Flying over a polyhedral terrain

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 + )approximation to the Lp-shortest path above a polyhedral terrain in O(n 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 a FPTAS for the problem in L1 metric, a ( 2 + )-factor approximation algorithm in Euclidean space, and a 2-approximation algorithm in the general Lp metric.

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Hamid Zarrabi-Zadeh
• Keywords: IPL 2006, IPL 2008, Polyhedral Terrain, Shortest Paths, Single-obstacle Polyhedral Terrain