Abstract

In this paper we show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(log n) using O(n) processors and linear space in the CRCW PRAM model. This is done by proving that a relaxed version of the quasi-greedy triangulation algorithm which produces edges which is at most (1+) longer than the shortest edge, where is some positive constant smaller than 1, still outputs a triangulation which is within a constant factor longer that the minimum weight triangulation. We also show that the approximation behavior of the greedy algorithm may deteriorate dramatically, i.e. (n) longer than a minimum weight triangulation, if the lengths of the edges are not computed with high precision.

Citations