TY - GEN

T1 - On shortest paths in polyhedral spaces

AU - Sharir, Micha

AU - Schorr, Amir

N1 - Publisher Copyright:
© 1984 ACM.

PY - 1984/12/1

Y1 - 1984/12/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84975882270&partnerID=8YFLogxK

U2 - 10.1145/800057.808676

DO - 10.1145/800057.808676

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AN - SCOPUS:84975882270

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 144

EP - 153

BT - Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984

PB - Association for Computing Machinery

T2 - 16th Annual ACM Symposium on Theory of Computing, STOC 1984

Y2 - 30 April 1984 through 2 May 1984

ER -