Minimum-link paths among obstacles in the plane

Authors:
Joseph S. B. Mitchell;Günter Rote;Gerhard Woeginger
Affiliations:
SORIE, Cornell University, Ithaca, NY;Institut für Mathematik, Technische Universität Graz, Kopernikusgasse 24, A-8010 Graz, Austria and University of Waterloo, Department of Optimatorics and Combination, Waterloo, Ontario, ...;Institut für Mathematik, Technische Universität Graz, Kopernikusgasse 24, A-8010 Graz, Austria
Venue:
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Year:
1990

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Abstract

Given a set of nonintersecting polygonal obstacles in the plane, the link distance between two points s and t is the minimum number of edges required to form a polygonal path connecting s to t that avoids all obstacles. We present an algorithm that computes the link distance (and a corresponding minimum-link path) between two points in time &Ogr;(E&agr;(n) log2 n) (and space &Ogr;(E)), where n is the total number of edges of the obstacles, E is the size of the visibility graph, and &agr;(n) denotes the extremely slowly growing inverse of Ackermann's function.