Determining approximate shortest paths on weighted polyhedral surfaces

Authors:
L. Aleksandrov;A. Maheshwari;J.-R. Sack
Affiliations:
Bulgarian Academy of Sciences, Sofia, Bulgaria;Carleton University, Ottawa, Ontario, Canada;Carleton University, Ottawa, Ontario, Canada
Venue:
Journal of the ACM (JACM)
Year:
2005

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Abstract

In this article, we present an approximation algorithm for solving the single source shortest paths problem on weighted polyhedral surfaces. We consider a polyhedral surface P as consisting of n triangular faces, where each face has an associated positive weight. The cost of travel through a face is the Euclidean distance traveled, multiplied by the face's weight. For a given parameter ϵ, 0 O(C(P)n/&sqrt;ϵ log n/ϵ log 1/ϵ) time, where C(P) captures geometric parameters and the weights of the faces of P.