Approximate Shortest Distances Among Smooth Obstacles in 3D
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
60:1-60:13
Regular Paper
Christian
Scheffer
Christian Scheffer
Jan
Vahrenhold
Jan Vahrenhold
10.4230/LIPIcs.ISAAC.2016.60
Creative Commons Attribution 3.0 Unported license
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