An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons

Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P . It is known that the problem has an Ω ( n + m log m ) time lower bound. Previously, a randomized algorithm was proposed [Barb...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete & computational geometry Jg. 70; H. 2; S. 426 - 454
1. Verfasser: Wang, Haitao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2023
Springer Nature B.V
Schlagworte:
ISSN:0179-5376, 1432-0444
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P . It is known that the problem has an Ω ( n + m log m ) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that solves the problem in O ( n + m log m ) expected time. The previous best deterministic algorithms solve the problem in O ( n log log n + m log m ) time [Oh, Barba, and Ahn, SoCG 2016] or in O ( n + m log m + m log 2 n ) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm that takes O ( n + m log m ) time, which is optimal. This answers affirmatively an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.
AbstractList Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P . It is known that the problem has an Ω ( n + m log m ) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that solves the problem in O ( n + m log m ) expected time. The previous best deterministic algorithms solve the problem in O ( n log log n + m log m ) time [Oh, Barba, and Ahn, SoCG 2016] or in O ( n + m log m + m log 2 n ) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm that takes O ( n + m log m ) time, which is optimal. This answers affirmatively an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.
Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P. It is known that the problem has an Ω(n+mlogm) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that solves the problem in O(n+mlogm) expected time. The previous best deterministic algorithms solve the problem in O(nloglogn+mlogm) time [Oh, Barba, and Ahn, SoCG 2016] or in O(n+mlogm+mlog2n) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm that takes O(n+mlogm) time, which is optimal. This answers affirmatively an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.
Author Wang, Haitao
Author_xml – sequence: 1
  givenname: Haitao
  orcidid: 0000-0001-8134-7409
  surname: Wang
  fullname: Wang, Haitao
  email: haitao.wang@usu.edu
  organization: Department of Computer Science, Utah State University
BookMark eNp9kMtKAzEUhoNUsK2-gKuA69GTScwky9LaKggKXrYhM820KTNJTeKib290BMFFV-fC_53LP0Ej551B6JLANQGobiIAu2UFlGWRs5IV_ASNCaO5ZIyN0BhIJYtbWvEzNIlxB1klQYxRPXP4aZ9srzu8MMmE3jobk23wrNv4YNO2x60PeGX82sTcXuqQtiam4tlbl_C7D955ixdWb4LuI7YOv9h-3xn87LvDxrt4jk5b3UVz8Run6G159zq_Lx6fVg_z2WPRUE5TURpimAayFnrdcirqlgnQkoGseM20rkgtaclFTWlbE9PyVrI1kTKXDRAQdIquhrn74D8-84lq5z-DyytVKZikkoOArCoHVRN8jMG0ah_y9-GgCKhvL9Xgpcpeqh8vFc-Q-Ac1NulkvUtB2-44Sgc05j1uY8LfVUeoL3C8isM
CitedBy_id crossref_primary_10_1007_s00454_025_00768_9
Cites_doi 10.1007/BF02189321
10.1137/S0097539793253577
10.1016/0022-0000(89)90045-7
10.1007/BF02187751
10.1137/S0097539795289604
10.1007/BF01553882
10.1016/0020-0190(91)90064-O
10.1016/j.comgeo.2015.10.009
10.1007/s00453-019-00651-z
10.1007/s00454-019-00063-4
10.1007/s00454-016-9796-0
10.1007/s00454-013-9527-8
10.1016/0022-0000(89)90041-X
10.1016/0166-218X(82)90065-8
10.1007/s00453-019-00624-2
10.1016/0020-0190(80)90064-2
10.1007/BF01377183
10.1145/322276.322289
10.1007/PL00009199
10.1109/SFCS.1982.58
10.1016/B978-044482537-7/50016-4
10.1137/1.9781611975482.25
10.1145/1542362.1542402
10.1016/B978-0-12-386870-1.50010-1
ContentType Journal Article
Copyright The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Copyright_xml – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
DBID AAYXX
CITATION
3V.
7SC
7TB
7XB
88I
8AL
8AO
8FD
8FE
8FG
8FK
8G5
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
GUQSH
HCIFZ
JQ2
K7-
KR7
L6V
L7M
L~C
L~D
M0N
M2O
M2P
M7S
MBDVC
P5Z
P62
PADUT
PHGZM
PHGZT
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOI 10.1007/s00454-022-00424-6
DatabaseName CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest Central (purchase pre-March 2016)
Science Database (Alumni Edition)
Computing Database (Alumni Edition)
ProQuest Pharma Collection
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Research Library (Alumni Edition)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
Technology collection
ProQuest One
ProQuest Central
Engineering Research Database
ProQuest Central Student
Research Library Prep (ProQuest)
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Computing Database
Research Library
Science Database
Engineering Database
Research Library (Corporate)
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
Research Library China
ProQuest Central Premium
ProQuest One Academic
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering collection
ProQuest Central Basic
DatabaseTitle CrossRef
Research Library Prep
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
Research Library (Alumni Edition)
ProQuest Pharma Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Research Library
Research Library China
ProQuest Central (New)
Advanced Technologies Database with Aerospace
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
ProQuest Computing
Engineering Database
ProQuest Science Journals (Alumni Edition)
ProQuest Central Basic
ProQuest Science Journals
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList
Research Library Prep
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central (NC Live)
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1432-0444
EndPage 454
ExternalDocumentID 10_1007_s00454_022_00424_6
GrantInformation_xml – fundername: National Science Foundation
  grantid: CCF-2005323
  funderid: http://dx.doi.org/10.13039/100000001
GroupedDBID -52
-5D
-5G
-BR
-DZ
-EM
-Y2
-~C
-~X
.4S
.86
.DC
06D
0R~
0VY
199
1N0
1SB
203
28-
29G
2J2
2JN
2JY
2KG
2KM
2LR
2P1
2VQ
2WC
2~H
30V
3V.
4.4
406
408
409
40D
40E
5GY
5QI
5VS
67Z
692
6NX
78A
88I
8AO
8FE
8FG
8FW
8G5
8TC
8UJ
95-
95.
95~
96X
AABHQ
AACDK
AAGAY
AAHNG
AAIAL
AAJBT
AAJKR
AAKPC
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYOK
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABBXA
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJCF
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABUWG
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIHN
ACIPV
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACREN
ACZOJ
ADHHG
ADHIR
ADIMF
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADYOE
ADZKW
AEAQA
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFEXP
AFGCZ
AFKRA
AFLOW
AFQWF
AFWTZ
AFYQB
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AI.
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMTXH
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARCSS
ARMRJ
ASPBG
AVWKF
AXYYD
AYJHY
AZFZN
AZQEC
B-.
BA0
BAPOH
BBWZM
BDATZ
BENPR
BGLVJ
BGNMA
BPHCQ
BSONS
C1A
CAG
CCPQU
COF
CS3
CSCUP
DDRTE
DL5
DNIVK
DPUIP
DU5
DWQXO
EBD
EBLON
EBS
EDO
EIOEI
EJD
ESBYG
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNUQQ
GNWQR
GQ6
GQ7
GQ8
GUQSH
GXS
H13
HCIFZ
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
HZ~
I-F
I09
IHE
IJ-
IKXTQ
ITM
IWAJR
IXC
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
JBSCW
JCJTX
JZLTJ
K6V
K7-
KDC
KOV
KOW
KQ8
L6V
LAS
LLZTM
LO0
M0N
M2O
M2P
M4Y
M7S
MA-
MQGED
N2Q
N9A
NB0
NDZJH
NPVJJ
NQJWS
NU0
O9-
O93
O9G
O9I
O9J
OAM
OK1
P19
P62
P9R
PADUT
PF0
PKN
PQQKQ
PROAC
PT4
PT5
PTHSS
Q2X
QOK
QOS
R4E
R89
R9I
REI
RHV
RIG
RNI
RNS
ROL
RPX
RSV
RYB
RZK
RZZ
S16
S1Z
S26
S27
S28
S3B
SAP
SCLPG
SDD
SDH
SHX
SISQX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
T16
TN5
TSG
TSK
TSV
TUC
TUS
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
VH1
W23
W48
WK8
YIN
YLTOR
Z45
Z7X
Z83
Z88
Z8R
Z8W
Z92
ZMTXR
ZWQNP
~EX
AAPKM
AAYXX
ABBRH
ABDBE
ABFSG
ABRTQ
ACSTC
ADHKG
AEZWR
AFDZB
AFFHD
AFHIU
AFOHR
AGQPQ
AHPBZ
AHWEU
AIXLP
AMVHM
ATHPR
AYFIA
CITATION
PHGZM
PHGZT
PQGLB
7SC
7TB
7XB
8AL
8FD
8FK
FR3
JQ2
KR7
L7M
L~C
L~D
MBDVC
PKEHL
PQEST
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c363t-2e1e4a01d8adf638bf480a940976b4aa71b93268b33fb1ef6f94d19933fc01083
IEDL.DBID RSV
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000847613700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0179-5376
IngestDate Thu Nov 27 13:52:18 EST 2025
Sat Nov 29 02:58:49 EST 2025
Tue Nov 18 21:16:18 EST 2025
Fri Feb 21 02:43:51 EST 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords 68Q25
68W40
Voronoi diagrams
Geodesic distance
Simple polygons
68U05
Shortest paths
Farthest sites
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c363t-2e1e4a01d8adf638bf480a940976b4aa71b93268b33fb1ef6f94d19933fc01083
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-8134-7409
OpenAccessLink https://link.springer.com/content/pdf/10.1007/s00454-022-00424-6.pdf
PQID 2849396080
PQPubID 31658
PageCount 29
ParticipantIDs proquest_journals_2849396080
crossref_primary_10_1007_s00454_022_00424_6
crossref_citationtrail_10_1007_s00454_022_00424_6
springer_journals_10_1007_s00454_022_00424_6
PublicationCentury 2000
PublicationDate 20230900
2023-09-00
20230901
PublicationDateYYYYMMDD 2023-09-01
PublicationDate_xml – month: 9
  year: 2023
  text: 20230900
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle Discrete & computational geometry
PublicationTitleAbbrev Discrete Comput Geom
PublicationYear 2023
Publisher Springer US
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer Nature B.V
References Bae, Korman, Okamoto (CR8) 2019; 77
Toussaint (CR28) 1989; 3
Hershberger, Suri (CR15) 1997; 26
Guibas, Hershberger (CR13) 1989; 39
Preparata, Shamos (CR26) 1985
CR18
Chazelle, Edelsbrunner, Grigni, Guibas, Hershberger, Sharir, Snoeyink (CR11) 1994; 12
Oh, Barba, Ahn (CR23) 2020; 82
CR10
Kirkpatrick, Snoeyink (CR17) 1995; 22
van Emde Boas (CR12) 1980; 10
Yao (CR30) 1981; 28
Oh, Ahn (CR22) 2020; 63
Aronov, Fortune, Wilfong (CR3) 1993; 9
Liu (CR19) 2020; 82
CR4
CR6
Avis (CR5) 1982; 4
Aronov (CR2) 1989; 4
CR9
Ahn, Barba, Bose, De Carufel, Korman, Oh (CR1) 2016; 56
Bae, Korman, Okamoto (CR7) 2013; 50
CR21
Pollack, Sharir, Rote (CR25) 1989; 4
CR20
Suri (CR27) 1989; 39
Papadopoulou, Lee (CR24) 1998; 20
Hershberger (CR14) 1991; 38
Wang (CR29) 2018; 9
Hershberger, Suri (CR16) 1999; 28
LJ Guibas (424_CR13) 1989; 39
424_CR6
424_CR4
J Hershberger (424_CR14) 1991; 38
B Chazelle (424_CR11) 1994; 12
E Oh (424_CR22) 2020; 63
P van Emde Boas (424_CR12) 1980; 10
G Toussaint (424_CR28) 1989; 3
J Hershberger (424_CR15) 1997; 26
H-K Ahn (424_CR1) 2016; 56
ACC Yao (424_CR30) 1981; 28
424_CR21
J Hershberger (424_CR16) 1999; 28
424_CR20
D Avis (424_CR5) 1982; 4
E Oh (424_CR23) 2020; 82
B Aronov (424_CR2) 1989; 4
C-H Liu (424_CR19) 2020; 82
B Aronov (424_CR3) 1993; 9
H Wang (424_CR29) 2018; 9
SW Bae (424_CR7) 2013; 50
D Kirkpatrick (424_CR17) 1995; 22
424_CR18
FP Preparata (424_CR26) 1985
R Pollack (424_CR25) 1989; 4
S Suri (424_CR27) 1989; 39
E Papadopoulou (424_CR24) 1998; 20
424_CR10
SW Bae (424_CR8) 2019; 77
424_CR9
References_xml – ident: CR18
– volume: 9
  start-page: 217
  issue: 3
  year: 1993
  end-page: 255
  ident: CR3
  article-title: The furthest-site geodesic Voronoĭ diagram
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/BF02189321
– volume: 26
  start-page: 1612
  issue: 6
  year: 1997
  end-page: 1634
  ident: CR15
  article-title: Matrix searching with the shortest-path metric
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539793253577
– volume: 39
  start-page: 220
  issue: 2
  year: 1989
  end-page: 235
  ident: CR27
  article-title: Computing geodesic furthest neighbors in simple polygons
  publication-title: J. Comput. System Sci.
  doi: 10.1016/0022-0000(89)90045-7
– ident: CR4
– volume: 4
  start-page: 611
  issue: 1
  year: 1989
  end-page: 626
  ident: CR25
  article-title: Computing the geodesic center of a simple polygon
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/BF02187751
– ident: CR10
– volume: 28
  start-page: 2215
  issue: 6
  year: 1999
  end-page: 2256
  ident: CR16
  article-title: An optimal algorithm for Euclidean shortest paths in the plane
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539795289604
– ident: CR6
– volume: 4
  start-page: 109
  issue: 1
  year: 1989
  end-page: 140
  ident: CR2
  article-title: On the geodesic Voronoĭ diagram of point sites in a simple polygon
  publication-title: Algorithmica
  doi: 10.1007/BF01553882
– volume: 38
  start-page: 231
  issue: 5
  year: 1991
  end-page: 235
  ident: CR14
  article-title: A new data structure for shortest path queries in a simple polygon
  publication-title: Inform. Process. Lett.
  doi: 10.1016/0020-0190(91)90064-O
– volume: 77
  start-page: 3
  year: 2019
  end-page: 9
  ident: CR8
  article-title: Computing the geodesic centers of a polygonal domain
  publication-title: Comput. Geom.
  doi: 10.1016/j.comgeo.2015.10.009
– year: 1985
  ident: CR26
  publication-title: Computational Geometry. Texts and Monographs in Computer Science
– ident: CR21
– volume: 22
  start-page: 353
  issue: 4
  year: 1995
  end-page: 370
  ident: CR17
  article-title: Tentative prune-and-search for computing fixed-points with applications to geometric computation
  publication-title: Fund. Inform.
– volume: 82
  start-page: 1434
  issue: 5
  year: 2020
  end-page: 1473
  ident: CR23
  article-title: The geodesic farthest-point Voronoi diagram in a simple polygon
  publication-title: Algorithmica
  doi: 10.1007/s00453-019-00651-z
– volume: 63
  start-page: 418
  issue: 2
  year: 2020
  end-page: 454
  ident: CR22
  article-title: Voronoi diagrams for a moderate-sized point-set in a simple polygon
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-019-00063-4
– volume: 56
  start-page: 836
  issue: 4
  year: 2016
  end-page: 859
  ident: CR1
  article-title: A linear-time algorithm for the geodesic center of a simple polygon
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-016-9796-0
– volume: 50
  start-page: 306
  issue: 2
  year: 2013
  end-page: 329
  ident: CR7
  article-title: The geodesic diameter of polygonal domains
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-013-9527-8
– volume: 3
  start-page: 9
  issue: 2
  year: 1989
  end-page: 42
  ident: CR28
  article-title: Computing geodesic properties inside a simple polygon
  publication-title: Rev. Intell. Artif.
– volume: 39
  start-page: 126
  issue: 2
  year: 1989
  end-page: 152
  ident: CR13
  article-title: Optimal shortest path queries in a simple polygon
  publication-title: J. Comput. System Sci.
  doi: 10.1016/0022-0000(89)90041-X
– ident: CR9
– volume: 4
  start-page: 81
  issue: 2
  year: 1982
  end-page: 86
  ident: CR5
  article-title: On the complexity of finding the convex hull of a set of points
  publication-title: Discrete Appl. Math.
  doi: 10.1016/0166-218X(82)90065-8
– volume: 82
  start-page: 915
  issue: 4
  year: 2020
  end-page: 937
  ident: CR19
  article-title: A nearly optimal algorithm for the geodesic Voronoi diagram of points in a simple polygon
  publication-title: Algorithmica
  doi: 10.1007/s00453-019-00624-2
– volume: 10
  start-page: 132
  issue: 3
  year: 1980
  end-page: 136
  ident: CR12
  article-title: On the lower bound for convex hull and maximal vector determination
  publication-title: Inform. Process. Lett.
  doi: 10.1016/0020-0190(80)90064-2
– volume: 12
  start-page: 54
  issue: 1
  year: 1994
  end-page: 68
  ident: CR11
  article-title: Ray shooting in polygons using geodesic triangulations
  publication-title: Algorithmica
  doi: 10.1007/BF01377183
– volume: 9
  start-page: 131
  year: 2018
  end-page: 190
  ident: CR29
  article-title: On the geodesic centers of polygonal domains
  publication-title: J. Comput. Geom.
– volume: 28
  start-page: 780
  issue: 4
  year: 1981
  end-page: 787
  ident: CR30
  article-title: A lower bound to finding convex hulls
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/322276.322289
– volume: 20
  start-page: 319
  issue: 4
  year: 1998
  end-page: 352
  ident: CR24
  article-title: A new approach for the geodesic Voronoi diagram of points in a simple polygon and other restricted polygonal domains
  publication-title: Algorithmica
  doi: 10.1007/PL00009199
– ident: CR20
– volume: 28
  start-page: 2215
  issue: 6
  year: 1999
  ident: 424_CR16
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539795289604
– volume: 10
  start-page: 132
  issue: 3
  year: 1980
  ident: 424_CR12
  publication-title: Inform. Process. Lett.
  doi: 10.1016/0020-0190(80)90064-2
– ident: 424_CR18
– volume: 9
  start-page: 131
  year: 2018
  ident: 424_CR29
  publication-title: J. Comput. Geom.
– ident: 424_CR10
  doi: 10.1109/SFCS.1982.58
– volume: 4
  start-page: 81
  issue: 2
  year: 1982
  ident: 424_CR5
  publication-title: Discrete Appl. Math.
  doi: 10.1016/0166-218X(82)90065-8
– volume: 63
  start-page: 418
  issue: 2
  year: 2020
  ident: 424_CR22
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-019-00063-4
– ident: 424_CR20
  doi: 10.1016/B978-044482537-7/50016-4
– volume: 12
  start-page: 54
  issue: 1
  year: 1994
  ident: 424_CR11
  publication-title: Algorithmica
  doi: 10.1007/BF01377183
– volume: 82
  start-page: 1434
  issue: 5
  year: 2020
  ident: 424_CR23
  publication-title: Algorithmica
  doi: 10.1007/s00453-019-00651-z
– volume: 28
  start-page: 780
  issue: 4
  year: 1981
  ident: 424_CR30
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/322276.322289
– volume: 38
  start-page: 231
  issue: 5
  year: 1991
  ident: 424_CR14
  publication-title: Inform. Process. Lett.
  doi: 10.1016/0020-0190(91)90064-O
– volume: 9
  start-page: 217
  issue: 3
  year: 1993
  ident: 424_CR3
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/BF02189321
– ident: 424_CR21
  doi: 10.1137/1.9781611975482.25
– volume: 4
  start-page: 611
  issue: 1
  year: 1989
  ident: 424_CR25
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/BF02187751
– volume: 26
  start-page: 1612
  issue: 6
  year: 1997
  ident: 424_CR15
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539793253577
– volume-title: Computational Geometry. Texts and Monographs in Computer Science
  year: 1985
  ident: 424_CR26
– volume: 20
  start-page: 319
  issue: 4
  year: 1998
  ident: 424_CR24
  publication-title: Algorithmica
  doi: 10.1007/PL00009199
– volume: 4
  start-page: 109
  issue: 1
  year: 1989
  ident: 424_CR2
  publication-title: Algorithmica
  doi: 10.1007/BF01553882
– volume: 39
  start-page: 220
  issue: 2
  year: 1989
  ident: 424_CR27
  publication-title: J. Comput. System Sci.
  doi: 10.1016/0022-0000(89)90045-7
– volume: 56
  start-page: 836
  issue: 4
  year: 2016
  ident: 424_CR1
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-016-9796-0
– volume: 22
  start-page: 353
  issue: 4
  year: 1995
  ident: 424_CR17
  publication-title: Fund. Inform.
– volume: 77
  start-page: 3
  year: 2019
  ident: 424_CR8
  publication-title: Comput. Geom.
  doi: 10.1016/j.comgeo.2015.10.009
– ident: 424_CR6
  doi: 10.1145/1542362.1542402
– volume: 82
  start-page: 915
  issue: 4
  year: 2020
  ident: 424_CR19
  publication-title: Algorithmica
  doi: 10.1007/s00453-019-00624-2
– ident: 424_CR4
  doi: 10.1016/B978-0-12-386870-1.50010-1
– ident: 424_CR9
– volume: 50
  start-page: 306
  issue: 2
  year: 2013
  ident: 424_CR7
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-013-9527-8
– volume: 39
  start-page: 126
  issue: 2
  year: 1989
  ident: 424_CR13
  publication-title: J. Comput. System Sci.
  doi: 10.1016/0022-0000(89)90041-X
– volume: 3
  start-page: 9
  issue: 2
  year: 1989
  ident: 424_CR28
  publication-title: Rev. Intell. Artif.
SSID ssj0004908
Score 2.3645244
Snippet Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi...
Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 426
SubjectTerms Algorithms
Apexes
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Geometry
Handbooks
Lower bounds
Mathematics
Mathematics and Statistics
Polygons
Voronoi graphs
SummonAdditionalLinks – databaseName: Science Database
  dbid: M2P
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Nb9QwEB1B6YEe6BeIhVL50BtYTeLgtU9oRVm4tF2ptOotsmOnRNombZNW4t8z43V2RSV64ZzYifSex2N7_B7AgVRlLqwruc5dggsU6bm2NuHGKJ8hiWTmXDCbGJ-cqMtLPYsbbl0sqxxiYgjUri1pj_wQw6gWmG6r5MvNLSfXKDpdjRYaz-EFZjYplXQdZ7PVvUgdHOmIdJxkS-KlmXB1LmjPcaplD6d_XP49Ma2yzUcHpGHemW7-7x9vwauYcbLJgiLb8Mw3O7A5uDmwOLh3YON4qeDa7YKdNOwUw8k1Nj2KJTNB05lN5lf4lf7XNcN8l333rfOINJsiB8l7i8_auunZBSkjtDU7qg3Vf3WsbthZTVLEbNbOf18h2V_D-fTbz68_ePRj4KWQoueZT31uktQp4yoct7bKVWI0KWZJmxszTi1lg8oKUdnUV7JCAlCBoKhKXPYp8QbWmrbxb4EJo2keFDJxWV59znSpxjrFfjVGUCH9CNIBjKKMYuXkmTEvljLLAcACASwCgIUcwcdlm5uFVMeTb-8NqBVx2HbFCrIRfBpwXz3-d2_vnu7tPbwkm_pFbdoerPV39_4DrJcPfd3d7QfS_gFc5fAc
  priority: 102
  providerName: ProQuest
Title An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons
URI https://link.springer.com/article/10.1007/s00454-022-00424-6
https://www.proquest.com/docview/2849396080
Volume 70
WOSCitedRecordID wos000847613700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAVX
  databaseName: SpringerLINK Contemporary 1997-Present
  customDbUrl:
  eissn: 1432-0444
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004908
  issn: 0179-5376
  databaseCode: RSV
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fT9swED4N2MN4oBsbovyo_LC3zVISp479WChl0kSJ1g2hvUR24kCkkqAmIPHfc3aTVkzbpO3lXmJbke_su5Pvvg_gIxdpyHSWUhlmHiYo3FCptUeVEiZAI-JBljmyiWg6FdfXMm6bwuqu2r17knQ39arZzaHFUVt97t7rKN-AraFFm7E5-uxq3Q0pHQ-dNTVqwUraVpnfr_HSHa1jzF-eRZ23mfT-7z_fwk4bXZLR0hzewStT7kKvY24g7UHehe2LFVpr_R70qCSXeHXc4dRxWx7j8JvJaH5TLYrm9o5gbEvOTZUZ1CqZoL1Zni0aV0XZkCuLglAVZFwoW-tVk6Iks8LCDpO4mj_doGF_gB-Ts--nX2jLvUBTxllDA-ObUHl-JlSW4xnVeSg8JS06FtehUpGvbeQnNGO59k3Oc1S2LQZkeYopnmB7sFlWpdkHwpS0Po9xLwvCfBjIVETSx3Ul3paMmz74nQqStAUmt_wY82QFqey2NMEtTdyWJrwPn1Zz7pewHH8dfdRpNmmPaJ2gX5YM8zfh9eFzp8n15z-vdvBvww_hjaWoX9alHcFms3gwx_A6fWyKejGArZOzafxtABtfI4ryIrh0MrYymqGMhz8HzsCfAd6u7Ck
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3BTtwwEB1RqNT2AJS2YgsUH-iptZrEqdc-VGjFdgta2K5UWnELduxApCWhJG3FT_GNjL3Jrlqp3DhwTjyS4zfjcTzzHsAOF2nMtEmpjE2ABxRuqdQ6oEoJGyGIeGSMF5vojkbi5ESOF-Cm7YVxZZVtTPSB2pSp-0f-AcOoZJhui2D38id1qlHudrWV0JjCYmiv_-CRrfp00Mf1fRtFg8_He_u0URWgKeOsppENbayC0AhlMkSfzmIRKOl4n7iOleqG2uU0QjOW6dBmPMNpuDI3lqV4eBEM7T6CpZgJ7jxq2KXzPkzpFfAcyKmjSWmadHyrnue6o6523t82Uv73RjjPbv-5kPX73GDloX2hVVhuMmrSm7rAc1iwxRqstGoVpAlea_DsaMZQW70A3SvIVwyXFzi035QEec5q0puc4azq8wuC-Tz5YktjEclkgD7mtMXouMyLmvxwzA9lTvq5cvVtFckL8i13VMtkXE6uz9CZX8L3e5n3K1gsysKuA2FKun2e8cBEcfYxkqnoyhDtStwhGLcdCNvFT9KGjN1pgkySGY20B0yCgEk8YBLegXezMZdTKpI7395sUZI0YalK5hDpwPsWZ_PH_7f2-m5r2_Bk__joMDk8GA034GmEieC0Dm8TFuurX3YLHqe_67y6euMdhsDpfePvFiS7S_8
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLULlQKGAWCjgA5zAahIHr31AaGG7UBWWiC_1FuzYaSNtk9IEUP8av46x19kVSPTWA-ckIzl5M56JZ94DeMRFkTJtCipTE2GBwi2VWkdUKWETBBFPjPFiE6PZTBwcyGwNfvWzMK6tso-JPlCbpnD_yHcwjEqG6baIdsrQFpFNpi9OvlGnIOVOWns5jQVE9u3ZTyzf2ud7E_zWj5Nkuvvp1RsaFAZowTjraGJjm6ooNkKZEpGoy1RESjoOKK5TpUaxdvmN0IyVOrYlL3FJruWNlQUWMoKh3UuwPmJY9Axg_eXuLPuwmsqUXg_PQZ460pQwsuMH9zzzHXWd9P7skfI_t8VVrvvX8azf9aab__P7ug7XQq5NxgvnuAFrtt6CzV7HgoSwtgVX3y25a9uboMc1eY-B9BgfnYRmIc9mTcbzQ1xVd3RMMNMnr21jLGKcTNH7nOoYzZqq7sgXxwnRVGRSKdf51pKqJh8rR8JMsmZ-dohufgs-X8i6b8Ogbmp7BwhT0mUAjEcmSctniSzESMZoV-LewbgdQtwDIS8CTbtTC5nnS4JpD54cwZN78OR8CE-Wz5wsSErOvXu7R0weAlabr-AyhKc95laX_23t7vnWHsIVhF3-dm-2fw82EswQFw162zDoTr_b-3C5-NFV7emD4D0Evl40AH8DRN9WUQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Optimal+Deterministic+Algorithm+for+Geodesic+Farthest-Point+Voronoi+Diagrams+in+Simple+Polygons&rft.jtitle=Discrete+%26+computational+geometry&rft.au=Wang%2C+Haitao&rft.date=2023-09-01&rft.issn=0179-5376&rft.eissn=1432-0444&rft.volume=70&rft.issue=2&rft.spage=426&rft.epage=454&rft_id=info:doi/10.1007%2Fs00454-022-00424-6&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00454_022_00424_6
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0179-5376&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0179-5376&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0179-5376&client=summon