On shortest paths in polyhedral spaces

Micha Sharir; Amir Schorr

doi:10.1145/800057.808676

On shortest paths in polyhedral spaces

Micha Sharir, Amir Schorr

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the problem of computing the shortest path between two points in two- or three-dimensional space bounded by polyhedral surfaces. In the 2-D case the problem is easily solved in time O(n2log n). In the general 3-D case the problem is quite hard to solve, and is not even discrete; we present a doublyexponential procedure for solving the discrete subproblem of determining the sequence of boundary edges through which the shortest path passes. The main result of this paper involves a favorable special case of the 3-D shortest path problem, namely that of finding the shortest path between two points along the surface of a convex polyhedron. We analyze this problem and solve it in time O(n 3 log n).

Original language	English
Title of host publication	Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984
Publisher	Association for Computing Machinery
Pages	144-153
Number of pages	10
ISBN (Electronic)	0897911334
DOIs	https://doi.org/10.1145/800057.808676
State	Published - 1 Dec 1984
Event	16th Annual ACM Symposium on Theory of Computing, STOC 1984 - Washington, United States Duration: 30 Apr 1984 → 2 May 1984

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	16th Annual ACM Symposium on Theory of Computing, STOC 1984
Country/Territory	United States
City	Washington
Period	30/04/84 → 2/05/84

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10.1145/800057.808676

Cite this

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title = "On shortest paths in polyhedral spaces",

abstract = "We consider the problem of computing the shortest path between two points in two- or three-dimensional space bounded by polyhedral surfaces. In the 2-D case the problem is easily solved in time O(n2log n). In the general 3-D case the problem is quite hard to solve, and is not even discrete; we present a doublyexponential procedure for solving the discrete subproblem of determining the sequence of boundary edges through which the shortest path passes. The main result of this paper involves a favorable special case of the 3-D shortest path problem, namely that of finding the shortest path between two points along the surface of a convex polyhedron. We analyze this problem and solve it in time O(n 3 log n).",

author = "Micha Sharir and Amir Schorr",

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Sharir, M & Schorr, A 1984, On shortest paths in polyhedral spaces. in Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 144-153, 16th Annual ACM Symposium on Theory of Computing, STOC 1984, Washington, United States, 30/04/84. https://doi.org/10.1145/800057.808676

On shortest paths in polyhedral spaces. / Sharir, Micha; Schorr, Amir.
Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Association for Computing Machinery, 1984. p. 144-153 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On shortest paths in polyhedral spaces

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