# 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).

### Duke Authors

### Cited Authors

- Varadarajan, KR; Agarwal, PK

### Published Date

- December 1, 1997

### Published In

### Start / End Page

- 182 - 191

### International Standard Serial Number (ISSN)

- 0272-5428

### Citation Source

- Scopus