On the all-pairs shortest path algorithm of Moffat and Takaoka

Abstract

We review how to solve the all-pairs shortest path problem in a non-negatively weighted digraph with n vertices in expected time O(n2 log n). This bound is shown to hold with high probability for a wide class of probability distributions on non-negatively weighted digraphs. We also prove that for a large class of probability distributions Ω(nlog n) time is necessary with high probability to compute shortest path distances with respect to a single source.