An Approximation Algorithm for Shortest Descending Paths
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 a simple approximation algorithm that solves the SDP problem on general terrains. Our algorithm discretizes the terrain with O(n^2 X / e) Steiner points so that after an O(n^2 X / e * log(n X /e))-time preprocessing phase for a given vertex s, we can determine a (1+e)-approximate SDP from s to any point v in O(n) time if v is either a vertex of the terrain or a Steiner point, and in O(n X /e) time otherwise. Here n is the size of the terrain, and X is a parameter of the geometry of the terrain.
Cite
@article{arxiv.0705.1364,
title = {An Approximation Algorithm for Shortest Descending Paths},
author = {Mustaq Ahmed and Anna Lubiw},
journal= {arXiv preprint arXiv:0705.1364},
year = {2007}
}