Approximate Shortest Distances Among Smooth Obstacles in 3D

Scheffer, Christian; Vahrenhold, Jan

doi:10.4230/LIPIcs.ISAAC.2016.60

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Approximate Shortest Distances Among Smooth Obstacles in 3D

Authors Christian Scheffer, Jan Vahrenhold

Part of: Volume: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: International Symposium on Algorithms and Computation (ISAAC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2016-12-07

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Document Identifiers

DOI: 10.4230/LIPIcs.ISAAC.2016.60
URN: urn:nbn:de:0030-drops-68292

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Keywords

Geodesic distances; approximation algorithm; epsilon sample

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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.

Cite As Get BibTex

Christian Scheffer and Jan Vahrenhold. Approximate Shortest Distances Among Smooth Obstacles in 3D. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 60:1-60:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ISAAC.2016.60

Author Details

Christian Scheffer

Jan Vahrenhold

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