Math @ Duke

Publications [#235443] of Pankaj K. Agarwal
Papers Submitted
 Agarwal, PK; HarPeled, S; Karia, M, Computing approximate shortest paths on convex polytopes,
Algorithmica (New York), vol. 33 no. 2
(2002),
pp. 227242, to appear in Algorithmica
(last updated on 2018/11/15)
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 ε 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 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 step we have added a heuristic that considerably improves the quality of the resulting path.


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