Using Pseudo Approximation Algorithms to Approximate Shortest Paths Above a Terrain

In this project, we address a general technique for constructing an ε-approximation algorithm out of a so-called pseudo approximation algorithm. We then show how this technique can be applied to the problem of finding the Lp-shortest path above a polyhedral terrain. Our results includes a new approximation algorithm that for any p ≥ 1, computes a (2(1− 1 p ) + ε)-factor approximation of the Lp-shortest path above a polyhedral terrain in O(nε lg n lg N ε ) time and O(n) space, where n is the number of vertices of the input terrain, and N is the maximum bit-length of the integers appearing in the input coordinates.