eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
60:1
60:13
10.4230/LIPIcs.ISAAC.2016.60
article
Approximate Shortest Distances Among Smooth Obstacles in 3D
Scheffer, Christian
Vahrenhold, Jan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.60/LIPIcs.ISAAC.2016.60.pdf
Geodesic distances; approximation algorithm; epsilon sample