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}
}
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Keywords: |
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Geodesic distances; approximation algorithm; epsilon sample |
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Collection: |
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27th International Symposium on Algorithms and Computation (ISAAC 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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07.12.2016 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)