Randomized geometric algorithms and pseudo-random generators

Abstract

The so called randomized incremental algorithms in computational geometry can be thought of as a generalization of Quicksort to higher dimensional geometric problems. They all construct the geometric complex in the given problem, such as a Voronoi diagram or a convex polytope, by adding the objects in the input set, one at a time, in a random order. The author shows that the expected running times of most of the randomized incremental algorithms in computational geometry do not change (up to a constant factor), when the sequence of additions is not truly random but is instead generated using only O(log n) random bits. The pseudo-random generator used is a generalization of the well known linear congruential generator. >