Computing the geodesic centers of a polygonal domain

Sang Won Bae; Matias Korman; Yoshio Okamoto

doi:10.1016/j.comgeo.2015.10.009

Computing the geodesic centers of a polygonal domain

Sang Won Bae, Matias Korman, Yoshio Okamoto

情報学研究科・システム情報科学専攻

研究成果: Article › 査読

1 被引用数 (Scopus)

抄録

We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n^12+ϵ) for any ϵ>0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(nlog⁡n)-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.

本文言語	English
ページ（範囲）	3-9
ページ数	7
ジャーナル	Computational Geometry: Theory and Applications
巻	77
DOI	https://doi.org/10.1016/j.comgeo.2015.10.009
出版ステータス	Published - 2019 3

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

文献へのアクセス

10.1016/j.comgeo.2015.10.009

フィンガープリント「Computing the geodesic centers of a polygonal domain」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{36dd4ccc8e3b45508618eec4a05f9e6b,

title = "Computing the geodesic centers of a polygonal domain",

abstract = "We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n12+ϵ) for any ϵ>0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(nlog⁡n)-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.",

keywords = "Exact algorithm, Geodesic center, Polygonal domain, Shortest path",

author = "Bae, {Sang Won} and Matias Korman and Yoshio Okamoto",

note = "Funding Information: A preliminary version of this paper was presented at the 26th Canadian Conference on Computational Geometry (CCCG{\textquoteright}14) [4]. Work by S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927). Work by M. Korman was partially supported by the ELC project (MEXT KAKENHI No. 24106008). Work by Y. Okamoto was partially supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan and Japan Society for the Promotion of Science, and the ELC project (Grant-in-Aid for Scientific Research on Innovative Areas, MEXT Japan).",

year = "2019",

month = mar,

doi = "10.1016/j.comgeo.2015.10.009",

language = "English",

volume = "77",

pages = "3--9",

journal = "Computational Geometry: Theory and Applications",

issn = "0925-7721",

publisher = "Elsevier",

}

TY - JOUR

T1 - Computing the geodesic centers of a polygonal domain

AU - Bae, Sang Won

AU - Korman, Matias

AU - Okamoto, Yoshio

N1 - Funding Information: A preliminary version of this paper was presented at the 26th Canadian Conference on Computational Geometry (CCCG’14) [4]. Work by S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927). Work by M. Korman was partially supported by the ELC project (MEXT KAKENHI No. 24106008). Work by Y. Okamoto was partially supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan and Japan Society for the Promotion of Science, and the ELC project (Grant-in-Aid for Scientific Research on Innovative Areas, MEXT Japan).

PY - 2019/3

Y1 - 2019/3

N2 - We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n12+ϵ) for any ϵ>0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(nlog⁡n)-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.

AB - We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n12+ϵ) for any ϵ>0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(nlog⁡n)-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.

KW - Exact algorithm

KW - Geodesic center

KW - Polygonal domain

KW - Shortest path

UR - http://www.scopus.com/inward/record.url?scp=85056577863&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056577863&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2015.10.009

DO - 10.1016/j.comgeo.2015.10.009

M3 - Article

AN - SCOPUS:85056577863

VL - 77

SP - 3

EP - 9

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

ER -