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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.20
URN: urn:nbn:de:0030-drops-72150
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7215/
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Bonnet, Édouard ; Miltzow, Tillmann

An Approximation Algorithm for the Art Gallery Problem

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LIPIcs-SoCG-2017-20.pdf (0.9 MB)


Abstract

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum-size set S such that every point in P is visible from a point in S. The set S is referred to as guards. Assuming integer coordinates and a specific general position on the vertices of P, we present the first O(log OPT)-approximation algorithm for the point guard problem. This algorithm combines ideas in papers of Efrat and Har-Peled and Deshpande et al. We also point out a mistake in the latter.

BibTeX - Entry

@InProceedings{bonnet_et_al:LIPIcs:2017:7215,
  author =	{{\'E}douard Bonnet and Tillmann Miltzow},
  title =	{{An Approximation Algorithm for the Art Gallery Problem}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7215},
  URN =		{urn:nbn:de:0030-drops-72150},
  doi =		{10.4230/LIPIcs.SoCG.2017.20},
  annote =	{Keywords: computational geometry, art gallery, approximation algorithm}
}

Keywords: computational geometry, art gallery, approximation algorithm
Seminar: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 08.06.2017


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