Computing approximate shortest paths on convex polytopes

P. K. Agarwal, Sariel Har-Peled, M. Karia

Research output: Contribution to journalArticlepeer-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 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.

Original languageEnglish (US)
Pages (from-to)227-242
Number of pages16
JournalAlgorithmica (New York)
Issue number2
StatePublished - 2002


  • Approximation algorithms
  • Covex polytopes
  • Path planning

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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