# Star unfolding of a polytope with applications

Published

Conference Paper

© Springer-Verlag Berlin Heidelberg 1990. We define the notion of a “star unfolding” of the surface P of a convex polytope with n vertices and use it to construct an algorithm for computing a small superset of the set of all sequences of edges traversed by shortest paths on P. It requires O(n6) time and produces O(n8) sequences, thereby improving an earlier algorithm of Sharir that in O(n8 log n) time produces O(n7) sequences, A variant of our algorithm runs in O(n5 log n) time and produces a more compact representation of size O(n5) for the same set of O(n6) sequences. In addition, we describe an O(n10) time procedure for computing the geodesic diameter of P, which is the maximum possible separation of two points on P, with the distance measured along P, improving an earlier O(n14 log n) algorithm of O’Rourke and Schevon.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Aronov, B; O’Rourke, J; Schevon, CA

### Published Date

- January 1, 1990

### Published In

### Volume / Issue

- 447 LNCS /

### Start / End Page

- 251 - 263

### Electronic International Standard Serial Number (EISSN)

- 1611-3349

### International Standard Serial Number (ISSN)

- 0302-9743

### International Standard Book Number 13 (ISBN-13)

- 9783540528463

### Digital Object Identifier (DOI)

- 10.1007/3-540-52846-6_94

### Citation Source

- Scopus