License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.12
URN: urn:nbn:de:0030-drops-104161
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10416/
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Barba, Luis

Optimal Algorithm for Geodesic Farthest-Point Voronoi Diagrams

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LIPIcs-SoCG-2019-12.pdf (0.6 MB)

Abstract

Let P be a 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. Given a set S of m sites being a subset of the vertices of P, we present the first randomized algorithm to compute the geodesic farthest-point Voronoi diagram of S in P running in expected O(n + m) time. That is, a partition of P into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic distance. This algorithm can be extended to run in expected O(n + m log m) time when S is an arbitrary set of m sites contained in P.

BibTeX - Entry

@InProceedings{barba:LIPIcs:2019:10416,
  author =	{Luis Barba},
  title =	{{Optimal Algorithm for Geodesic Farthest-Point Voronoi Diagrams}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10416},
  URN =		{urn:nbn:de:0030-drops-104161},
  doi =		{10.4230/LIPIcs.SoCG.2019.12},
  annote =	{Keywords: Geodesic distance, simple polygons, farthest-point Voronoi diagram}
}

Keywords: Geodesic distance, simple polygons, farthest-point Voronoi diagram
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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