A faster algorithm for the all-pairs shortest path problem and its application

Abstract

We design a faster algorithm for the all-pairs shortest path problem under the RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n3(log log n/log n)1/2) to T(n) = O(n3(log log n)2/log n). We extend the algorithm to a parallel algorithm for DMM, whose time complexity is O(log n) and number of processors is T(n)/log n. As an application, we show how to speed up the algorithm for the maximum subarray problem. © Springer-Verlag Berlin Heidelberg 2004.