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.2017.49
URN: urn:nbn:de:0030-drops-78413
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7841/
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Hershberger, John ; Kumar, Neeraj ; Suri, Subhash

Shortest Paths in the Plane with Obstacle Violations

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LIPIcs-ESA-2017-49.pdf (0.5 MB)

Abstract

We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for k <= h. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all destinations in the same region of the map have the same combinatorial shortest path passing through at most k obstacles. We prove a tight bound of Theta(kn) on the size of this map, and show that it can be computed in O(k^2 n log n) time, where n is the total number of obstacle vertices.

BibTeX - Entry

@InProceedings{hershberger_et_al:LIPIcs:2017:7841,
  author =	{John Hershberger and Neeraj Kumar and Subhash Suri},
  title =	{{Shortest Paths in the Plane with Obstacle Violations}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7841},
  URN =		{urn:nbn:de:0030-drops-78413},
  doi =		{10.4230/LIPIcs.ESA.2017.49},
  annote =	{Keywords: Shortest paths, Polygonal obstacles, Continuous Dijkstra, Obstacle crossing, Visibility}
}

Keywords: Shortest paths, Polygonal obstacles, Continuous Dijkstra, Obstacle crossing, Visibility
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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