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.ESA.2016.19
URN: urn:nbn:de:0030-drops-63700
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6370/
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Bonnet, Édouard ; Miltzow, Tillmann

Parameterized Hardness of Art Gallery Problems

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LIPIcs-ESA-2016-19.pdf (0.7 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 set S such that every point in P is visible from a point in S.
The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as a guard. For both variants, we rule out a f(k)*n^{o(k/log k)} algorithm, for any computable function f, where k := |S| is the number of guards, unless the Exponential Time Hypothesis fails. These lower bounds almost match the n^{O(k)} algorithms that exist for both problems.

BibTeX - Entry

@InProceedings{bonnet_et_al:LIPIcs:2016:6370,
  author =	{{\'E}douard Bonnet and Tillmann Miltzow},
  title =	{{Parameterized Hardness of Art Gallery Problems}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6370},
  URN =		{urn:nbn:de:0030-drops-63700},
  doi =		{10.4230/LIPIcs.ESA.2016.19},
  annote =	{Keywords: art gallery problem, computational geometry, parameterized complexity, ETH-based lower bound, geometric set cover/hitting set}
}

Keywords: art gallery problem, computational geometry, parameterized complexity, ETH-based lower bound, geometric set cover/hitting set
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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