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.SoCG.2023.49
URN: urn:nbn:de:0030-drops-178994
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17899/
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Lubiw, Anna ; Naredla, Anurag Murty

The Geodesic Edge Center of a Simple Polygon

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LIPIcs-SoCG-2023-49.pdf (0.8 MB)

Abstract

The geodesic edge center of a polygon is a point c inside the polygon that minimizes the maximum geodesic distance from c to any edge of the polygon, where geodesic distance is the shortest path distance inside the polygon. We give a linear-time algorithm to find a geodesic edge center of a simple polygon. This improves on the previous O(n log n) time algorithm by Lubiw and Naredla [European Symposium on Algorithms, 2021]. The algorithm builds on an algorithm to find the geodesic vertex center of a simple polygon due to Pollack, Sharir, and Rote [Discrete & Computational Geometry, 1989] and an improvement to linear time by Ahn, Barba, Bose, De Carufel, Korman, and Oh [Discrete & Computational Geometry, 2016].
The geodesic edge center can easily be found from the geodesic farthest-edge Voronoi diagram of the polygon. Finding that Voronoi diagram in linear time is an open question, although the geodesic nearest edge Voronoi diagram (the medial axis) can be found in linear time. As a first step of our geodesic edge center algorithm, we give a linear-time algorithm to find the geodesic farthest-edge Voronoi diagram restricted to the polygon boundary.

BibTeX - Entry

@InProceedings{lubiw_et_al:LIPIcs.SoCG.2023.49,
  author =	{Lubiw, Anna and Naredla, Anurag Murty},
  title =	{{The Geodesic Edge Center of a Simple Polygon}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{49:1--49:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17899},
  URN =		{urn:nbn:de:0030-drops-178994},
  doi =		{10.4230/LIPIcs.SoCG.2023.49},
  annote =	{Keywords: geodesic center of polygon, farthest edges, farthest-segment Voronoi diagram}
}

Keywords: geodesic center of polygon, farthest edges, farthest-segment Voronoi diagram
Collection: 39th International Symposium on Computational Geometry (SoCG 2023)
Issue Date: 2023
Date of publication: 09.06.2023

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