Approximating shortest paths on a nonconvex polyhedron
Published
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