Approximating Geometric Bottleneck Shortest Paths

Authors:
Prosenjit Bose;Anil Maheshwari;Giri Narasimhan;Michiel H. M. Smid;Norbert Zeh
Affiliations:
-;-;-;-;-
Venue:
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Year:
2003

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Abstract

In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: Given two points p and q of S and a real number L, compute (or approximate) a shortest path in the subgraph of the complete graph on S consisting of all edges whose length is less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on minimum spanning trees, spanners, the Delaunay triangulation, and planar separators.