A New Algorithm for Finding All Shortest Paths in a Graph of Positive Arcs in Average Time $O(n^2 \log ^2 n)$

Abstract

We present a new algorithm for finding the shortest path between each pair of nodes in a directed nonnegatively weighted graph. Our algorithm has average running time $O(n^2 \log ^2 n)$ where the graph has n nodes in contrast to previous algorithms in the literature, all of whose average running times are $O(n^3 )$ for this problem.