Computing approximate shortest paths on convex polytopes

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

Research output: Contribution to conferencePaper

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

Original languageEnglish (US)
Pages270-279
Number of pages10
DOIs
StatePublished - Jan 1 2000
Externally publishedYes
Event16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong
Duration: Jun 12 2000Jun 14 2000

Other

Other16th Annual Symposium on Computational Geometry
CityHong Kong, Hong Kong
Period6/12/006/14/00

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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    Agarwal, P. K., Har-Peled, S., & Karia, M. (2000). Computing approximate shortest paths on convex polytopes. 270-279. Paper presented at 16th Annual Symposium on Computational Geometry, Hong Kong, Hong Kong, . https://doi.org/10.1145/336154.336213