule	NOUN
app01-4651	153	3	in	in	ADP
app01-4651	153	4	our	our	PRON
app01-4651	153	5	implementation	implementation	NOUN
app01-4651	153	6	,	,	PUNCT
app01-4651	153	7	we	we	PRON
app01-4651	153	8	firstly	firstly	ADV
app01-4651	153	9	branch	branch	VERB
app01-4651	153	10	the	the	DET
app01-4651	153	11	most	most	ADV
app01-4651	153	12	promising	promising	ADJ
app01-4651	153	13	nodes	node	NOUN
app01-4651	153	14	,	,	PUNCT
app01-4651	153	15	in	in	ADP
app01-4651	153	16	which	which	PRON
app01-4651	153	17	the	the	DET
app01-4651	153	18	integer	integer	ADJ
app01-4651	153	19	infeasibility	infeasibility	NOUN
app01-4651	153	20	of	of	ADP
app01-4651	153	21	the	the	DET
app01-4651	153	22	convex	convex	NOUN
app01-4651	153	23	relaxation	relaxation	NOUN
app01-4651	153	24	is	be	AUX
app01-4651	153	25	minimal	minimal	ADJ
app01-4651	153	26	.	.	PUNCT
app01-4651	154	1	for	for	ADP
app01-4651	154	2	the	the	DET
app01-4651	154	3	linear	linear	ADJ
app01-4651	154	4	relaxation	relaxation	NOUN
app01-4651	154	5	,	,	PUNCT
app01-4651	154	6	we	we	PRON
app01-4651	154	7	have	have	AUX
app01-4651	154	8	iinf	iinf	VERB
app01-4651	154	9	=	=	PUNCT
app01-4651	154	10	∑	∑	PUNCT
app01-4651	154	11	i∈h	i∈h	VERB
app01-4651	154	12	∑	∑	PUNCT
app01-4651	154	13	j∈w	j∈w	PROPN
app01-4651	154	14	∑	∑	PROPN
app01-4651	154	15	k∈t	k∈t	NOUN
app01-4651	154	16	(	(	PUNCT
app01-4651	154	17	xi	xi	PROPN
app01-4651	154	18	,	,	PUNCT
app01-4651	154	19	j	j	PROPN
app01-4651	154	20	,	,	PUNCT
app01-4651	154	21	k	k	PROPN
app01-4651	155	1	−	−	PROPN
app01-4651	156	1	x2	x2	INTJ
app01-4651	157	1	i	i	PROPN
app01-4651	157	2	,	,	PUNCT
app01-4651	157	3	j	j	PROPN
app01-4651	157	4	,	,	PUNCT
app01-4651	157	5	k	k	PROPN
app01-4651	157	6	)	)	PUNCT
app01-4651	157	7	,	,	PUNCT
app01-4651	157	8	(	(	PUNCT
app01-4651	157	9	30	30	NUM
app01-4651	157	10	)	)	PUNCT
app01-4651	157	11	or	or	CCONJ
app01-4651	157	12	iinf	iinf	ADJ
app01-4651	157	13	=	=	SYM
app01-4651	157	14	nt	nt	PROPN
app01-4651	157	15	,	,	PUNCT
app01-4651	157	16	hnt	hnt	PROPN
app01-4651	157	17	,	,	PUNCT
app01-4651	157	18	wnt	wnt	PROPN
app01-4651	157	19	−	−	PUNCT
app01-4651	157	20	∑	∑	PUNCT
app01-4651	157	21	i∈h	i∈h	VERB
app01-4651	157	22	∑	∑	PUNCT
app01-4651	157	23	j∈w	j∈w	PROPN
app01-4651	157	24	∑	∑	PUNCT
app01-4651	157	25	k∈t	k∈t	NOUN
app01-4651	158	1	y2	y2	INTJ
app01-4651	159	1	i	i	PROPN
app01-4651	159	2	,	,	PUNCT
app01-4651	159	3	j	j	PROPN
app01-4651	159	4	,	,	PUNCT
app01-4651	159	5	k	k	PROPN
app01-4651	159	6	(	(	PUNCT
app01-4651	159	7	31	31	NUM
app01-4651	159	8	)	)	PUNCT
app01-4651	159	9	for	for	ADP
app01-4651	159	10	the	the	DET
app01-4651	159	11	semidefinite	semidefinite	PROPN
app01-4651	159	12	relaxation	relaxation	NOUN
app01-4651	159	13	.	.	PUNCT
app01-4651	160	1	if	if	SCONJ
app01-4651	160	2	iinf	iinf	ADJ
app01-4651	160	3	=	=	SYM
app01-4651	160	4	0	0	PROPN
app01-4651	160	5	,	,	PUNCT
app01-4651	160	6	a	a	DET
app01-4651	160	7	feasible	feasible	ADJ
app01-4651	160	8	solution	solution	NOUN
app01-4651	160	9	to	to	ADP
app01-4651	160	10	the	the	DET
app01-4651	160	11	original	original	ADJ
app01-4651	160	12	problem	problem	NOUN
app01-4651	160	13	was	be	AUX
app01-4651	160	14	found	find	VERB
app01-4651	160	15	.	.	PUNCT
app01-4651	161	1	3.2	3.2	NUM
app01-4651	161	2	.	.	PUNCT
app01-4651	162	1	variables	variable	NOUN
app01-4651	162	2	ordering	order	VERB
app01-4651	162	3	in	in	ADP
app01-4651	162	4	each	each	DET
app01-4651	162	5	node	node	NOUN
app01-4651	162	6	to	to	PART
app01-4651	162	7	be	be	AUX
app01-4651	162	8	branched	branch	VERB
app01-4651	162	9	,	,	PUNCT
app01-4651	162	10	we	we	PRON
app01-4651	162	11	have	have	VERB
app01-4651	162	12	to	to	PART
app01-4651	162	13	define	define	VERB
app01-4651	162	14	variables	variable	NOUN
app01-4651	162	15	that	that	PRON
app01-4651	162	16	will	will	AUX
app01-4651	162	17	be	be	AUX
app01-4651	162	18	fixed	fix	VERB
app01-4651	162	19	.	.	PUNCT
app01-4651	163	1	it	it	PRON
app01-4651	163	2	seems	seem	VERB
app01-4651	163	3	to	to	PART
app01-4651	163	4	be	be	AUX
app01-4651	163	5	advantageous	advantageous	ADJ
app01-4651	163	6	to	to	PART
app01-4651	163	7	fix	fix	VERB
app01-4651	163	8	the	the	DET
app01-4651	163	9	variables	variable	NOUN
app01-4651	163	10	corresponding	correspond	VERB
app01-4651	163	11	to	to	ADP
app01-4651	163	12	the	the	DET
app01-4651	163	13	most	most	ADV
app01-4651	163	14	difficult	difficult	ADJ
app01-4651	163	15	position	position	NOUN
app01-4651	163	16	,	,	PUNCT
app01-4651	163	17	i.e.	i.e.	X
app01-4651	163	18	,	,	PUNCT
app01-4651	163	19	to	to	ADP
app01-4651	163	20	the	the	DET
app01-4651	163	21	position	position	NOUN
app01-4651	163	22	with	with	ADP
app01-4651	163	23	the	the	DET
app01-4651	163	24	highest	high	ADJ
app01-4651	163	25	integer	integer	NOUN
app01-4651	163	26	infeasibility	infeasibility	NOUN
app01-4651	163	27	.	.	PUNCT
app01-4651	164	1	in	in	ADP
app01-4651	164	2	the	the	DET
app01-4651	164	3	case	case	NOUN
app01-4651	164	4	of	of	ADP
app01-4651	164	5	the	the	DET
app01-4651	164	6	linear	linear	ADJ
app01-4651	164	7	relaxation	relaxation	NOUN
app01-4651	164	8	,	,	PUNCT
app01-4651	164	9	the	the	DET
app01-4651	164	10	to	to	PART
app01-4651	164	11	-	-	PUNCT
app01-4651	164	12	be	be	AUX
app01-4651	164	13	-	-	PUNCT
app01-4651	164	14	fixed	fix	VERB
app01-4651	164	15	position	position	NOUN
app01-4651	164	16	(	(	PUNCT
app01-4651	164	17	i	i	PROPN
app01-4651	164	18	,	,	PUNCT
app01-4651	164	19	j	j	PROPN
app01-4651	164	20	)	)	PUNCT
app01-4651	164	21	requires	require	VERB
app01-4651	164	22	max	max	PROPN
app01-4651	164	23	∀i∈h,∀j∈w	∀i∈h,∀j∈w	PROPN
app01-4651	164	24	∑	∑	PROPN
app01-4651	164	25	k∈t	k∈t	NOUN
app01-4651	164	26	(	(	PUNCT
app01-4651	164	27	xi	xi	PROPN
app01-4651	164	28	,	,	PUNCT
app01-4651	164	29	j	j	PROPN
app01-4651	164	30	,	,	PUNCT
app01-4651	164	31	k	k	PROPN
app01-4651	165	1	−	−	PROPN
app01-4651	166	1	x2	x2	INTJ
app01-4651	167	1	i	i	PROPN
app01-4651	167	2	,	,	PUNCT
app01-4651	167	3	j	j	PROPN
app01-4651	167	4	,	,	PUNCT
app01-4651	167	5	k	k	PROPN
app01-4651	167	6	)	)	PUNCT
app01-4651	167	7	.	.	PUNCT
app01-4651	168	1	(	(	PUNCT
app01-4651	168	2	32	32	NUM
app01-4651	168	3	)	)	PUNCT
app01-4651	168	4	similarly	similarly	ADV
app01-4651	168	5	,	,	PUNCT
app01-4651	168	6	for	for	ADP
app01-4651	168	7	the	the	DET
app01-4651	168	8	semidefinite	semidefinite	PROPN
app01-4651	168	9	relaxation	relaxation	NOUN
app01-4651	168	10	we	we	PRON
app01-4651	168	11	write	write	VERB
app01-4651	168	12	max	max	PROPN
app01-4651	168	13	∀i∈h,∀j∈w	∀i∈h,∀j∈w	PROPN
app01-4651	168	14	(	(	PUNCT
app01-4651	168	15	nt	not	PART
app01-4651	168	16	−	−	PROPN
app01-4651	168	17	∑	∑	PROPN
app01-4651	168	18	k∈t	k∈t	NOUN
app01-4651	169	1	y2	y2	INTJ
app01-4651	170	1	i	i	PROPN
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app01-4651	170	3	j	j	PROPN
app01-4651	170	4	,	,	PUNCT
app01-4651	170	5	k	k	PROPN
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app01-4651	170	7	.	.	PUNCT
app01-4651	171	1	(	(	PUNCT
app01-4651	171	2	33	33	NUM
app01-4651	171	3	)	)	PUNCT
app01-4651	171	4	4	4	NUM
app01-4651	171	5	.	.	PUNCT
app01-4651	172	1	examples	example	NOUN
app01-4651	172	2	building	build	VERB
app01-4651	172	3	upon	upon	SCONJ
app01-4651	172	4	the	the	DET
app01-4651	172	5	previous	previous	ADJ
app01-4651	172	6	sections	section	NOUN
app01-4651	172	7	,	,	PUNCT
app01-4651	172	8	we	we	PRON
app01-4651	172	9	implemented	implement	VERB
app01-4651	172	10	a	a	DET
app01-4651	172	11	custom	custom	NOUN
app01-4651	172	12	branch	branch	NOUN
app01-4651	172	13	and	and	CCONJ
app01-4651	172	14	bound	bind	VERB
app01-4651	172	15	algorithm	algorithm	NOUN
app01-4651	172	16	in	in	ADP
app01-4651	172	17	c++	c++	NOUN
app01-4651	172	18	.	.	PUNCT
app01-4651	173	1	the	the	DET
app01-4651	173	2	linear	linear	ADJ
app01-4651	173	3	relaxations	relaxation	NOUN
app01-4651	173	4	are	be	AUX
app01-4651	173	5	solved	solve	VERB
app01-4651	173	6	using	use	VERB
app01-4651	173	7	gurobi	gurobi	NOUN
app01-4651	174	1	[	[	X
app01-4651	174	2	34	34	NUM
app01-4651	174	3	]	]	PUNCT
app01-4651	174	4	,	,	PUNCT
app01-4651	174	5	the	the	DET
app01-4651	174	6	semidefinite	semidefinite	NOUN
app01-4651	174	7	programming	programming	NOUN
app01-4651	174	8	relaxations	relaxation	NOUN
app01-4651	174	9	are	be	AUX
app01-4651	174	10	optimized	optimize	VERB
app01-4651	174	11	by	by	ADP
app01-4651	174	12	mosek	mosek	PROPN
app01-4651	174	13	[	[	X
app01-4651	174	14	35	35	NUM
app01-4651	174	15	]	]	PUNCT
app01-4651	174	16	.	.	PUNCT
app01-4651	175	1	as	as	SCONJ
app01-4651	175	2	gurobi	gurobi	NOUN
app01-4651	175	3	contains	contain	VERB
app01-4651	175	4	a	a	DET
app01-4651	175	5	build	build	NOUN
app01-4651	175	6	-	-	PUNCT
app01-4651	175	7	in	in	ADP
app01-4651	175	8	state	state	NOUN
app01-4651	175	9	-	-	PUNCT
app01-4651	175	10	ofthe	ofthe	NOUN
app01-4651	175	11	-	-	PUNCT
app01-4651	175	12	art	art	NOUN
app01-4651	175	13	branch	branch	NOUN
app01-4651	175	14	and	and	CCONJ
app01-4651	175	15	cut	cut	VERB
app01-4651	175	16	algorithm	algorithm	NOUN
app01-4651	175	17	,	,	PUNCT
app01-4651	175	18	usable	usable	ADJ
app01-4651	175	19	only	only	ADV
app01-4651	175	20	for	for	ADP
app01-4651	175	21	the	the	DET
app01-4651	175	22	linear	linear	ADJ
app01-4651	175	23	relaxations	relaxation	NOUN
app01-4651	175	24	,	,	PUNCT
app01-4651	175	25	we	we	PRON
app01-4651	175	26	also	also	ADV
app01-4651	175	27	measured	measure	VERB
app01-4651	175	28	its	its	PRON
app01-4651	175	29	performance	performance	NOUN
app01-4651	175	30	.	.	PUNCT
app01-4651	176	1	five	five	NUM
app01-4651	176	2	tile	tile	NOUN
app01-4651	176	3	sets	set	NOUN
app01-4651	176	4	were	be	AUX
app01-4651	176	5	tested	test	VERB
app01-4651	176	6	altogether	altogether	ADV
app01-4651	176	7	:	:	PUNCT
app01-4651	176	8	jeandel	jeandel	PROPN
app01-4651	176	9	’s	’s	PART
app01-4651	176	10	11	11	NUM
app01-4651	176	11	tiles	tile	NOUN
app01-4651	176	12	over	over	ADP
app01-4651	176	13	4	4	NUM
app01-4651	176	14	colors	color	NOUN
app01-4651	176	15	[	[	X
app01-4651	176	16	16	16	NUM
app01-4651	176	17	]	]	PUNCT
app01-4651	176	18	,	,	PUNCT
app01-4651	176	19	čulík	čulík	PROPN
app01-4651	176	20	’s	’s	PART
app01-4651	176	21	13	13	NUM
app01-4651	176	22	tiles	tile	NOUN
app01-4651	176	23	[	[	X
app01-4651	176	24	15	15	NUM
app01-4651	176	25	]	]	PUNCT
app01-4651	176	26	,	,	PUNCT
app01-4651	176	27	ammann	ammann	PROPN
app01-4651	176	28	’s	’s	PART
app01-4651	176	29	16	16	NUM
app01-4651	176	30	tiles	tile	NOUN
app01-4651	176	31	[	[	X
app01-4651	176	32	12	12	NUM
app01-4651	176	33	]	]	PUNCT
app01-4651	176	34	,	,	PUNCT
app01-4651	176	35	lauchli	lauchli	PROPN
app01-4651	176	36	’s	’s	PART
app01-4651	176	37	40	40	NUM
app01-4651	176	38	tiles	tile	NOUN
app01-4651	177	1	[	[	X
app01-4651	177	2	12	12	NUM
app01-4651	177	3	]	]	PUNCT
app01-4651	177	4	,	,	PUNCT
app01-4651	177	5	and	and	CCONJ
app01-4651	177	6	nurmi	nurmi	PROPN
app01-4651	177	7	’s	’s	PART
app01-4651	177	8	1bounding	1bounding	PROPN
app01-4651	177	9	occurs	occur	VERB
app01-4651	177	10	only	only	ADV
app01-4651	177	11	if	if	SCONJ
app01-4651	177	12	an	an	DET
app01-4651	177	13	objective	objective	ADJ
app01-4651	177	14	fuction	fuction	NOUN
app01-4651	177	15	is	be	AUX
app01-4651	177	16	employed	employ	VERB
app01-4651	177	17	.	.	PUNCT
app01-4651	178	1	139	139	NUM
app01-4651	178	2	marek	marek	PROPN
app01-4651	178	3	tyburec	tyburec	NOUN
app01-4651	178	4	,	,	PUNCT
app01-4651	178	5	jan	jan	PROPN
app01-4651	178	6	zeman	zeman	PROPN
app01-4651	178	7	acta	acta	PROPN
app01-4651	178	8	polytechnica	polytechnica	PROPN
app01-4651	178	9	ctu	ctu	NOUN
app01-4651	178	10	proceedings	proceeding	NOUN
app01-4651	178	11	11(4	11(4	NUM
app01-4651	178	12	)	)	PUNCT
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app01-4651	179	2	16	16	NUM
app01-4651	179	3	]	]	SYM
app01-4651	179	4	13(5	13(5	X
app01-4651	179	5	)	)	PUNCT
app01-4651	180	1	[	[	X
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app01-4651	180	3	]	]	SYM
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app01-4651	180	5	)	)	PUNCT
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app01-4651	181	2	12	12	NUM
app01-4651	181	3	]	]	SYM
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app01-4651	181	5	)	)	PUNCT
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app01-4651	182	2	8	8	NUM
app01-4651	182	3	]	]	PUNCT
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app01-4651	182	5	)	)	PUNCT
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app01-4651	183	2	19	19	NUM
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app01-4651	183	4	tile	tile	NOUN
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app01-4651	183	6	tiling	tile	VERB
app01-4651	183	7	sample	sample	NOUN
app01-4651	183	8	lp	lp	NOUN
app01-4651	183	9	5×	5×	NOUN
app01-4651	183	10	5	5	NUM
app01-4651	183	11	0.13	0.13	NUM
app01-4651	183	12	s/12	s/12	PROPN
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app01-4651	186	1	0.01	0.01	NUM
app01-4651	186	2	s/1	s/1	PROPN
app01-4651	186	3	rel	rel	NOUN
app01-4651	186	4	.	.	PROPN
app01-4651	186	5	0.01	0.01	NUM
app01-4651	186	6	s/1	s/1	PROPN
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app01-4651	186	8	.	.	PUNCT
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app01-4651	187	1	5×	5×	NOUN
app01-4651	187	2	5	5	NUM
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app01-4651	192	2	6×	6×	NOUN
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app01-4651	192	5	s/12	s/12	PROPN
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app01-4651	193	2	s/17	s/17	PROPN
app01-4651	193	3	rel	rel	NOUN
app01-4651	193	4	.	.	PROPN
app01-4651	193	5	0.02	0.02	NUM
app01-4651	193	6	s/1	s/1	PROPN
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app01-4651	193	10	s/1	s/1	PROPN
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app01-4651	193	12	.	.	PUNCT
app01-4651	194	1	sdp	sdp	NOUN
app01-4651	194	2	6×	6×	NOUN
app01-4651	194	3	6	6	NUM
app01-4651	194	4	69.60	69.60	NUM
app01-4651	194	5	s/34	s/34	NOUN
app01-4651	194	6	rel	rel	NOUN
app01-4651	194	7	.	.	PUNCT
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app01-4651	196	2	s/33	s/33	ADJ
app01-4651	196	3	rel	rel	NOUN
app01-4651	196	4	.	.	PROPN
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app01-4651	196	8	.	.	PUNCT
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app01-4651	197	4	151.82	151.82	NUM
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app01-4651	197	6	rel	rel	NOUN
app01-4651	197	7	.	.	PUNCT
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app01-4651	198	3	s	s	PART
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app01-4651	199	4	.	.	PUNCT
app01-4651	200	1	lpg	lpg	VERB
app01-4651	200	2	15×	15×	NUM
app01-4651	200	3	15	15	NUM
app01-4651	200	4	0.06	0.06	NUM
app01-4651	200	5	s/0	s/0	PRON
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app01-4651	201	4	.	.	PUNCT
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app01-4651	204	4	.	.	PUNCT
app01-4651	205	1	lp	lp	NOUN
app01-4651	205	2	20×	20×	NUM
app01-4651	205	3	20	20	NUM
app01-4651	205	4	1545.94	1545.94	NUM
app01-4651	205	5	s/26137	s/26137	NOUN
app01-4651	205	6	rel	rel	NOUN
app01-4651	205	7	.	.	PUNCT
app01-4651	206	1	over	over	ADP
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app01-4651	206	3	s	s	PART
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app01-4651	206	7	.	.	PUNCT
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app01-4651	207	2	s/41	s/41	PROPN
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app01-4651	209	2	20×	20×	NUM
app01-4651	209	3	20	20	NUM
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app01-4651	209	5	s/0	s/0	DET
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app01-4651	222	4	.	.	PUNCT
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app01-4651	223	4	.	.	PUNCT
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app01-4651	223	19	.	.	PUNCT
app01-4651	224	1	lp	lp	NOUN
app01-4651	224	2	and	and	CCONJ
app01-4651	224	3	sdp	sdp	NOUN
app01-4651	224	4	denote	denote	NOUN
app01-4651	224	5	custom	custom	NOUN
app01-4651	224	6	developed	develop	VERB
app01-4651	224	7	branch	branch	NOUN
app01-4651	224	8	and	and	CCONJ
app01-4651	224	9	bound	bind	VERB
app01-4651	224	10	method	method	NOUN
app01-4651	224	11	supplied	supply	VERB
app01-4651	224	12	with	with	ADP
app01-4651	224	13	the	the	DET
app01-4651	224	14	linear	linear	ADJ
app01-4651	224	15	and	and	CCONJ
app01-4651	224	16	semidefinite	semidefinite	PROPN
app01-4651	224	17	relaxation	relaxation	NOUN
app01-4651	224	18	,	,	PUNCT
app01-4651	224	19	respectively	respectively	ADV
app01-4651	224	20	;	;	PUNCT
app01-4651	224	21	lpg	lpg	NOUN
app01-4651	224	22	stands	stand	VERB
app01-4651	224	23	for	for	ADP
app01-4651	224	24	gurobi	gurobi	NOUN
app01-4651	224	25	cut	cut	VERB
app01-4651	224	26	-	-	PUNCT
app01-4651	224	27	and	and	CCONJ
app01-4651	224	28	-	-	PUNCT
app01-4651	224	29	branch	branch	NOUN
app01-4651	224	30	method	method	NOUN
app01-4651	224	31	and	and	CCONJ
app01-4651	224	32	the	the	DET
app01-4651	224	33	linear	linear	ADJ
app01-4651	224	34	relaxation	relaxation	NOUN
app01-4651	224	35	.	.	PUNCT
app01-4651	225	1	set	set	NOUN
app01-4651	225	2	of	of	ADP
app01-4651	225	3	30	30	NUM
app01-4651	225	4	corner	corner	NOUN
app01-4651	225	5	tiles	tile	NOUN
app01-4651	225	6	[	[	X
app01-4651	225	7	19	19	NUM
app01-4651	225	8	]	]	PUNCT
app01-4651	225	9	.	.	PUNCT
app01-4651	226	1	the	the	DET
app01-4651	226	2	tile	tile	NOUN
app01-4651	226	3	sets	set	NOUN
app01-4651	226	4	were	be	AUX
app01-4651	226	5	selected	select	VERB
app01-4651	226	6	to	to	PART
app01-4651	226	7	sample	sample	VERB
app01-4651	226	8	different	different	ADJ
app01-4651	226	9	construction	construction	NOUN
app01-4651	226	10	methods	method	NOUN
app01-4651	226	11	,	,	PUNCT
app01-4651	226	12	tile	tile	NOUN
app01-4651	226	13	set	set	VERB
app01-4651	226	14	sizes	size	NOUN
app01-4651	226	15	,	,	PUNCT
app01-4651	226	16	and	and	CCONJ
app01-4651	226	17	numbers	number	NOUN
app01-4651	226	18	of	of	ADP
app01-4651	226	19	colors	color	NOUN
app01-4651	226	20	used	use	VERB
app01-4651	226	21	.	.	PUNCT
app01-4651	227	1	results	result	NOUN
app01-4651	227	2	of	of	ADP
app01-4651	227	3	the	the	DET
app01-4651	227	4	benchmarks	benchmark	NOUN
app01-4651	227	5	,	,	PUNCT
app01-4651	227	6	ran	run	VERB
app01-4651	227	7	on	on	ADP
app01-4651	227	8	the	the	DET
app01-4651	227	9	intel	intel	PROPN
app01-4651	227	10	®	®	NOUN
app01-4651	227	11	core	core	NOUN
app01-4651	227	12	™	™	VERB
app01-4651	227	13	i5	i5	ADJ
app01-4651	227	14	-	-	PUNCT
app01-4651	227	15	4210h	4210h	NOUN
app01-4651	227	16	processor	processor	NOUN
app01-4651	227	17	,	,	PUNCT
app01-4651	227	18	are	be	AUX
app01-4651	227	19	summarized	summarize	VERB
app01-4651	227	20	in	in	ADP
app01-4651	227	21	table	table	NOUN
app01-4651	227	22	1	1	NUM
app01-4651	227	23	.	.	PUNCT
app01-4651	228	1	they	they	PRON
app01-4651	228	2	indicate	indicate	VERB
app01-4651	228	3	that	that	SCONJ
app01-4651	228	4	the	the	DET
app01-4651	228	5	linear	linear	ADJ
app01-4651	228	6	relaxation	relaxation	NOUN
app01-4651	228	7	surpassed	surpass	VERB
app01-4651	228	8	the	the	DET
app01-4651	228	9	semidefinite	semidefinite	NOUN
app01-4651	228	10	one	one	NUM
app01-4651	228	11	in	in	ADP
app01-4651	228	12	terms	term	NOUN
app01-4651	228	13	of	of	ADP
app01-4651	228	14	speed	speed	NOUN
app01-4651	228	15	and	and	CCONJ
app01-4651	228	16	in	in	ADP
app01-4651	228	17	the	the	DET
app01-4651	228	18	number	number	NOUN
app01-4651	228	19	of	of	ADP
app01-4651	228	20	explored	explore	VERB
app01-4651	228	21	nodes	node	NOUN
app01-4651	228	22	.	.	PUNCT
app01-4651	229	1	the	the	DET
app01-4651	229	2	latter	latter	ADJ
app01-4651	229	3	results	result	NOUN
app01-4651	229	4	from	from	ADP
app01-4651	229	5	the	the	DET
app01-4651	229	6	property	property	NOUN
app01-4651	229	7	of	of	ADP
app01-4651	229	8	the	the	DET
app01-4651	229	9	simplex	simplex	NOUN
app01-4651	229	10	algorithm	algorithm	NOUN
app01-4651	229	11	,	,	PUNCT
app01-4651	229	12	used	use	VERB
app01-4651	229	13	for	for	ADP
app01-4651	229	14	the	the	DET
app01-4651	229	15	solution	solution	NOUN
app01-4651	229	16	of	of	ADP
app01-4651	229	17	linear	linear	ADJ
app01-4651	229	18	relaxations	relaxation	NOUN
app01-4651	229	19	,	,	PUNCT
app01-4651	229	20	to	to	PART
app01-4651	229	21	terminate	terminate	VERB
app01-4651	229	22	in	in	ADP
app01-4651	229	23	vertices	vertex	NOUN
app01-4651	229	24	of	of	ADP
app01-4651	229	25	the	the	DET
app01-4651	229	26	feasible	feasible	ADJ
app01-4651	229	27	space	space	NOUN
app01-4651	229	28	polytope	polytope	NOUN
app01-4651	229	29	.	.	PUNCT
app01-4651	230	1	these	these	PRON
app01-4651	230	2	are	be	AUX
app01-4651	230	3	more	more	ADV
app01-4651	230	4	likely	likely	ADJ
app01-4651	230	5	integer	integer	NOUN
app01-4651	230	6	-	-	PUNCT
app01-4651	230	7	feasible	feasible	ADJ
app01-4651	230	8	than	than	ADP
app01-4651	230	9	an	an	DET
app01-4651	230	10	interior	interior	ADJ
app01-4651	230	11	point	point	NOUN
app01-4651	230	12	found	find	VERB
app01-4651	230	13	by	by	ADP
app01-4651	230	14	the	the	DET
app01-4651	230	15	interior	interior	ADJ
app01-4651	230	16	-	-	PUNCT
app01-4651	230	17	point	point	NOUN
app01-4651	230	18	algorithm	algorithm	NOUN
app01-4651	230	19	,	,	PUNCT
app01-4651	230	20	used	use	VERB
app01-4651	230	21	for	for	ADP
app01-4651	230	22	the	the	DET
app01-4651	230	23	solution	solution	NOUN
app01-4651	230	24	of	of	ADP
app01-4651	230	25	semidefinite	semidefinite	PROPN
app01-4651	230	26	programs	program	NOUN
app01-4651	230	27	.	.	PUNCT
app01-4651	231	1	comparison	comparison	NOUN
app01-4651	231	2	of	of	ADP
app01-4651	231	3	our	our	PRON
app01-4651	231	4	branch	branch	NOUN
app01-4651	231	5	and	and	CCONJ
app01-4651	231	6	bound	bind	VERB
app01-4651	231	7	algorithm	algorithm	NOUN
app01-4651	231	8	and	and	CCONJ
app01-4651	231	9	gurobi	gurobi	PROPN
app01-4651	231	10	’s	’s	PART
app01-4651	231	11	build	build	VERB
app01-4651	231	12	-	-	PUNCT
app01-4651	231	13	in	in	ADP
app01-4651	231	14	branch	branch	NOUN
app01-4651	231	15	and	and	CCONJ
app01-4651	231	16	cut	cut	VERB
app01-4651	231	17	,	,	PUNCT
app01-4651	231	18	both	both	PRON
app01-4651	231	19	using	use	VERB
app01-4651	231	20	the	the	DET
app01-4651	231	21	linear	linear	ADJ
app01-4651	231	22	relaxation	relaxation	NOUN
app01-4651	231	23	,	,	PUNCT
app01-4651	231	24	is	be	AUX
app01-4651	231	25	even	even	ADV
app01-4651	231	26	clearer	clear	ADJ
app01-4651	231	27	.	.	PUNCT
app01-4651	232	1	our	our	PRON
app01-4651	232	2	implementation	implementation	NOUN
app01-4651	232	3	lacks	lack	VERB
app01-4651	232	4	heuristics	heuristic	NOUN
app01-4651	232	5	,	,	PUNCT
app01-4651	232	6	parallelism	parallelism	NOUN
app01-4651	232	7	,	,	PUNCT
app01-4651	232	8	and	and	CCONJ
app01-4651	232	9	generation	generation	NOUN
app01-4651	232	10	of	of	ADP
app01-4651	232	11	cuts	cut	NOUN
app01-4651	232	12	,	,	PUNCT
app01-4651	232	13	consequently	consequently	ADV
app01-4651	232	14	being	be	AUX
app01-4651	232	15	inefficient	inefficient	ADJ
app01-4651	232	16	for	for	ADP
app01-4651	232	17	tile	tile	NOUN
app01-4651	232	18	sets	set	NOUN
app01-4651	232	19	with	with	ADP
app01-4651	232	20	large	large	ADJ
app01-4651	232	21	number	number	NOUN
app01-4651	232	22	of	of	ADP
app01-4651	232	23	degrees	degree	NOUN
app01-4651	232	24	of	of	ADP
app01-4651	232	25	freedom	freedom	NOUN
app01-4651	232	26	,	,	PUNCT
app01-4651	232	27	such	such	ADJ
app01-4651	232	28	as	as	ADP
app01-4651	232	29	the	the	DET
app01-4651	232	30	čulík	čulík	NOUN
app01-4651	232	31	one	one	NUM
app01-4651	232	32	.	.	PUNCT
app01-4651	233	1	5	5	NUM
app01-4651	233	2	.	.	X
app01-4651	233	3	conclusions	conclusion	NOUN
app01-4651	233	4	in	in	ADP
app01-4651	233	5	this	this	DET
app01-4651	233	6	contribution	contribution	NOUN
app01-4651	234	1	,	,	PUNCT
app01-4651	234	2	we	we	PRON
app01-4651	234	3	demonstrated	demonstrate	VERB
app01-4651	234	4	that	that	SCONJ
app01-4651	234	5	the	the	DET
app01-4651	234	6	tiling	tile	VERB
app01-4651	234	7	generation	generation	NOUN
app01-4651	234	8	problem	problem	NOUN
app01-4651	234	9	of	of	ADP
app01-4651	234	10	finite	finite	ADJ
app01-4651	234	11	-	-	ADJ
app01-4651	234	12	sized	sized	ADJ
app01-4651	234	13	areas	area	NOUN
app01-4651	234	14	can	can	AUX
app01-4651	234	15	be	be	AUX
app01-4651	234	16	formulated	formulate	VERB
app01-4651	234	17	as	as	ADP
app01-4651	234	18	an	an	DET
app01-4651	234	19	integer	integer	NOUN
app01-4651	234	20	optimization	optimization	NOUN
app01-4651	234	21	problem	problem	NOUN
app01-4651	234	22	;	;	PUNCT
app01-4651	234	23	and	and	CCONJ
app01-4651	234	24	we	we	PRON
app01-4651	234	25	also	also	ADV
app01-4651	234	26	introduced	introduce	VERB
app01-4651	234	27	its	its	PRON
app01-4651	234	28	linear	linear	ADJ
app01-4651	234	29	and	and	CCONJ
app01-4651	234	30	semidefinite	semidefinite	NOUN
app01-4651	234	31	programming	programming	NOUN
app01-4651	234	32	relaxations	relaxation	NOUN
app01-4651	234	33	.	.	PUNCT
app01-4651	235	1	both	both	DET
app01-4651	235	2	the	the	DET
app01-4651	235	3	relaxations	relaxation	NOUN
app01-4651	235	4	were	be	AUX
app01-4651	235	5	employed	employ	VERB
app01-4651	235	6	in	in	ADP
app01-4651	235	7	the	the	DET
app01-4651	235	8	branch	branch	NOUN
app01-4651	235	9	and	and	CCONJ
app01-4651	235	10	bound	bind	VERB
app01-4651	235	11	method	method	NOUN
app01-4651	235	12	and	and	CCONJ
app01-4651	235	13	benchmarked	benchmarke	VERB
app01-4651	235	14	on	on	ADP
app01-4651	235	15	five	five	NUM
app01-4651	235	16	tile	tile	NOUN
app01-4651	235	17	sets	set	NOUN
app01-4651	235	18	.	.	PUNCT
app01-4651	236	1	the	the	DET
app01-4651	236	2	results	result	NOUN
app01-4651	236	3	indicate	indicate	VERB
app01-4651	236	4	that	that	SCONJ
app01-4651	236	5	the	the	DET
app01-4651	236	6	linear	linear	ADJ
app01-4651	236	7	relaxation	relaxation	NOUN
app01-4651	236	8	is	be	AUX
app01-4651	236	9	more	more	ADV
app01-4651	236	10	suitable	suitable	ADJ
app01-4651	236	11	for	for	ADP
app01-4651	236	12	practical	practical	ADJ
app01-4651	236	13	applications	application	NOUN
app01-4651	236	14	.	.	PUNCT
app01-4651	237	1	6	6	NUM
app01-4651	237	2	.	.	PUNCT
app01-4651	237	3	nomenclature	nomenclature	ADJ
app01-4651	237	4	list	list	NOUN
app01-4651	237	5	of	of	ADP
app01-4651	237	6	symbols	symbol	NOUN
app01-4651	237	7	a	a	DET
app01-4651	237	8	rectangular	rectangular	ADJ
app01-4651	237	9	area	area	NOUN
app01-4651	237	10	c	c	NOUN
app01-4651	237	11	color	color	NOUN
app01-4651	237	12	set	set	VERB
app01-4651	237	13	h	h	NOUN
app01-4651	237	14	set	set	NOUN
app01-4651	237	15	of	of	ADP
app01-4651	237	16	rows	row	NOUN
app01-4651	237	17	t	t	PROPN
app01-4651	237	18	tile	tile	NOUN
app01-4651	237	19	set	set	VERB
app01-4651	237	20	w	w	NOUN
app01-4651	237	21	set	set	NOUN
app01-4651	237	22	of	of	ADP
app01-4651	237	23	columns	column	NOUN
app01-4651	237	24	c	c	PROPN
app01-4651	237	25	color	color	NOUN
app01-4651	237	26	iterator	iterator	NOUN
app01-4651	237	27	ek	ek	PROPN
app01-4651	237	28	east	east	PROPN
app01-4651	237	29	edge	edge	PROPN
app01-4651	237	30	color	color	NOUN
app01-4651	237	31	of	of	ADP
app01-4651	237	32	the	the	DET
app01-4651	237	33	tile	tile	NOUN
app01-4651	238	1	k	k	PROPN
app01-4651	239	1	i	i	PRON
app01-4651	239	2	row	row	VERB
app01-4651	239	3	iterator	iterator	NOUN
app01-4651	239	4	j	j	PROPN
app01-4651	239	5	column	column	PROPN
app01-4651	239	6	iterator	iterator	NOUN
app01-4651	239	7	k	k	PROPN
app01-4651	239	8	,	,	PUNCT
app01-4651	239	9	`	`	PUNCT
app01-4651	239	10	,	,	PUNCT
app01-4651	239	11	m	m	VERB
app01-4651	239	12	tile	tile	NOUN
app01-4651	239	13	iterators	iterator	NOUN
app01-4651	239	14	nc	nc	PROPN
app01-4651	239	15	number	number	NOUN
app01-4651	239	16	of	of	ADP
app01-4651	239	17	colors	color	NOUN
app01-4651	239	18	in	in	ADP
app01-4651	239	19	c	c	PROPN
app01-4651	239	20	nk	nk	PROPN
app01-4651	239	21	north	north	PROPN
app01-4651	239	22	edge	edge	NOUN
app01-4651	239	23	color	color	NOUN
app01-4651	239	24	of	of	ADP
app01-4651	239	25	the	the	DET
app01-4651	239	26	tile	tile	NOUN
app01-4651	239	27	k	k	PROPN
app01-4651	239	28	sk	sk	PROPN
app01-4651	239	29	south	south	PROPN
app01-4651	239	30	edge	edge	NOUN
app01-4651	239	31	color	color	NOUN
app01-4651	239	32	of	of	ADP
app01-4651	239	33	the	the	DET
app01-4651	239	34	tile	tile	NOUN
app01-4651	239	35	k	k	PROPN
app01-4651	240	1	nt	nt	PROPN
app01-4651	240	2	,	,	PUNCT
app01-4651	240	3	h	h	PRON
app01-4651	240	4	number	number	NOUN
app01-4651	240	5	of	of	ADP
app01-4651	240	6	rows	row	NOUN
app01-4651	240	7	in	in	ADP
app01-4651	240	8	h	h	PROPN
app01-4651	240	9	nt	not	PART
app01-4651	240	10	,	,	PUNCT
app01-4651	240	11	w	w	ADJ
app01-4651	240	12	number	number	NOUN
app01-4651	240	13	of	of	ADP
app01-4651	240	14	columns	column	NOUN
app01-4651	240	15	in	in	ADP
app01-4651	240	16	w	w	PROPN
app01-4651	240	17	xi	xi	PROPN
app01-4651	240	18	,	,	PUNCT
app01-4651	240	19	j	j	PROPN
app01-4651	240	20	,	,	PUNCT
app01-4651	240	21	k	k	PROPN
app01-4651	240	22	design	design	NOUN
app01-4651	240	23	variable	variable	NOUN
app01-4651	240	24	,	,	PUNCT
app01-4651	240	25	xi	xi	PROPN
app01-4651	240	26	,	,	PUNCT
app01-4651	240	27	j	j	PROPN
app01-4651	240	28	,	,	PUNCT
app01-4651	240	29	k	k	PROPN
app01-4651	240	30	∈	∈	PROPN
app01-4651	240	31	{	{	PUNCT
app01-4651	240	32	0	0	NUM
app01-4651	240	33	,	,	PUNCT
app01-4651	240	34	1	1	NUM
app01-4651	240	35	}	}	SYM
app01-4651	240	36	yi	yi	PROPN
app01-4651	240	37	,	,	PUNCT
app01-4651	240	38	j	j	PROPN
app01-4651	240	39	,	,	PUNCT
app01-4651	240	40	k	k	PROPN
app01-4651	240	41	design	design	NOUN
app01-4651	240	42	variable	variable	NOUN
app01-4651	240	43	,	,	PUNCT
app01-4651	240	44	yi	yi	PROPN
app01-4651	240	45	,	,	PUNCT
app01-4651	240	46	j	j	PROPN
app01-4651	240	47	,	,	PUNCT
app01-4651	240	48	k	k	PROPN
app01-4651	240	49	∈	∈	PROPN
app01-4651	240	50	{	{	PUNCT
app01-4651	240	51	−1	−1	NOUN
app01-4651	240	52	,	,	PUNCT
app01-4651	240	53	1	1	NUM
app01-4651	240	54	}	}	PUNCT
app01-4651	240	55	wk	wk	X
app01-4651	240	56	west	west	PROPN
app01-4651	240	57	edge	edge	NOUN
app01-4651	240	58	color	color	NOUN
app01-4651	240	59	of	of	ADP
app01-4651	240	60	the	the	DET
app01-4651	240	61	tile	tile	NOUN
app01-4651	240	62	k	k	PROPN
app01-4651	240	63	iinf	iinf	ADJ
app01-4651	240	64	integer	integer	NOUN
app01-4651	240	65	infeasibility	infeasibility	PROPN
app01-4651	240	66	140	140	NUM
app01-4651	240	67	vol	vol	NOUN
app01-4651	240	68	.	.	PUNCT
app01-4651	241	1	13/2017	13/2017	NUM
app01-4651	241	2	optimization	optimization	NOUN
app01-4651	241	3	approach	approach	NOUN
app01-4651	241	4	to	to	ADP
app01-4651	241	5	tiling	tile	VERB
app01-4651	241	6	of	of	ADP
app01-4651	241	7	finite	finite	ADJ
app01-4651	241	8	areas	area	NOUN
app01-4651	241	9	with	with	ADP
app01-4651	241	10	wang	wang	PROPN
app01-4651	241	11	tiles	tiles	PROPN
app01-4651	241	12	acknowledgements	acknowledgement	NOUN
app01-4651	241	13	this	this	DET
app01-4651	241	14	work	work	NOUN
app01-4651	241	15	was	be	AUX
app01-4651	241	16	supported	support	VERB
app01-4651	241	17	partly	partly	ADV
app01-4651	241	18	by	by	ADP
app01-4651	241	19	the	the	DET
app01-4651	241	20	grant	grant	PROPN
app01-4651	241	21	agency	agency	NOUN
app01-4651	241	22	of	of	ADP
app01-4651	241	23	the	the	DET
app01-4651	241	24	ctu	ctu	NOUN
app01-4651	241	25	in	in	ADP
app01-4651	241	26	prague	prague	PROPN
app01-4651	241	27	,	,	PUNCT
app01-4651	241	28	sgs17/042	sgs17/042	NOUN
app01-4651	241	29	/	/	SYM
app01-4651	241	30	ohk1/1t/11	ohk1/1t/11	PROPN
app01-4651	241	31	,	,	PUNCT
app01-4651	241	32	by	by	ADP
app01-4651	241	33	the	the	DET
app01-4651	241	34	grant	grant	PROPN
app01-4651	241	35	agency	agency	NOUN
app01-4651	241	36	of	of	ADP
app01-4651	241	37	the	the	DET
app01-4651	241	38	czech	czech	PROPN
app01-4651	241	39	republic	republic	NOUN
app01-4651	241	40	,	,	PUNCT
app01-4651	241	41	gačr	gačr	VERB
app01-4651	241	42	15	15	NUM
app01-4651	241	43	-	-	PUNCT
app01-4651	241	44	07299s	07299s	NUM
app01-4651	241	45	,	,	PUNCT
app01-4651	241	46	by	by	ADP
app01-4651	241	47	the	the	DET
app01-4651	241	48	ministry	ministry	PROPN
app01-4651	241	49	of	of	ADP
app01-4651	241	50	industry	industry	NOUN
app01-4651	241	51	and	and	CCONJ
app01-4651	241	52	trade	trade	NOUN
app01-4651	241	53	,	,	PUNCT
app01-4651	241	54	mpo	mpo	PROPN
app01-4651	241	55	fv10202	fv10202	PROPN
app01-4651	241	56	,	,	PUNCT
app01-4651	241	57	and	and	CCONJ
app01-4651	241	58	by	by	ADP
app01-4651	241	59	the	the	DET
app01-4651	241	60	technology	technology	NOUN
app01-4651	241	61	agency	agency	NOUN
app01-4651	241	62	of	of	ADP
app01-4651	241	63	the	the	DET
app01-4651	241	64	czech	czech	PROPN
app01-4651	241	65	republic	republic	NOUN
app01-4651	241	66	,	,	PUNCT
app01-4651	241	67	tačr	tačr	PROPN
app01-4651	241	68	th02020420	th02020420	NOUN
app01-4651	241	69	.	.	PUNCT
app01-4651	242	1	references	reference	NOUN
app01-4651	242	2	[	[	X
app01-4651	242	3	1	1	NUM
app01-4651	242	4	]	]	PUNCT
app01-4651	242	5	h.	h.	PROPN
app01-4651	242	6	wang	wang	PROPN
app01-4651	242	7	.	.	PUNCT
app01-4651	243	1	dominoes	domino	NOUN
app01-4651	243	2	and	and	CCONJ
app01-4651	243	3	the	the	DET
app01-4651	243	4	aea	aea	PROPN
app01-4651	243	5	case	case	NOUN
app01-4651	243	6	of	of	ADP
app01-4651	243	7	the	the	DET
app01-4651	243	8	decision	decision	NOUN
app01-4651	243	9	problem	problem	NOUN
app01-4651	243	10	.	.	PUNCT
app01-4651	244	1	symposium	symposium	NOUN
app01-4651	244	2	on	on	ADP
app01-4651	244	3	the	the	DET
app01-4651	244	4	mathematical	mathematical	ADJ
app01-4651	244	5	theory	theory	NOUN
app01-4651	244	6	of	of	ADP
app01-4651	244	7	automata	automata	NOUN
app01-4651	244	8	pp	pp	X
app01-4651	244	9	.	.	PUNCT
app01-4651	245	1	23–55	23–55	NUM
app01-4651	245	2	,	,	PUNCT
app01-4651	245	3	1962	1962	NUM
app01-4651	245	4	.	.	PUNCT
app01-4651	246	1	[	[	X
app01-4651	246	2	2	2	X
app01-4651	246	3	]	]	PUNCT
app01-4651	246	4	h.	h.	PROPN
app01-4651	246	5	wang	wang	PROPN
app01-4651	246	6	.	.	PUNCT
app01-4651	247	1	proving	prove	VERB
app01-4651	247	2	theorems	theorem	NOUN
app01-4651	247	3	by	by	ADP
app01-4651	247	4	pattern	pattern	NOUN
app01-4651	247	5	recognition	recognition	PROPN
app01-4651	247	6	ii	ii	PROPN
app01-4651	247	7	.	.	PUNCT
app01-4651	247	8	bell	bell	PROPN
app01-4651	247	9	system	system	PROPN
app01-4651	247	10	technical	technical	PROPN
app01-4651	247	11	journal	journal	PROPN
app01-4651	247	12	40(1):1–41	40(1):1–41	NUM
app01-4651	247	13	,	,	PUNCT
app01-4651	247	14	1961	1961	NUM
app01-4651	247	15	.	.	PUNCT
app01-4651	248	1	doi:10.1002	doi:10.1002	NOUN
app01-4651	248	2	/	/	SYM
app01-4651	248	3	j.1538	j.1538	NOUN
app01-4651	248	4	-	-	PUNCT
app01-4651	248	5	7305.1961.tb03975.x	7305.1961.tb03975.x	NUM
app01-4651	248	6	.	.	PUNCT
app01-4651	249	1	[	[	X
app01-4651	249	2	3	3	NUM
app01-4651	249	3	]	]	PUNCT
app01-4651	249	4	a.	a.	NOUN
app01-4651	249	5	m.	m.	NOUN
app01-4651	249	6	turing	ture	VERB
app01-4651	249	7	.	.	PUNCT
app01-4651	250	1	on	on	ADP
app01-4651	250	2	computable	computable	ADJ
app01-4651	250	3	numbers	number	NOUN
app01-4651	250	4	,	,	PUNCT
app01-4651	250	5	with	with	ADP
app01-4651	250	6	an	an	DET
app01-4651	250	7	application	application	NOUN
app01-4651	250	8	to	to	ADP
app01-4651	250	9	the	the	DET
app01-4651	250	10	entscheidungsproblem	entscheidungsproblem	NOUN
app01-4651	250	11	.	.	PUNCT
app01-4651	251	1	proceedings	proceeding	NOUN
app01-4651	251	2	of	of	ADP
app01-4651	251	3	the	the	DET
app01-4651	251	4	london	london	PROPN
app01-4651	251	5	mathematical	mathematical	PROPN
app01-4651	251	6	society	society	PROPN
app01-4651	251	7	s2	s2	PROPN
app01-4651	251	8	-	-	PUNCT
app01-4651	251	9	42(1):230–265	42(1):230–265	PROPN
app01-4651	251	10	,	,	PUNCT
app01-4651	251	11	1937	1937	NUM
app01-4651	251	12	.	.	PUNCT
app01-4651	252	1	doi:10.1112	doi:10.1112	PROPN
app01-4651	252	2	/	/	SYM
app01-4651	252	3	plms	plms	PROPN
app01-4651	252	4	/	/	SYM
app01-4651	252	5	s2	s2	PROPN
app01-4651	252	6	-	-	PUNCT
app01-4651	252	7	42.1.230	42.1.230	NOUN
app01-4651	252	8	.	.	PUNCT
app01-4651	253	1	[	[	X
app01-4651	253	2	4	4	NUM
app01-4651	253	3	]	]	PUNCT
app01-4651	253	4	m.	m.	NOUN
app01-4651	253	5	davis	davis	PROPN
app01-4651	253	6	.	.	PUNCT
app01-4651	253	7	computability	computability	PROPN
app01-4651	253	8	&	&	CCONJ
app01-4651	253	9	unsolvability	unsolvability	PROPN
app01-4651	253	10	.	.	PUNCT
app01-4651	254	1	dover	dover	PROPN
app01-4651	254	2	books	book	NOUN
app01-4651	254	3	on	on	ADP
app01-4651	254	4	computer	computer	NOUN
app01-4651	254	5	science	science	NOUN
app01-4651	254	6	series	series	PROPN
app01-4651	254	7	.	.	PUNCT
app01-4651	255	1	dover	dover	PROPN
app01-4651	255	2	,	,	PUNCT
app01-4651	255	3	1958	1958	NUM
app01-4651	255	4	.	.	PUNCT
app01-4651	256	1	[	[	X
app01-4651	256	2	5	5	NUM
app01-4651	256	3	]	]	PUNCT
app01-4651	256	4	a.	a.	PROPN
app01-4651	256	5	s.	s.	PROPN
app01-4651	256	6	kahr	kahr	PROPN
app01-4651	256	7	,	,	PUNCT
app01-4651	256	8	e.	e.	PROPN
app01-4651	256	9	f.	f.	PROPN
app01-4651	256	10	moore	moore	PROPN
app01-4651	256	11	,	,	PUNCT
app01-4651	256	12	h.	h.	PROPN
app01-4651	256	13	wang	wang	PROPN
app01-4651	256	14	.	.	PUNCT
app01-4651	256	15	entscheidungsproblem	entscheidungsproblem	PROPN
app01-4651	256	16	reduced	reduce	VERB
app01-4651	256	17	to	to	ADP
app01-4651	256	18	the	the	DET
app01-4651	256	19	∀∃∀	∀∃∀	NOUN
app01-4651	256	20	case	case	NOUN
app01-4651	256	21	.	.	PUNCT
app01-4651	257	1	proceedings	proceeding	NOUN
app01-4651	257	2	of	of	ADP
app01-4651	257	3	the	the	DET
app01-4651	257	4	national	national	PROPN
app01-4651	257	5	academy	academy	PROPN
app01-4651	257	6	of	of	ADP
app01-4651	257	7	sciences	sciences	PROPN
app01-4651	257	8	48(3):365–377	48(3):365–377	PROPN
app01-4651	257	9	,	,	PUNCT
app01-4651	257	10	1962	1962	NUM
app01-4651	257	11	.	.	PUNCT
app01-4651	258	1	[	[	X
app01-4651	258	2	6	6	NUM
app01-4651	258	3	]	]	PUNCT
app01-4651	258	4	r.	r.	PROPN
app01-4651	258	5	berger	berger	PROPN
app01-4651	258	6	.	.	PUNCT
app01-4651	259	1	the	the	DET
app01-4651	259	2	undecidability	undecidability	NOUN
app01-4651	259	3	of	of	ADP
app01-4651	259	4	the	the	DET
app01-4651	259	5	domino	domino	NOUN
app01-4651	259	6	problem	problem	NOUN
app01-4651	259	7	.	.	PUNCT
app01-4651	260	1	66	66	NUM
app01-4651	260	2	.	.	PUNCT
app01-4651	261	1	american	american	PROPN
app01-4651	261	2	mathematical	mathematical	PROPN
app01-4651	261	3	society	society	NOUN
app01-4651	261	4	(	(	PUNCT
app01-4651	261	5	ams	ams	PROPN
app01-4651	261	6	)	)	PUNCT
app01-4651	261	7	,	,	PUNCT
app01-4651	261	8	1966	1966	NUM
app01-4651	261	9	.	.	PUNCT
app01-4651	262	1	doi:10.1090	doi:10.1090	NOUN
app01-4651	262	2	/	/	SYM
app01-4651	262	3	memo/0066	memo/0066	ADJ
app01-4651	262	4	.	.	PUNCT
app01-4651	263	1	[	[	X
app01-4651	263	2	7	7	X
app01-4651	263	3	]	]	X
app01-4651	263	4	r.	r.	PROPN
app01-4651	263	5	berger	berger	PROPN
app01-4651	263	6	.	.	PUNCT
app01-4651	264	1	the	the	DET
app01-4651	264	2	undecidability	undecidability	NOUN
app01-4651	264	3	of	of	ADP
app01-4651	264	4	the	the	DET
app01-4651	264	5	domino	domino	NOUN
app01-4651	264	6	problem	problem	NOUN
app01-4651	264	7	.	.	PUNCT
app01-4651	265	1	ph.d	ph.d	PROPN
app01-4651	265	2	.	.	PUNCT
app01-4651	266	1	thesis	thesis	PROPN
app01-4651	266	2	,	,	PUNCT
app01-4651	266	3	harvard	harvard	PROPN
app01-4651	266	4	university	university	PROPN
app01-4651	266	5	,	,	PUNCT
app01-4651	266	6	1964	1964	NUM
app01-4651	266	7	.	.	PUNCT
app01-4651	267	1	[	[	X
app01-4651	267	2	8	8	NUM
app01-4651	267	3	]	]	X
app01-4651	267	4	h.	h.	PROPN
app01-4651	267	5	wang	wang	PROPN
app01-4651	267	6	.	.	PUNCT
app01-4651	268	1	notes	note	NOUN
app01-4651	268	2	on	on	ADP
app01-4651	268	3	a	a	DET
app01-4651	268	4	class	class	NOUN
app01-4651	268	5	of	of	ADP
app01-4651	268	6	tiling	tile	VERB
app01-4651	268	7	problems	problem	NOUN
app01-4651	268	8	.	.	PUNCT
app01-4651	269	1	fundamenta	fundamenta	PROPN
app01-4651	269	2	mathematicae	mathematicae	PROPN
app01-4651	269	3	82(4):295–305	82(4):295–305	PROPN
app01-4651	269	4	,	,	PUNCT
app01-4651	269	5	1975	1975	NUM
app01-4651	269	6	.	.	PUNCT
app01-4651	270	1	[	[	X
app01-4651	270	2	9	9	NUM
app01-4651	270	3	]	]	X
app01-4651	270	4	d.	d.	PROPN
app01-4651	270	5	e.	e.	PROPN
app01-4651	270	6	knuth	knuth	PROPN
app01-4651	270	7	.	.	PUNCT
app01-4651	271	1	the	the	DET
app01-4651	271	2	art	art	NOUN
app01-4651	271	3	of	of	ADP
app01-4651	271	4	computer	computer	NOUN
app01-4651	271	5	programming	programming	NOUN
app01-4651	271	6	.	.	PUNCT
app01-4651	272	1	vol	vol	NOUN
app01-4651	272	2	.	.	PROPN
app01-4651	273	1	1	1	NUM
app01-4651	273	2	:	:	PUNCT
app01-4651	273	3	fundamental	fundamental	ADJ
app01-4651	273	4	algorithms	algorithm	NOUN
app01-4651	273	5	.	.	PUNCT
app01-4651	274	1	addison	addison	PROPN
app01-4651	274	2	-	-	PUNCT
app01-4651	274	3	wesley	wesley	PROPN
app01-4651	274	4	publishing	publishing	PROPN
app01-4651	274	5	co.	co.	PROPN
app01-4651	274	6	,	,	PUNCT
app01-4651	274	7	reading	reading	NOUN
app01-4651	274	8	,	,	PUNCT
app01-4651	274	9	mass.-london	mass.-london	ADJ
app01-4651	274	10	-	-	ADJ
app01-4651	274	11	don	don	ADJ
app01-4651	274	12	mills	mill	NOUN
app01-4651	274	13	,	,	PUNCT
app01-4651	274	14	ont	ont	NOUN
app01-4651	274	15	,	,	PUNCT
app01-4651	274	16	1968	1968	NUM
app01-4651	274	17	.	.	PUNCT
app01-4651	275	1	[	[	X
app01-4651	275	2	10	10	NUM
app01-4651	275	3	]	]	PUNCT
app01-4651	275	4	b.	b.	PROPN
app01-4651	275	5	poizat	poizat	NOUN
app01-4651	275	6	.	.	PUNCT
app01-4651	276	1	une	une	PROPN
app01-4651	276	2	théorie	théorie	PROPN
app01-4651	276	3	finiement	finiement	PROPN
app01-4651	276	4	axiomatisable	axiomatisable	ADJ
app01-4651	276	5	et	et	PROPN
app01-4651	276	6	superstable	superstable	NOUN
app01-4651	276	7	.	.	PUNCT
app01-4651	277	1	groupe	groupe	PROPN
app01-4651	277	2	d’étude	d’étude	NUM
app01-4651	277	3	des	des	X
app01-4651	277	4	théories	théorie	NOUN
app01-4651	277	5	stables	stable	NOUN
app01-4651	277	6	3(1):1–9	3(1):1–9	NUM
app01-4651	277	7	,	,	PUNCT
app01-4651	277	8	1980	1980	NUM
app01-4651	277	9	.	.	PUNCT
app01-4651	278	1	[	[	X
app01-4651	278	2	11	11	NUM
app01-4651	278	3	]	]	X
app01-4651	278	4	r.	r.	PROPN
app01-4651	278	5	m.	m.	PROPN
app01-4651	278	6	robinson	robinson	PROPN
app01-4651	278	7	.	.	PUNCT
app01-4651	279	1	undecidability	undecidability	PROPN
app01-4651	279	2	and	and	CCONJ
app01-4651	279	3	nonperiodicity	nonperiodicity	NOUN
app01-4651	279	4	for	for	ADP
app01-4651	279	5	tilings	tiling	NOUN
app01-4651	279	6	of	of	ADP
app01-4651	279	7	the	the	DET
app01-4651	279	8	plane	plane	NOUN
app01-4651	279	9	.	.	PUNCT
app01-4651	280	1	inventiones	inventione	NOUN
app01-4651	280	2	mathematicae	mathematicae	PROPN
app01-4651	280	3	12(3):177–209	12(3):177–209	NUM
app01-4651	280	4	,	,	PUNCT
app01-4651	280	5	1971	1971	NUM
app01-4651	280	6	.	.	PUNCT
app01-4651	281	1	doi:10.1007	doi:10.1007	NOUN
app01-4651	281	2	/	/	SYM
app01-4651	281	3	bf01418780	bf01418780	NOUN
app01-4651	281	4	.	.	PUNCT
app01-4651	282	1	[	[	X
app01-4651	282	2	12	12	NUM
app01-4651	282	3	]	]	X
app01-4651	282	4	b.	b.	PROPN
app01-4651	282	5	grünbaum	grünbaum	PROPN
app01-4651	282	6	,	,	PUNCT
app01-4651	282	7	g.	g.	PROPN
app01-4651	282	8	c.	c.	PROPN
app01-4651	282	9	shephard	shephard	PROPN
app01-4651	282	10	.	.	PUNCT
app01-4651	283	1	tilings	tiling	NOUN
app01-4651	283	2	and	and	CCONJ
app01-4651	283	3	patterns	pattern	NOUN
app01-4651	283	4	.	.	PUNCT
app01-4651	284	1	freeman	freeman	PROPN
app01-4651	284	2	,	,	PUNCT
app01-4651	284	3	1987	1987	NUM
app01-4651	284	4	.	.	PUNCT
app01-4651	285	1	[	[	X
app01-4651	285	2	13	13	NUM
app01-4651	285	3	]	]	X
app01-4651	285	4	r.	r.	PROPN
app01-4651	285	5	m.	m.	PROPN
app01-4651	285	6	robinson	robinson	PROPN
app01-4651	285	7	.	.	PROPN
app01-4651	286	1	undecidable	undecidable	ADJ
app01-4651	286	2	tiling	tile	VERB
app01-4651	286	3	problems	problem	NOUN
app01-4651	286	4	in	in	ADP
app01-4651	286	5	the	the	DET
app01-4651	286	6	hyperbolic	hyperbolic	ADJ
app01-4651	286	7	plane	plane	NOUN
app01-4651	286	8	.	.	PUNCT
app01-4651	287	1	inventiones	inventione	NOUN
app01-4651	287	2	mathematicae	mathematicae	PROPN
app01-4651	287	3	44(3):259–264	44(3):259–264	PROPN
app01-4651	287	4	,	,	PUNCT
app01-4651	287	5	1978	1978	NUM
app01-4651	287	6	.	.	PUNCT
app01-4651	288	1	doi:10.1007	doi:10.1007	PROPN
app01-4651	288	2	/	/	SYM
app01-4651	288	3	bf01403163	bf01403163	PROPN
app01-4651	288	4	.	.	PUNCT
app01-4651	289	1	[	[	X
app01-4651	289	2	14	14	NUM
app01-4651	289	3	]	]	X
app01-4651	289	4	j.	j.	PROPN
app01-4651	289	5	kari	kari	PROPN
app01-4651	289	6	.	.	PUNCT
app01-4651	290	1	a	a	DET
app01-4651	290	2	small	small	ADJ
app01-4651	290	3	aperiodic	aperiodic	ADJ
app01-4651	290	4	set	set	NOUN
app01-4651	290	5	of	of	ADP
app01-4651	290	6	wang	wang	PROPN
app01-4651	290	7	tiles	tiles	PROPN
app01-4651	290	8	.	.	PUNCT
app01-4651	291	1	discrete	discrete	ADJ
app01-4651	291	2	mathematics	mathematic	NOUN
app01-4651	291	3	160(1	160(1	NUM
app01-4651	291	4	-	-	SYM
app01-4651	291	5	3):259–264	3):259–264	NUM
app01-4651	291	6	,	,	PUNCT
app01-4651	291	7	1996	1996	NUM
app01-4651	291	8	.	.	PUNCT
app01-4651	292	1	doi:10.1016/0012	doi:10.1016/0012	VERB
app01-4651	292	2	-	-	PUNCT
app01-4651	292	3	365x(95)00120	365x(95)00120	NUM
app01-4651	292	4	-	-	PUNCT
app01-4651	292	5	l.	l.	NOUN
app01-4651	292	6	[	[	X
app01-4651	292	7	15	15	NUM
app01-4651	292	8	]	]	PUNCT
app01-4651	292	9	k.	k.	PROPN
app01-4651	292	10	čulík	čulík	PROPN
app01-4651	292	11	.	.	PUNCT
app01-4651	293	1	an	an	DET
app01-4651	293	2	aperiodic	aperiodic	ADJ
app01-4651	293	3	set	set	NOUN
app01-4651	293	4	of	of	ADP
app01-4651	293	5	13	13	NUM
app01-4651	293	6	wang	wang	PROPN
app01-4651	293	7	tiles	tile	NOUN
app01-4651	293	8	.	.	PUNCT
app01-4651	294	1	discrete	discrete	ADJ
app01-4651	294	2	mathematics	mathematic	NOUN
app01-4651	294	3	160(1	160(1	NUM
app01-4651	294	4	-	-	SYM
app01-4651	294	5	3):245–251	3):245–251	NUM
app01-4651	294	6	,	,	PUNCT
app01-4651	294	7	1996	1996	NUM
app01-4651	294	8	.	.	PUNCT
app01-4651	295	1	doi:10.1016	doi:10.1016	PROPN
app01-4651	295	2	/	/	SYM
app01-4651	295	3	s0012	s0012	NOUN
app01-4651	295	4	-	-	PUNCT
app01-4651	295	5	365x(96)00118	365x(96)00118	NUM
app01-4651	295	6	-	-	SYM
app01-4651	295	7	5	5	NUM
app01-4651	295	8	.	.	PUNCT
app01-4651	296	1	[	[	X
app01-4651	296	2	16	16	NUM
app01-4651	296	3	]	]	X
app01-4651	296	4	e.	e.	PROPN
app01-4651	296	5	jeandel	jeandel	PROPN
app01-4651	296	6	,	,	PUNCT
app01-4651	296	7	m.	m.	NOUN
app01-4651	296	8	rao	rao	PROPN
app01-4651	296	9	.	.	PUNCT
app01-4651	297	1	an	an	DET
app01-4651	297	2	aperiodic	aperiodic	ADJ
app01-4651	297	3	set	set	NOUN
app01-4651	297	4	of	of	ADP
app01-4651	297	5	11	11	NUM
app01-4651	297	6	wang	wang	PROPN
app01-4651	297	7	tiles	tile	NOUN
app01-4651	297	8	,	,	PUNCT
app01-4651	297	9	2015	2015	NUM
app01-4651	297	10	.	.	PUNCT
app01-4651	298	1	arxiv:1506.06492v1	arxiv:1506.06492v1	X
app01-4651	298	2	.	.	PUNCT
app01-4651	299	1	[	[	X
app01-4651	299	2	17	17	NUM
app01-4651	299	3	]	]	PUNCT
app01-4651	299	4	a.	a.	NOUN
app01-4651	299	5	lagae	lagae	PROPN
app01-4651	299	6	,	,	PUNCT
app01-4651	299	7	p.	p.	PROPN
app01-4651	299	8	dutré	dutré	PROPN
app01-4651	299	9	.	.	PUNCT
app01-4651	300	1	an	an	DET
app01-4651	300	2	alternative	alternative	NOUN
app01-4651	300	3	for	for	ADP
app01-4651	300	4	wang	wang	PROPN
app01-4651	300	5	tiles	tiles	PROPN
app01-4651	300	6	.	.	PUNCT
app01-4651	301	1	acm	acm	PROPN
app01-4651	301	2	transactions	transaction	NOUN
app01-4651	301	3	on	on	ADP
app01-4651	301	4	graphics	graphic	NOUN
app01-4651	301	5	25(4):1442–1459	25(4):1442–1459	NUM
app01-4651	301	6	,	,	PUNCT
app01-4651	301	7	2006	2006	NUM
app01-4651	301	8	.	.	PUNCT
app01-4651	302	1	doi:10.1145/1183287.1183296	doi:10.1145/1183287.1183296	NOUN
app01-4651	302	2	.	.	PUNCT
app01-4651	303	1	[	[	X
app01-4651	303	2	18	18	NUM
app01-4651	303	3	]	]	PUNCT
app01-4651	303	4	a.	a.	NOUN
app01-4651	303	5	lagae	lagae	PROPN
app01-4651	303	6	,	,	PUNCT
app01-4651	303	7	j.	j.	PROPN
app01-4651	303	8	kari	kari	PROPN
app01-4651	303	9	,	,	PUNCT
app01-4651	303	10	p.	p.	PROPN
app01-4651	303	11	dutré	dutré	PROPN
app01-4651	303	12	.	.	PUNCT
app01-4651	304	1	aperiodic	aperiodic	ADJ
app01-4651	304	2	sets	set	NOUN
app01-4651	304	3	of	of	ADP
app01-4651	304	4	square	square	ADJ
app01-4651	304	5	tiles	tile	NOUN
app01-4651	304	6	with	with	ADP
app01-4651	304	7	colored	colored	ADJ
app01-4651	304	8	corners	corner	NOUN
app01-4651	304	9	.	.	PUNCT
app01-4651	305	1	report	report	NOUN
app01-4651	305	2	cw	cw	NOUN
app01-4651	305	3	460	460	NUM
app01-4651	305	4	,	,	PUNCT
app01-4651	305	5	2006	2006	NUM
app01-4651	305	6	.	.	PUNCT
app01-4651	306	1	[	[	X
app01-4651	306	2	19	19	NUM
app01-4651	306	3	]	]	X
app01-4651	306	4	t.	t.	NOUN
app01-4651	306	5	nurmi	nurmi	NOUN
app01-4651	306	6	.	.	PUNCT
app01-4651	307	1	from	from	ADP
app01-4651	307	2	checkerboard	checkerboard	NOUN
app01-4651	307	3	to	to	ADP
app01-4651	307	4	cloverfield	cloverfield	PROPN
app01-4651	307	5	:	:	PUNCT
app01-4651	307	6	using	use	VERB
app01-4651	307	7	wang	wang	PROPN
app01-4651	307	8	tiles	tile	NOUN
app01-4651	307	9	in	in	ADP
app01-4651	307	10	seamless	seamless	ADJ
app01-4651	307	11	non	non	ADJ
app01-4651	307	12	-	-	ADJ
app01-4651	307	13	periodic	periodic	ADJ
app01-4651	307	14	patterns	pattern	NOUN
app01-4651	307	15	.	.	PUNCT
app01-4651	308	1	bridges	bridge	NOUN
app01-4651	308	2	finland	finland	PROPN
app01-4651	308	3	conference	conference	NOUN
app01-4651	308	4	proceedings	proceeding	NOUN
app01-4651	308	5	2016	2016	NUM
app01-4651	308	6	.	.	PUNCT
app01-4651	309	1	[	[	X
app01-4651	309	2	20	20	NUM
app01-4651	309	3	]	]	PUNCT
app01-4651	309	4	j.	j.	PROPN
app01-4651	309	5	kari	kari	PROPN
app01-4651	309	6	.	.	PUNCT
app01-4651	310	1	reversibility	reversibility	NOUN
app01-4651	310	2	of	of	ADP
app01-4651	310	3	2d	2d	NUM
app01-4651	310	4	cellular	cellular	ADJ
app01-4651	310	5	automata	automata	NOUN
app01-4651	310	6	is	be	AUX
app01-4651	310	7	undecidable	undecidable	ADJ
app01-4651	310	8	.	.	PUNCT
app01-4651	311	1	physica	physica	NOUN
app01-4651	311	2	d	d	NOUN
app01-4651	311	3	:	:	PUNCT
app01-4651	311	4	nonlinear	nonlinear	ADJ
app01-4651	311	5	phenomena	phenomena	NOUN
app01-4651	311	6	45(13):379–385	45(13):379–385	NUM
app01-4651	311	7	,	,	PUNCT
app01-4651	311	8	1990	1990	NUM
app01-4651	311	9	.	.	PUNCT
app01-4651	312	1	doi:10.1016/0167	doi:10.1016/0167	VERB
app01-4651	312	2	-	-	PUNCT
app01-4651	312	3	2789(90)90195	2789(90)90195	NUM
app01-4651	312	4	-	-	NOUN
app01-4651	312	5	u.	u.	NOUN
app01-4651	312	6	[	[	X
app01-4651	312	7	21	21	NUM
app01-4651	312	8	]	]	PUNCT
app01-4651	312	9	m.	m.	PROPN
app01-4651	312	10	f.	f.	PROPN
app01-4651	312	11	cohen	cohen	PROPN
app01-4651	312	12	,	,	PUNCT
app01-4651	312	13	j.	j.	PROPN
app01-4651	312	14	shade	shade	PROPN
app01-4651	312	15	,	,	PUNCT
app01-4651	312	16	s.	s.	PROPN
app01-4651	312	17	hiller	hiller	PROPN
app01-4651	312	18	,	,	PUNCT
app01-4651	312	19	o.	o.	PROPN
app01-4651	312	20	deussen	deussen	PROPN
app01-4651	312	21	.	.	PUNCT
app01-4651	313	1	wang	wang	PROPN
app01-4651	313	2	tiles	tile	NOUN
app01-4651	313	3	for	for	ADP
app01-4651	313	4	image	image	NOUN
app01-4651	313	5	and	and	CCONJ
app01-4651	313	6	texture	texture	NOUN
app01-4651	313	7	generation	generation	NOUN
app01-4651	313	8	.	.	PUNCT
app01-4651	314	1	acm	acm	PROPN
app01-4651	314	2	transactions	transaction	NOUN
app01-4651	314	3	on	on	ADP
app01-4651	314	4	graphics	graphic	NOUN
app01-4651	314	5	22(3):287	22(3):287	NUM
app01-4651	314	6	,	,	PUNCT
app01-4651	314	7	2003	2003	NUM
app01-4651	314	8	.	.	PUNCT
app01-4651	315	1	doi:10.1145/882262.882265	doi:10.1145/882262.882265	NOUN
app01-4651	315	2	.	.	PUNCT
app01-4651	316	1	[	[	X
app01-4651	316	2	22	22	NUM
app01-4651	316	3	]	]	X
app01-4651	316	4	e.	e.	PROPN
app01-4651	316	5	winfree	winfree	PROPN
app01-4651	316	6	,	,	PUNCT
app01-4651	316	7	f.	f.	PROPN
app01-4651	316	8	liu	liu	PROPN
app01-4651	316	9	,	,	PUNCT
app01-4651	316	10	l.	l.	PROPN
app01-4651	316	11	a.	a.	PROPN
app01-4651	316	12	wenzler	wenzler	PROPN
app01-4651	316	13	,	,	PUNCT
app01-4651	316	14	n.	n.	PROPN
app01-4651	316	15	c.	c.	PROPN
app01-4651	316	16	seeman	seeman	PROPN
app01-4651	316	17	.	.	PUNCT
app01-4651	316	18	design	design	NOUN
app01-4651	316	19	and	and	CCONJ
app01-4651	316	20	self	self	NOUN
app01-4651	316	21	-	-	PUNCT
app01-4651	316	22	assembly	assembly	NOUN
app01-4651	316	23	of	of	ADP
app01-4651	316	24	two	two	NUM
app01-4651	316	25	-	-	PUNCT
app01-4651	316	26	dimensional	dimensional	ADJ
app01-4651	316	27	dna	dna	NOUN
app01-4651	316	28	crystals	crystal	NOUN
app01-4651	316	29	.	.	PUNCT
app01-4651	317	1	nature	nature	NOUN
app01-4651	317	2	394(6693):539–544	394(6693):539–544	NUM
app01-4651	317	3	,	,	PUNCT
app01-4651	317	4	1998	1998	NUM
app01-4651	317	5	.	.	PUNCT
app01-4651	318	1	doi:10.1038/28998	doi:10.1038/28998	X
app01-4651	318	2	.	.	PUNCT
app01-4651	319	1	[	[	X
app01-4651	319	2	23	23	NUM
app01-4651	319	3	]	]	X
app01-4651	319	4	j.	j.	PROPN
app01-4651	319	5	novák	novák	PROPN
app01-4651	319	6	,	,	PUNCT
app01-4651	319	7	a.	a.	PROPN
app01-4651	319	8	kučerová	kučerová	PROPN
app01-4651	319	9	,	,	PUNCT
app01-4651	319	10	j.	j.	PROPN
app01-4651	319	11	zeman	zeman	PROPN
app01-4651	319	12	.	.	PUNCT
app01-4651	320	1	compressing	compress	VERB
app01-4651	320	2	random	random	ADJ
app01-4651	320	3	microstructures	microstructure	NOUN
app01-4651	320	4	via	via	ADP
app01-4651	320	5	stochastic	stochastic	ADJ
app01-4651	320	6	wang	wang	PROPN
app01-4651	320	7	tilings	tiling	NOUN
app01-4651	320	8	.	.	PUNCT
app01-4651	321	1	physical	physical	ADJ
app01-4651	321	2	review	review	NOUN
app01-4651	321	3	e	e	PROPN
app01-4651	321	4	86(4	86(4	NUM
app01-4651	321	5	)	)	PUNCT
app01-4651	321	6	,	,	PUNCT
app01-4651	321	7	2012	2012	NUM
app01-4651	321	8	.	.	PUNCT
app01-4651	322	1	doi:10.1103	doi:10.1103	NOUN
app01-4651	322	2	/	/	SYM
app01-4651	322	3	physreve.86.040104	physreve.86.040104	NOUN
app01-4651	322	4	.	.	PUNCT
app01-4651	323	1	[	[	X
app01-4651	323	2	24	24	NUM
app01-4651	323	3	]	]	PUNCT
app01-4651	323	4	m.	m.	NOUN
app01-4651	323	5	doškář	doškář	PROPN
app01-4651	323	6	,	,	PUNCT
app01-4651	323	7	j.	j.	PROPN
app01-4651	323	8	novák	novák	PROPN
app01-4651	323	9	,	,	PUNCT
app01-4651	323	10	j.	j.	PROPN
app01-4651	323	11	zeman	zeman	PROPN
app01-4651	323	12	.	.	PUNCT
app01-4651	323	13	aperiodic	aperiodic	ADJ
app01-4651	323	14	compression	compression	NOUN
app01-4651	323	15	and	and	CCONJ
app01-4651	323	16	reconstruction	reconstruction	NOUN
app01-4651	323	17	of	of	ADP
app01-4651	323	18	real	real	ADJ
app01-4651	323	19	-	-	PUNCT
app01-4651	323	20	world	world	NOUN
app01-4651	323	21	material	material	NOUN
app01-4651	323	22	systems	system	NOUN
app01-4651	323	23	based	base	VERB
app01-4651	323	24	on	on	ADP
app01-4651	323	25	wang	wang	PROPN
app01-4651	323	26	tiles	tiles	PROPN
app01-4651	323	27	.	.	PUNCT
app01-4651	324	1	physical	physical	ADJ
app01-4651	324	2	review	review	NOUN
app01-4651	324	3	e	e	PROPN
app01-4651	324	4	90(6	90(6	NOUN
app01-4651	324	5	)	)	PUNCT
app01-4651	324	6	,	,	PUNCT
app01-4651	324	7	2014	2014	NUM
app01-4651	324	8	.	.	PUNCT
app01-4651	325	1	doi:10.1103	doi:10.1103	NOUN
app01-4651	325	2	/	/	SYM
app01-4651	325	3	physreve.90.062118	physreve.90.062118	NOUN
app01-4651	325	4	.	.	PUNCT
app01-4651	326	1	[	[	X
app01-4651	326	2	25	25	NUM
app01-4651	326	3	]	]	PUNCT
app01-4651	326	4	m.	m.	NOUN
app01-4651	326	5	doškář	doškář	PROPN
app01-4651	326	6	,	,	PUNCT
app01-4651	326	7	j.	j.	PROPN
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app01-4651	326	9	.	.	PUNCT
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app01-4651	327	2	jigsaw	jigsaw	NOUN
app01-4651	327	3	puzzle	puzzle	NOUN
app01-4651	327	4	framework	framework	NOUN
app01-4651	327	5	for	for	ADP
app01-4651	327	6	homogenization	homogenization	NOUN
app01-4651	327	7	of	of	ADP
app01-4651	327	8	high	high	ADJ
app01-4651	327	9	porosity	porosity	NOUN
app01-4651	327	10	foams	foam	NOUN
app01-4651	327	11	.	.	PUNCT
app01-4651	328	1	computers	computer	NOUN
app01-4651	328	2	&	&	CCONJ
app01-4651	328	3	structures	structure	NOUN
app01-4651	328	4	166:33–41	166:33–41	NUM
app01-4651	328	5	,	,	PUNCT
app01-4651	328	6	2016	2016	NUM
app01-4651	328	7	.	.	PUNCT
app01-4651	329	1	doi:10.1016	doi:10.1016	PROPN
app01-4651	329	2	/	/	SYM
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app01-4651	329	4	.	.	PUNCT
app01-4651	330	1	[	[	X
app01-4651	330	2	26	26	NUM
app01-4651	330	3	]	]	PUNCT
app01-4651	330	4	m.	m.	NOUN
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app01-4651	330	6	.	.	PUNCT
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app01-4651	331	2	-	-	PUNCT
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app01-4651	331	4	optimization	optimization	NOUN
app01-4651	331	5	of	of	ADP
app01-4651	331	6	truss	truss	NOUN
app01-4651	331	7	structures	structure	NOUN
app01-4651	331	8	composed	compose	VERB
app01-4651	331	9	of	of	ADP
app01-4651	331	10	wang	wang	PROPN
app01-4651	331	11	tiles	tiles	PROPN
app01-4651	331	12	,	,	PUNCT
app01-4651	331	13	master	master	NOUN
app01-4651	331	14	thesis	thesis	NOUN
app01-4651	331	15	,	,	PUNCT
app01-4651	331	16	czech	czech	PROPN
app01-4651	331	17	technical	technical	PROPN
app01-4651	331	18	university	university	PROPN
app01-4651	331	19	in	in	ADP
app01-4651	331	20	prague	prague	PROPN
app01-4651	331	21	,	,	PUNCT
app01-4651	331	22	2017	2017	NUM
app01-4651	331	23	.	.	PUNCT
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app01-4651	332	2	/	/	SYM
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app01-4651	332	4	.	.	PUNCT
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app01-4651	333	2	27	27	NUM
app01-4651	333	3	]	]	PUNCT
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app01-4651	333	5	lagae	lagae	PROPN
app01-4651	333	6	,	,	PUNCT
app01-4651	333	7	p.	p.	PROPN
app01-4651	333	8	dutré	dutré	PROPN
app01-4651	333	9	.	.	PUNCT
app01-4651	334	1	a	a	DET
app01-4651	334	2	procedural	procedural	ADJ
app01-4651	334	3	object	object	NOUN
app01-4651	334	4	distribution	distribution	NOUN
app01-4651	334	5	function	function	NOUN
app01-4651	334	6	.	.	PUNCT
app01-4651	335	1	acm	acm	PROPN
app01-4651	335	2	transactions	transaction	NOUN
app01-4651	335	3	on	on	ADP
app01-4651	335	4	graphics	graphic	NOUN
app01-4651	335	5	24(4):1442–1461	24(4):1442–1461	NUM
app01-4651	335	6	,	,	PUNCT
app01-4651	335	7	2005	2005	NUM
app01-4651	335	8	.	.	PUNCT
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app01-4651	336	2	.	.	PUNCT
app01-4651	337	1	[	[	X
app01-4651	337	2	28	28	NUM
app01-4651	337	3	]	]	X
app01-4651	337	4	d.	d.	PROPN
app01-4651	337	5	myers	myers	PROPN
app01-4651	337	6	.	.	PUNCT
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app01-4651	338	2	tilings	tiling	NOUN
app01-4651	338	3	of	of	ADP
app01-4651	338	4	the	the	DET
app01-4651	338	5	plane	plane	NOUN
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app01-4651	340	2	.	.	PUNCT
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app01-4651	344	2	.	.	PUNCT
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app01-4651	345	6	.	.	PUNCT
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app01-4651	346	4	-	-	PUNCT
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app01-4651	346	6	-	-	PUNCT
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app01-4651	349	3	,	,	PUNCT
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app01-4651	349	5	.	.	PUNCT
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app01-4651	350	3	]	]	PUNCT
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app01-4651	352	8	.	.	PUNCT
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app01-4651	353	2	.	.	PUNCT
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app01-4651	354	5	.	.	PUNCT
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app01-4651	355	2	-	-	PUNCT
app01-4651	355	3	1	1	NUM
app01-4651	355	4	-	-	PUNCT
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app01-4651	355	6	-	-	PUNCT
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app01-4651	355	8	-	-	PUNCT
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app01-4651	355	10	.	.	PUNCT
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app01-4651	356	3	]	]	PUNCT
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app01-4651	356	9	.	.	PUNCT
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app01-4651	358	13	.	.	PUNCT
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app01-4651	360	5	.	.	PUNCT
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app01-4651	361	4	-	-	PUNCT
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app01-4651	361	6	-	-	PUNCT
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app01-4651	361	8	-	-	PUNCT
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