Abstract

We consider the problem of path planning above a polyhedral terrain and present a new algorithm that for any p ges 1, computes a (c + epsi)-approximation to the Lp-shortest path above a polyhedral terrain in O(n/epsi log n log log n) time and O(n log n) space, where n is the number of vertices of the terrain, and c = 2(p-1)p/. This leads to an epsi-approximation algorithm for the problem in L1 metric, and a (radic2 + epsi)-factor approximation algorithm in Euclidean space

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