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.SOCG.2015.111
URN: urn:nbn:de:0030-drops-50941
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5094/
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Har-Peled, Sariel

Shortest Path in a Polygon using Sublinear Space

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Abstract

We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon P with n vertices in a read only memory, and additional working memory of size m, the new algorithm computes the shortest path (in P) in O(n^2 / m) expected time, assuming m = O(n / log^2 n). This requires several new tools, which we believe to be of independent interest.

Specifically, we show that violator space problems, an abstraction of low dimensional linear-programming (and LP-type problems), can be solved using constant space and expected linear time, by modifying Seidel's linear programming algorithm and using pseudo-random sequences.

BibTeX - Entry

@InProceedings{harpeled:LIPIcs:2015:5094,
  author =	{Sariel Har-Peled},
  title =	{{Shortest Path in a Polygon using Sublinear Space}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{111--125},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Lars Arge and J{\'a}nos Pach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5094},
  URN =		{urn:nbn:de:0030-drops-50941},
  doi =		{10.4230/LIPIcs.SOCG.2015.111},
  annote =	{Keywords: Shortest path, violator spaces, limited space}
}

Keywords: Shortest path, violator spaces, limited space
Collection: 31st International Symposium on Computational Geometry (SoCG 2015)
Issue Date: 2015
Date of publication: 12.06.2015

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