id	sid	tid	token	lemma	pos
jw827942g84	1	1	the	the	DET
jw827942g84	1	2	topic	topic	NOUN
jw827942g84	1	3	of	of	ADP
jw827942g84	1	4	geometric	geometric	ADJ
jw827942g84	1	5	object	object	NOUN
jw827942g84	1	6	approximation	approximation	NOUN
jw827942g84	1	7	focuses	focus	VERB
jw827942g84	1	8	on	on	ADP
jw827942g84	1	9	computing	compute	VERB
jw827942g84	1	10	structurally	structurally	ADV
jw827942g84	1	11	or	or	CCONJ
jw827942g84	1	12	geometrically	geometrically	ADV
jw827942g84	1	13	simpler	simple	ADJ
jw827942g84	1	14	objects	object	NOUN
jw827942g84	1	15	to	to	PART
jw827942g84	1	16	approximate	approximate	VERB
jw827942g84	1	17	an	an	DET
jw827942g84	1	18	input	input	NOUN
jw827942g84	1	19	complex	complex	ADJ
jw827942g84	1	20	object	object	NOUN
jw827942g84	1	21	.	.	PUNCT
jw827942g84	2	1	this	this	PRON
jw827942g84	2	2	is	be	AUX
jw827942g84	2	3	a	a	DET
jw827942g84	2	4	fundamental	fundamental	ADJ
jw827942g84	2	5	and	and	CCONJ
jw827942g84	2	6	important	important	ADJ
jw827942g84	2	7	research	research	NOUN
jw827942g84	2	8	topic	topic	NOUN
jw827942g84	2	9	in	in	ADP
jw827942g84	2	10	computational	computational	ADJ
jw827942g84	2	11	geometry	geometry	NOUN
jw827942g84	2	12	and	and	CCONJ
jw827942g84	2	13	has	have	VERB
jw827942g84	2	14	many	many	ADJ
jw827942g84	2	15	applications	application	NOUN
jw827942g84	2	16	.	.	PUNCT
jw827942g84	3	1	in	in	ADP
jw827942g84	3	2	this	this	DET
jw827942g84	3	3	dissertation	dissertation	NOUN
jw827942g84	3	4	,	,	PUNCT
jw827942g84	3	5	we	we	PRON
jw827942g84	3	6	study	study	VERB
jw827942g84	3	7	a	a	DET
jw827942g84	3	8	number	number	NOUN
jw827942g84	3	9	of	of	ADP
jw827942g84	3	10	geometric	geometric	ADJ
jw827942g84	3	11	approximation	approximation	NOUN
jw827942g84	3	12	problems	problem	NOUN
jw827942g84	3	13	.	.	PUNCT
jw827942g84	4	1	specifically	specifically	ADV
jw827942g84	4	2	,	,	PUNCT
jw827942g84	4	3	we	we	PRON
jw827942g84	4	4	study	study	VERB
jw827942g84	4	5	the	the	DET
jw827942g84	4	6	problems	problem	NOUN
jw827942g84	4	7	of	of	ADP
jw827942g84	4	8	approximating	approximate	VERB
jw827942g84	4	9	a	a	DET
jw827942g84	4	10	set	set	NOUN
jw827942g84	4	11	of	of	ADP
jw827942g84	4	12	points	point	NOUN
jw827942g84	4	13	in	in	ADP
jw827942g84	4	14	the	the	DET
jw827942g84	4	15	plane	plane	NOUN
jw827942g84	4	16	by	by	ADP
jw827942g84	4	17	a	a	DET
jw827942g84	4	18	functional	functional	ADJ
jw827942g84	4	19	curve	curve	NOUN
jw827942g84	4	20	as	as	ADV
jw827942g84	4	21	well	well	ADV
jw827942g84	4	22	as	as	ADP
jw827942g84	4	23	other	other	ADJ
jw827942g84	4	24	variants	variant	NOUN
jw827942g84	4	25	which	which	PRON
jw827942g84	4	26	include	include	VERB
jw827942g84	4	27	the	the	DET
jw827942g84	4	28	weighted	weighted	ADJ
jw827942g84	4	29	points	point	NOUN
jw827942g84	4	30	,	,	PUNCT
jw827942g84	4	31	in	in	ADP
jw827942g84	4	32	the	the	DET
jw827942g84	4	33	presence	presence	NOUN
jw827942g84	4	34	of	of	ADP
jw827942g84	4	35	outliers	outlier	NOUN
jw827942g84	4	36	,	,	PUNCT
jw827942g84	4	37	and	and	CCONJ
jw827942g84	4	38	the	the	DET
jw827942g84	4	39	3	3	NUM
jw827942g84	4	40	-	-	PUNCT
jw827942g84	4	41	d	d	NOUN
jw827942g84	4	42	extensions	extension	NOUN
jw827942g84	4	43	.	.	PUNCT
jw827942g84	5	1	further	far	ADV
jw827942g84	5	2	,	,	PUNCT
jw827942g84	5	3	we	we	PRON
jw827942g84	5	4	develop	develop	VERB
jw827942g84	5	5	a	a	DET
jw827942g84	5	6	new	new	ADJ
jw827942g84	5	7	type	type	NOUN
jw827942g84	5	8	of	of	ADP
jw827942g84	5	9	outlier	outlier	NOUN
jw827942g84	5	10	-	-	PUNCT
jw827942g84	5	11	handling	handling	NOUN
jw827942g84	5	12	algorithms	algorithm	NOUN
jw827942g84	5	13	,	,	PUNCT
jw827942g84	5	14	which	which	PRON
jw827942g84	5	15	not	not	PART
jw827942g84	5	16	only	only	ADV
jw827942g84	5	17	detect	detect	VERB
jw827942g84	5	18	the	the	DET
jw827942g84	5	19	outliers	outlier	NOUN
jw827942g84	5	20	but	but	CCONJ
jw827942g84	5	21	also	also	ADV
jw827942g84	5	22	accommodate	accommodate	VERB
jw827942g84	5	23	their	their	PRON
jw827942g84	5	24	impact	impact	NOUN
jw827942g84	5	25	.	.	PUNCT
jw827942g84	6	1	in	in	ADP
jw827942g84	6	2	addition	addition	NOUN
jw827942g84	6	3	,	,	PUNCT
jw827942g84	6	4	we	we	PRON
jw827942g84	6	5	study	study	VERB
jw827942g84	6	6	the	the	DET
jw827942g84	6	7	problems	problem	NOUN
jw827942g84	6	8	of	of	ADP
jw827942g84	6	9	approximating	approximate	VERB
jw827942g84	6	10	a	a	DET
jw827942g84	6	11	piecewise	piecewise	NOUN
jw827942g84	6	12	linear	linear	ADJ
jw827942g84	6	13	nonnegative	nonnegative	ADJ
jw827942g84	6	14	functional	functional	ADJ
jw827942g84	6	15	curve	curve	NOUN
jw827942g84	6	16	in	in	ADP
jw827942g84	6	17	the	the	DET
jw827942g84	6	18	plane	plane	NOUN
jw827942g84	6	19	by	by	ADP
jw827942g84	6	20	a	a	DET
jw827942g84	6	21	set	set	NOUN
jw827942g84	6	22	of	of	ADP
jw827942g84	6	23	'	'	PUNCT
jw827942g84	6	24	simpler	simple	ADJ
jw827942g84	6	25	'	'	PUNCT
jw827942g84	6	26	nonnegative	nonnegative	ADJ
jw827942g84	6	27	curves	curve	NOUN
jw827942g84	6	28	,	,	PUNCT
jw827942g84	6	29	which	which	PRON
jw827942g84	6	30	can	can	AUX
jw827942g84	6	31	be	be	AUX
jw827942g84	6	32	a	a	DET
jw827942g84	6	33	nonincreasing	nonincrease	VERB
jw827942g84	6	34	curve	curve	NOUN
jw827942g84	6	35	and	and	CCONJ
jw827942g84	6	36	a	a	DET
jw827942g84	6	37	nondecreasing	nondecrease	VERB
jw827942g84	6	38	curve	curve	NOUN
jw827942g84	6	39	,	,	PUNCT
jw827942g84	6	40	or	or	CCONJ
jw827942g84	6	41	a	a	DET
jw827942g84	6	42	set	set	NOUN
jw827942g84	6	43	of	of	ADP
jw827942g84	6	44	unimodal	unimodal	ADJ
jw827942g84	6	45	curves	curve	NOUN
jw827942g84	6	46	,	,	PUNCT
jw827942g84	6	47	or	or	CCONJ
jw827942g84	6	48	a	a	DET
jw827942g84	6	49	piecewise	piecewise	NOUN
jw827942g84	6	50	linear	linear	NOUN
jw827942g84	6	51	curve	curve	NOUN
jw827942g84	6	52	with	with	ADP
jw827942g84	6	53	fewer	few	ADJ
jw827942g84	6	54	peaks	peak	NOUN
jw827942g84	6	55	.	.	PUNCT
jw827942g84	7	1	finally	finally	ADV
jw827942g84	7	2	,	,	PUNCT
jw827942g84	7	3	we	we	PRON
jw827942g84	7	4	study	study	VERB
jw827942g84	7	5	the	the	DET
jw827942g84	7	6	obnoxious	obnoxious	ADJ
jw827942g84	7	7	line	line	NOUN
jw827942g84	7	8	problem	problem	NOUN
jw827942g84	7	9	,	,	PUNCT
jw827942g84	7	10	which	which	PRON
jw827942g84	7	11	can	can	AUX
jw827942g84	7	12	be	be	AUX
jw827942g84	7	13	viewed	view	VERB
jw827942g84	7	14	as	as	ADP
jw827942g84	7	15	a	a	DET
jw827942g84	7	16	dual	dual	ADJ
jw827942g84	7	17	version	version	NOUN
jw827942g84	7	18	of	of	ADP
jw827942g84	7	19	the	the	DET
jw827942g84	7	20	geometric	geometric	ADJ
jw827942g84	7	21	approximation	approximation	NOUN
jw827942g84	7	22	problem	problem	NOUN
jw827942g84	7	23	.	.	PUNCT
jw827942g84	8	1	given	give	VERB
jw827942g84	8	2	a	a	DET
jw827942g84	8	3	set	set	NOUN
jw827942g84	8	4	of	of	ADP
jw827942g84	8	5	polygons	polygon	NOUN
jw827942g84	8	6	in	in	ADP
jw827942g84	8	7	the	the	DET
jw827942g84	8	8	plane	plane	NOUN
jw827942g84	8	9	,	,	PUNCT
jw827942g84	8	10	the	the	DET
jw827942g84	8	11	goal	goal	NOUN
jw827942g84	8	12	of	of	ADP
jw827942g84	8	13	the	the	DET
jw827942g84	8	14	obnoxious	obnoxious	ADJ
jw827942g84	8	15	line	line	NOUN
jw827942g84	8	16	problem	problem	NOUN
jw827942g84	8	17	is	be	AUX
jw827942g84	8	18	to	to	PART
jw827942g84	8	19	compute	compute	VERB
jw827942g84	8	20	a	a	DET
jw827942g84	8	21	line	line	NOUN
jw827942g84	8	22	which	which	PRON
jw827942g84	8	23	maximizes	maximize	VERB
jw827942g84	8	24	its	its	PRON
jw827942g84	8	25	minimum	minimum	ADJ
jw827942g84	8	26	distance	distance	NOUN
jw827942g84	8	27	to	to	ADP
jw827942g84	8	28	all	all	DET
jw827942g84	8	29	polygons	polygon	NOUN
jw827942g84	8	30	and	and	CCONJ
jw827942g84	8	31	the	the	DET
jw827942g84	8	32	line	line	NOUN
jw827942g84	8	33	is	be	AUX
jw827942g84	8	34	required	require	VERB
jw827942g84	8	35	to	to	PART
jw827942g84	8	36	intersect	intersect	VERB
jw827942g84	8	37	the	the	DET
jw827942g84	8	38	convex	convex	ADJ
jw827942g84	8	39	hull	hull	NOUN
jw827942g84	8	40	of	of	ADP
jw827942g84	8	41	all	all	DET
jw827942g84	8	42	polygons	polygon	NOUN
jw827942g84	8	43	.	.	PUNCT
jw827942g84	9	1	all	all	DET
jw827942g84	9	2	these	these	DET
jw827942g84	9	3	problems	problem	NOUN
jw827942g84	9	4	are	be	AUX
jw827942g84	9	5	motivated	motivate	VERB
jw827942g84	9	6	by	by	ADP
jw827942g84	9	7	real	real	ADJ
jw827942g84	9	8	applications	application	NOUN
jw827942g84	9	9	.	.	PUNCT
jw827942g84	10	1	we	we	PRON
jw827942g84	10	2	develop	develop	VERB
jw827942g84	10	3	efficient	efficient	ADJ
jw827942g84	10	4	exact	exact	ADJ
jw827942g84	10	5	algorithms	algorithm	NOUN
jw827942g84	10	6	for	for	ADP
jw827942g84	10	7	most	most	ADJ
jw827942g84	10	8	of	of	ADP
jw827942g84	10	9	the	the	DET
jw827942g84	10	10	problems	problem	NOUN
jw827942g84	10	11	.	.	PUNCT
jw827942g84	11	1	some	some	PRON
jw827942g84	11	2	of	of	ADP
jw827942g84	11	3	our	our	PRON
jw827942g84	11	4	algorithms	algorithm	NOUN
jw827942g84	11	5	are	be	AUX
jw827942g84	11	6	first	first	ADV
jw827942g84	11	7	-	-	PUNCT
jw827942g84	11	8	known	know	VERB
jw827942g84	11	9	while	while	SCONJ
jw827942g84	11	10	others	other	NOUN
jw827942g84	11	11	improve	improve	VERB
jw827942g84	11	12	the	the	DET
jw827942g84	11	13	previous	previous	ADJ
jw827942g84	11	14	work	work	NOUN
jw827942g84	11	15	in	in	ADP
jw827942g84	11	16	terms	term	NOUN
jw827942g84	11	17	of	of	ADP
jw827942g84	11	18	the	the	DET
jw827942g84	11	19	running	run	VERB
jw827942g84	11	20	time	time	NOUN
jw827942g84	11	21	and	and	CCONJ
jw827942g84	11	22	space	space	NOUN
jw827942g84	11	23	.	.	PUNCT
jw827942g84	12	1	our	our	PRON
jw827942g84	12	2	algorithms	algorithm	NOUN
jw827942g84	12	3	are	be	AUX
jw827942g84	12	4	based	base	VERB
jw827942g84	12	5	on	on	ADP
jw827942g84	12	6	combinations	combination	NOUN
jw827942g84	12	7	of	of	ADP
jw827942g84	12	8	interesting	interesting	ADJ
jw827942g84	12	9	algorithmic	algorithmic	ADJ
jw827942g84	12	10	techniques	technique	NOUN
jw827942g84	12	11	,	,	PUNCT
jw827942g84	12	12	geometric	geometric	ADJ
jw827942g84	12	13	observations	observation	NOUN
jw827942g84	12	14	,	,	PUNCT
jw827942g84	12	15	problem	problem	NOUN
jw827942g84	12	16	modeling	modeling	NOUN
jw827942g84	12	17	and	and	CCONJ
jw827942g84	12	18	careful	careful	ADJ
jw827942g84	12	19	analysis	analysis	NOUN
jw827942g84	12	20	.	.	PUNCT
jw827942g84	13	1	in	in	ADP
jw827942g84	13	2	addition	addition	NOUN
jw827942g84	13	3	,	,	PUNCT
jw827942g84	13	4	for	for	ADP
jw827942g84	13	5	solving	solve	VERB
jw827942g84	13	6	these	these	DET
jw827942g84	13	7	problems	problem	NOUN
jw827942g84	13	8	,	,	PUNCT
jw827942g84	13	9	we	we	PRON
jw827942g84	13	10	develop	develop	VERB
jw827942g84	13	11	a	a	DET
jw827942g84	13	12	number	number	NOUN
jw827942g84	13	13	of	of	ADP
jw827942g84	13	14	new	new	ADJ
jw827942g84	13	15	data	datum	NOUN
jw827942g84	13	16	structures	structure	NOUN
jw827942g84	13	17	,	,	PUNCT
jw827942g84	13	18	e.g.	e.g.	ADV
jw827942g84	13	19	,	,	PUNCT
jw827942g84	13	20	vertical	vertical	ADJ
jw827942g84	13	21	hull	hull	NOUN
jw827942g84	13	22	width	width	NOUN
jw827942g84	13	23	query	query	NOUN
jw827942g84	13	24	,	,	PUNCT
jw827942g84	13	25	2	2	NUM
jw827942g84	13	26	-	-	PUNCT
jw827942g84	13	27	d	d	NOUN
jw827942g84	13	28	sublist	sublist	ADJ
jw827942g84	13	29	query	query	NOUN
jw827942g84	13	30	,	,	PUNCT
jw827942g84	13	31	3	3	NUM
jw827942g84	13	32	-	-	PUNCT
jw827942g84	13	33	d	d	NOUN
jw827942g84	13	34	sublist	sublist	ADJ
jw827942g84	13	35	query	query	NOUN
jw827942g84	13	36	,	,	PUNCT
jw827942g84	13	37	q	q	X
jw827942g84	13	38	-	-	NOUN
jw827942g84	13	39	range	range	NOUN
jw827942g84	13	40	-	-	PUNCT
jw827942g84	13	41	minimia	minimia	NOUN
jw827942g84	13	42	,	,	PUNCT
jw827942g84	13	43	simplicial	simplicial	ADJ
jw827942g84	13	44	thickness	thickness	NOUN
jw827942g84	13	45	query	query	NOUN
jw827942g84	13	46	,	,	PUNCT
jw827942g84	13	47	etc	etc	X
jw827942g84	13	48	.	.	X
jw827942g84	13	49	,	,	PUNCT
jw827942g84	13	50	which	which	PRON
jw827942g84	13	51	are	be	AUX
jw827942g84	13	52	interesting	interesting	ADJ
jw827942g84	13	53	in	in	ADP
jw827942g84	13	54	their	their	PRON
jw827942g84	13	55	own	own	ADJ
jw827942g84	13	56	rights	right	NOUN
jw827942g84	13	57	and	and	CCONJ
jw827942g84	13	58	can	can	AUX
jw827942g84	13	59	easily	easily	ADV
jw827942g84	13	60	find	find	VERB
jw827942g84	13	61	other	other	ADJ
jw827942g84	13	62	applications	application	NOUN
jw827942g84	13	63	.	.	PUNCT