Shortest descending paths through given faces

Authors:
Mustaq Ahmed;Anna Lubiw
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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Abstract

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path from s to t in a polyhedral terrain. We give some properties of such paths. In the case where the face sequence is specified, we show that the shortest descending path is unique, and use convex optimization to give an @e-approximation algorithm that computes the path in O(n^3^.^5log(1@e)) time.