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Approximation Algorithms for Shortest Descending Paths in Terrains (0805.1401v1)
Published 9 May 2008 in cs.CG and cs.DS
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 (SDP) from s to t in a polyhedral terrain. We give two approximation algorithms (more precisely, FPTASs) that solve the SDP problem on general terrains. Both algorithms are simple, robust and easy to implement.