A simpler algorithm for the all pairs shortest path problem with O(n 2 log n) expected time

Abstract

The best known expected time for the all pairs shortest path problem on a directed graph with non-negative edge costs is O(n2log n) by Moffat and Takaoka. Let the solution set be the set of vertices to which the given algorithm has established shortest paths. The Moffat-Takaoka algorithm maintains complexities before and after the critical point in balance, which is the moment when the size of the solution set is n-n/log n. In this paper, we remove the concept of critical point and the data structure, called a batch list, whereby we make the algorithm simpler and seamless, resulting in a simpler analysis and speed-up. © 2010 Springer-Verlag.