Math @ Duke

Publications [#235423] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; HarPeled, S; Karia, M, Computing approximate shortest paths on convex polytopes,
in Sixteenth Annual Symposium on Computational Geometry,
Proceedings of the Annual Symposium on Computational Geometry
(2000),
pp. 270279
(last updated on 2018/02/18)
Abstract: The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t∈P, and a parameter ε>0, it computes a path between s and t on P whose length is at most (1+ε) times the length of the shortest path between those points. It first constructs in time O(n/√ε) a graph of size O(1/ε4), computes a shortest path on this graph, and projects the path onto the surface in O(n/ε) time, where n is the number of vertices of P. In the postprocessing we have added a heuristic that considerably improves the quality of the resulting path.


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