Two-Point Euclidean Shortest Path Queries in the Plane (Extended Abstract) (1999)
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BibTeX
@MISC{Chiang99two-pointeuclidean,
author = {Yi-Chen Chiang and J.S.B. Mitchell},
title = {Two-Point Euclidean Shortest Path Queries in the Plane (Extended Abstract)},
year = {1999}
}
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Abstract
) To appear in Proc. Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '99), January 17-19, 1999 Yi-Jen Chiang Joseph S. B. Mitchell y Abstract We consider the two-point query version of the fundamental geometric shortest path problem: Given a set h of polygonal obstacles in the plane, having a total of n vertices, build a data structure such that for any two query points s and t we can efficiently determine the length, d(s; t), of an Euclidean shortest obstacle-avoiding path, ß(s; t), from s to t. Additionally, our data structure should allow one to report the path ß(s; t), in time proportional to its (combinatorial) size. We present various methods for solving this two-point query problem, including algorithms with o(n), O(log n+h), O(h log n), O(log 2 n) or optimal O(log n) query times, using polynomial-space data structures, with various tradeoffs between space and query time. While several results have been known for approximate two-point Euclidean shortest p...
