Approximate Shortest Distances Among Smooth Obstacles in 3D

Authors Christian Scheffer, Jan Vahrenhold

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Christian Scheffer
Jan Vahrenhold

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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)


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.
  • Geodesic distances; approximation algorithm; epsilon sample


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