Shortest paths and negative cycle detection in graphs with negative weights. I, The Bellman-Ford-Moore algorithm revisited

Abstract

Since the mid 1950's when Bellman, Ford, and Moore developped their shortest path algorithm various attempts were made to beat the O(nm) barrier without success. For the special case of integer weights Goldberg's algorithm gave a theoretical improvement, but the algorithm isn't competative in praxis. This technical report is part one of a summary of existing n-pass algorithms and some new variations. In this part we consider the classical algorithm and variations that differ only in the data structure used to maintain the set of nodes to be scanned in the current and following pass. We unify notation and give some experimental results for the average case on various graph classes.