License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2021.59
URN: urn:nbn:de:0030-drops-138585
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13858/
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Wang, Haitao

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

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LIPIcs-SoCG-2021-59.pdf (0.9 MB)

Abstract

Given 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+mlog m) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that can solve the problem in O(n+mlog m) expected time. The previous best deterministic algorithms solve the problem in O(nlog log n+ mlog m) time [Oh, Barba, and Ahn, SoCG 2016] or in O(n+mlog m+mlog² n) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm of O(n+mlog m) time, which is optimal. This answers an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.

BibTeX - Entry

@InProceedings{wang:LIPIcs.SoCG.2021.59,
  author =	{Wang, Haitao},
  title =	{{An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{59:1--59:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13858},
  URN =		{urn:nbn:de:0030-drops-138585},
  doi =		{10.4230/LIPIcs.SoCG.2021.59},
  annote =	{Keywords: farthest-sites, Voronoi diagrams, triple-point geodesic center, simple polygons}
}

Keywords: farthest-sites, Voronoi diagrams, triple-point geodesic center, simple polygons
Collection: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue Date: 2021
Date of publication: 02.06.2021

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