Abstract
An algorithm is presented that finds the shortest path between two points on a polyhedral surface in O(n 5) time, where n is the number of vertices on the surface, thereby establishing that the problem can be solved in polynomial time. The path is confined to the surface, and shortest is defined in terms of Euclidean distance. The algorithm is an extension of methods developed by Sharir and Schorr for finding the shortest path on a convex polyhedron. We relax the convexity assumption, only requiring that the surface be orientable.
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References
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M. Sharir and A. Schorr, "On shortest paths in polyhedral spaces," Proc. 16th Symp. on Theory of Computing (1984), 144–153; full version: Technical Report 84–001, Tel Aviv University, Mar. 1984.
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© 1984 Springer-Verlag Berlin Heidelberg
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O'Rourke, J., Suri, S., Booth, H. (1984). Shortest paths on polyhedral surfaces. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024013
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DOI: https://doi.org/10.1007/BFb0024013
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Print ISBN: 978-3-540-13912-6
Online ISBN: 978-3-540-39136-4
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