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.ISAAC.2019.11
URN: urn:nbn:de:0030-drops-115075
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11507/
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Inkulu, R. ; Kapoor, Sanjiv

Approximate Euclidean Shortest Paths in Polygonal Domains

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LIPIcs-ISAAC-2019-11.pdf (0.6 MB)

Abstract

Given a set P of h pairwise disjoint simple polygonal obstacles in R^2 defined with n vertices, we compute a sketch Omega of P whose size is independent of n, depending only on h and the input parameter epsilon. We utilize Omega to compute a (1+epsilon)-approximate geodesic shortest path between the two given points in O(n + h((lg n) + (lg h)^(1+delta) + (1/epsilon) lg(h/epsilon)))) time. Here, epsilon is a user parameter, and delta is a small positive constant (resulting from the time for triangulating the free space of P using the algorithm in [Bar-Yehuda and Chazelle, 1994]). Moreover, we devise a (2+epsilon)-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.

BibTeX - Entry

@InProceedings{inkulu_et_al:LIPIcs:2019:11507,
  author =	{R. Inkulu and Sanjiv Kapoor},
  title =	{{Approximate Euclidean Shortest Paths in Polygonal Domains}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11507},
  URN =		{urn:nbn:de:0030-drops-115075},
  doi =		{10.4230/LIPIcs.ISAAC.2019.11},
  annote =	{Keywords: Computational Geometry, Geometric Shortest Paths, Approximation Algorithms}
}

Keywords: Computational Geometry, Geometric Shortest Paths, Approximation Algorithms
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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