Computing approximate shortest paths on convex polytopes

Pankaj K. Agarwal, Sariel Har-Peled, Meetesh Karia

Research output: Contribution to conferencePaperpeer-review


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 post-processing we have added a heuristic that considerably improves the quality of the resulting path.

Original languageEnglish (US)
Number of pages10
StatePublished - 2000
Externally publishedYes
Event16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong
Duration: Jun 12 2000Jun 14 2000


Other16th Annual Symposium on Computational Geometry
CityHong Kong, Hong Kong

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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