Approximating shortest paths on a nonconvex polyhedron


Journal Article

We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in ℝ3 and two points s and t on P, constructs a path on P between s and t whose length is at most 7(1 + ε)dP(s, t), where dP(s, t) is the length of the shortest path between s and t on P, and ε > 0 is an arbitrarily small positive constant. The algorithm runs in O(n5/3 log5/3 n) time, where n is the number of vertices in P. We also present a slightly faster algorithm that runs in O(n8/5 log8/5 n) time and returns a path whose length is at most 15(1 + ε)dP(s, t). © 2000 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Varadarajan, KR; Agarwal, PK

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 30 / 4

Start / End Page

  • 1321 - 1340

International Standard Serial Number (ISSN)

  • 0097-5397

Digital Object Identifier (DOI)

  • 10.1137/S0097539799352759

Citation Source

  • Scopus