Shortest rectilinear paths among weighted obstacles

Authors:
D. T. Lee;T. H. Chen;C. D. Yang
Affiliations:
Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL;Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL;Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL
Venue:
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Year:
1990

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Abstract

In this paper we study a rectilinear shortest path problem among weighted obstacles. Instead of restricting a path to totally avoid obstacles we allow a path to pass through them at extra costs. The extra costs are represented by the weights of the obstacles. We aim to find a shortest rectilinear path between two distinguished points among a set of weighted obstacles. By using a graph-theoretical approach, we obtain two algorithms which run in &Ogr;(nlog2 n) time and &Ogr;(n log n) space and in &Ogr;(n log3/2 n) time and space, respectively, where n is the number of the vertices of obstacles.