A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon

Hee Kap Ahn; Luis Barba; Prosenjit Bose; Jean Lou De Carufel; Matias Korman; Eunjin Oh

doi:10.4230/LIPIcs.SOCG.2015.209

A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon

Hee Kap Ahn, Luis Barba, Prosenjit Bose, Jean Lou De Carufel, Matias Korman, Eunjin Oh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 Citations (Scopus)

Abstract

Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an O(n log n)-time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.

Original language	English
Title of host publication	31st International Symposium on Computational Geometry, SoCG 2015
Editors	Janos Pach, Janos Pach, Lars Arge
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	209-223
Number of pages	15
ISBN (Electronic)	9783939897835
DOIs	https://doi.org/10.4230/LIPIcs.SOCG.2015.209
Publication status	Published - 2015 Jun 1
Externally published	Yes
Event	31st International Symposium on Computational Geometry, SoCG 2015 - Eindhoven, Netherlands Duration: 2015 Jun 22 → 2015 Jun 25

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	34
ISSN (Print)	1868-8969

Other

Other	31st International Symposium on Computational Geometry, SoCG 2015
Country	Netherlands
City	Eindhoven
Period	15/6/22 → 15/6/25

Keywords

1-center problem
Facility location
Geodesic distance
Simple polygons

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.SOCG.2015.209

Fingerprint Dive into the research topics of 'A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon'. Together they form a unique fingerprint.

Cite this

Ahn, H. K., Barba, L., Bose, P., De Carufel, J. L., Korman, M., & Oh, E. (2015). A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon. In J. Pach, J. Pach, & L. Arge (Eds.), 31st International Symposium on Computational Geometry, SoCG 2015 (pp. 209-223). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 34). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SOCG.2015.209

A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon. / Ahn, Hee Kap; Barba, Luis; Bose, Prosenjit; De Carufel, Jean Lou; Korman, Matias; Oh, Eunjin.

31st International Symposium on Computational Geometry, SoCG 2015. ed. / Janos Pach; Janos Pach; Lars Arge. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2015. p. 209-223 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 34).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ahn, HK, Barba, L, Bose, P, De Carufel, JL, Korman, M & Oh, E 2015, A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon. in J Pach, J Pach & L Arge (eds), 31st International Symposium on Computational Geometry, SoCG 2015. Leibniz International Proceedings in Informatics, LIPIcs, vol. 34, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 209-223, 31st International Symposium on Computational Geometry, SoCG 2015, Eindhoven, Netherlands, 15/6/22. https://doi.org/10.4230/LIPIcs.SOCG.2015.209

Ahn HK, Barba L, Bose P, De Carufel JL, Korman M, Oh E. A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon. In Pach J, Pach J, Arge L, editors, 31st International Symposium on Computational Geometry, SoCG 2015. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2015. p. 209-223. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.SOCG.2015.209

Ahn, Hee Kap ; Barba, Luis ; Bose, Prosenjit ; De Carufel, Jean Lou ; Korman, Matias ; Oh, Eunjin. / A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon. 31st International Symposium on Computational Geometry, SoCG 2015. editor / Janos Pach ; Janos Pach ; Lars Arge. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2015. pp. 209-223 (Leibniz International Proceedings in Informatics, LIPIcs).

@inproceedings{ffb1f1bad9664dbbb10cd4bd4c742246,

title = "A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon",

abstract = "Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an O(n log n)-time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.",

keywords = "1-center problem, Facility location, Geodesic distance, Simple polygons",

author = "Ahn, {Hee Kap} and Luis Barba and Prosenjit Bose and {De Carufel}, {Jean Lou} and Matias Korman and Eunjin Oh",

year = "2015",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SOCG.2015.209",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "209--223",

editor = "Janos Pach and Janos Pach and Lars Arge",

booktitle = "31st International Symposium on Computational Geometry, SoCG 2015",

note = "31st International Symposium on Computational Geometry, SoCG 2015 ; Conference date: 22-06-2015 Through 25-06-2015",

}

TY - GEN

T1 - A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon

AU - Ahn, Hee Kap

AU - Barba, Luis

AU - Bose, Prosenjit

AU - De Carufel, Jean Lou

AU - Korman, Matias

AU - Oh, Eunjin

PY - 2015/6/1

Y1 - 2015/6/1

N2 - Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an O(n log n)-time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.

AB - Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an O(n log n)-time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.

KW - 1-center problem

KW - Facility location

KW - Geodesic distance

KW - Simple polygons

UR - http://www.scopus.com/inward/record.url?scp=84951972893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951972893&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SOCG.2015.209

DO - 10.4230/LIPIcs.SOCG.2015.209

M3 - Conference contribution

AN - SCOPUS:84951972893

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 209

EP - 223

BT - 31st International Symposium on Computational Geometry, SoCG 2015

A2 - Pach, Janos

A2 - Arge, Lars

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 31st International Symposium on Computational Geometry, SoCG 2015

Y2 - 22 June 2015 through 25 June 2015

ER -