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The Visibility Center of a Simple Polygon

Authors Anna Lubiw, Anurag Murty Naredla



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Author Details

Anna Lubiw
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Anurag Murty Naredla
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada

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Anna Lubiw and Anurag Murty Naredla. The Visibility Center of a Simple Polygon. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 65:1-65:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ESA.2021.65

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Visibility
  • Shortest Paths
  • Simple Polygons
  • Facility Location

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References

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