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.ESA.2021.65
URN: urn:nbn:de:0030-drops-146466
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14646/
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Lubiw, Anna ; Naredla, Anurag Murty

The Visibility Center of a Simple Polygon

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LIPIcs-ESA-2021-65.pdf (2 MB)

Abstract

We introduce the visibility center of a set of points inside a polygon - a point c_V such that the maximum geodesic distance from c_V to see any point in the set is minimized. For a simple polygon of n vertices and a set of m points inside it, we give an O((n+m) log (n+m)) time algorithm to find the visibility center. We find the visibility center of all points in a simple polygon in O(n log n) time.
Our algorithm reduces the visibility center problem to the problem of finding the geodesic center of a set of half-polygons inside a polygon, which is of independent interest. We give an O((n+k) log (n+k)) time algorithm for this problem, where k is the number of half-polygons.

BibTeX - Entry

@InProceedings{lubiw_et_al:LIPIcs.ESA.2021.65,
  author =	{Lubiw, Anna and Naredla, Anurag Murty},
  title =	{{The Visibility Center of a Simple Polygon}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{65:1--65:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14646},
  URN =		{urn:nbn:de:0030-drops-146466},
  doi =		{10.4230/LIPIcs.ESA.2021.65},
  annote =	{Keywords: Visibility, Shortest Paths, Simple Polygons, Facility Location}
}

Keywords: Visibility, Shortest Paths, Simple Polygons, Facility Location
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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