ON SHORTEST PATHS AMIDST CONVEX POLYHEDRA.

Micha Sharir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let K be a 3-D convex polyhedron having n vertices. A sequence xi of edges of K is called a shortest-path sequence if there exist two points X, Y on the surface S of K such that xi is the sequence of edges crossed by the shortest path from X to Y along S. We show that the number of shortest-path sequences for K is polynomial in n, and as a consequence prove that the shortest path between two points in 3-space which must avoid the interiors of a fixed number of disjoint convex polyhedral obstacles, can be calculated in time polynomial in the total number of vertices of these obstacles (but exponential in the number of obstacles).

Original languageEnglish
Pages (from-to)561-572
Number of pages12
JournalSIAM Journal on Computing
Volume16
Issue number3
DOIs
StatePublished - 1987
Externally publishedYes

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