Journal article
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM, Vol.44(4), pp.567-584
07/1997
DOI: 10.1145/263867.263869
Abstract
Given a convex polytope P with n faces in ℝ 3 , points ∈ ∂P, and a parameter 0 < ϵ ≤ 1, we present an algorithm that constructs a path on ∂P from s to t whose length is at most (1 + ϵ) d p (s, t) , where d p (s, t) is the length of the shortest path between s and t on ∂P. The algorithm runs in O(n log 1/ϵ + 1/ϵ 3 ) time, and is relatively simple. The running time is O(n + 1/ϵ 3 ) if we only want the approximate shortest path distance and not the path itself. We also present an extension of the algorithm that computes approximate shortest path distances from a given source point on ∂P to all vertices of P .
Details
- Title: Subtitle
- Approximating shortest paths on a convex polytope in three dimensions
- Creators
- Pankaj K. Agarwal - Duke UniversitySariel Har-Peled - Tel Aviv UniversityMicha Sharir - New York UniversityKasturi R. Varadarajan - Duke University
- Resource Type
- Journal article
- Publication Details
- Journal of the ACM, Vol.44(4), pp.567-584
- DOI
- 10.1145/263867.263869
- ISSN
- 0004-5411
- eISSN
- 1557-735X
- Language
- English
- Date published
- 07/1997
- Academic Unit
- Computer Science
- Record Identifier
- 9984259469302771
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