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DOI: 10.4230/LIPIcs.ISAAC.2016.60
URN: urn:nbn:de:0030-drops-68292
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6829/
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Scheffer, Christian ; Vahrenhold, Jan

Approximate Shortest Distances Among Smooth Obstacles in 3D

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LIPIcs-ISAAC-2016-60.pdf (0.5 MB)


Abstract

We consider the classic all-pairs-shortest-paths (APSP) problem in a three-dimensional environment where paths have to avoid a set of smooth obstacles whose surfaces are represented by discrete point sets with n sample points in total. We show that if the point sets represent epsilon-samples of the underlying surfaces, (1 ± O(sqrt{epsilon}))-approximations of the distances between all pairs of sample points can be computed in O(n^{5/2} log^2 n) time.

BibTeX - Entry

@InProceedings{scheffer_et_al:LIPIcs:2016:6829,
  author =	{Christian Scheffer and Jan Vahrenhold},
  title =	{{Approximate Shortest Distances Among Smooth Obstacles in 3D}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{60:1--60:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6829},
  URN =		{urn:nbn:de:0030-drops-68292},
  doi =		{10.4230/LIPIcs.ISAAC.2016.60},
  annote =	{Keywords: Geodesic distances; approximation algorithm; epsilon sample}
}

Keywords: Geodesic distances; approximation algorithm; epsilon sample
Seminar: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 02.12.2016


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