Finding real-valued single-source shortest paths in o(n3) expected time

Given an n-vertex, m-edge directed network G with real costs on the edges and a designated source vertex s, we give a new algorithm to compute shortest paths from s. Our algorithm is a simple deterministic one with O(n(2) log n) expected running time over a large class of input distributions. This is the first strongly polynomial algorithm in over 35 years to improve upon some aspect of the O(nm) running time of the Bellman-Ford algorithm. The result extends to an O(n(2) log n) expected running time algorithm for finding the minimum mean cycle, an improvement over Karp's O(nm) worst-case time bound when the underlying graph is dense. Both of our time bounds are shown to be achieved with high probability. (C) 1998 Academic Press.