Flying over a polyhedral terrain

Authors:
Hamid Zarrabi-Zadeh
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Venue:
Information Processing Letters
Year:
2008

Citing 5
Cited 1

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Abstract

We consider the problem of computing shortest paths in three-dimensions in the presence of a single-obstacle polyhedral terrain, and present a new algorithm that for any p=1, computes a (c+@e)-approximation to the L"p-shortest path above a polyhedral terrain in O(n@elognloglogn) time and O(nlogn) space, where n is the number of vertices of the terrain, and c=2^(^p^-^1^)^/^p. This leads to a FPTAS for the problem in L"1 metric, a (2+@e)-factor approximation algorithm in Euclidean space, and a 2-approximation algorithm in the general L"p metric.