Quickest paths in anisotropic media

Authors:
Radwa El Shawi;Joachim Gudmundsson
Affiliations:
School of Information Technology, University of Sydney and NICTA, Sydney, Australia;School of Information Technology, University of Sydney and NICTA, Sydney, Australia
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

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Abstract

In this paper we study the quickest path problem where speed is direction-dependent (anisotropic). The problem arises in sailing, robotics, aircraft navigation, and routing of autonomous vehicles, where the speed is affected by the direction of waves, winds or slope of the terrain. We present an approximation algorithm to find a quickest path for a point robot moving in planar subdivision, where each face is assigned a translational flow that reflects the cost of travelling within this face. Our main contribution is a data structure that given a subdivision with translational flows returns a (1 + ε)-approximate quickest path in the subdivision between any two query points in the plane.