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 proceedingConference 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 languageEnglish
Title of host publication31st International Symposium on Computational Geometry, SoCG 2015
EditorsJanos Pach, Janos Pach, Lars Arge
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages209-223
Number of pages15
ISBN (Electronic)9783939897835
DOIs
Publication statusPublished - 2015 Jun 1
Externally publishedYes
Event31st International Symposium on Computational Geometry, SoCG 2015 - Eindhoven, Netherlands
Duration: 2015 Jun 222015 Jun 25

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume34
ISSN (Print)1868-8969

Other

Other31st International Symposium on Computational Geometry, SoCG 2015
CountryNetherlands
CityEindhoven
Period15/6/2215/6/25

Keywords

  • 1-center problem
  • Facility location
  • Geodesic distance
  • Simple polygons

ASJC Scopus subject areas

  • Software

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  • 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