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

Abstract

Given an n-vertex 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(n2 log n) expected running time over a large class of input distributions. The shortest path problem is an old and fundamental problem with a host of applications. Our algorithm is the first strongly-polynomial algorithm in over 35 years to improve upon some aspect of the running time of the celebrated Bellman-Ford algorithm for arbitrary networks, with any type of cost assignments.