On the empirical efficiency of the Vertex Contraction algorithm for detecting negative cost cycles in networks

Abstract

In this paper, we present a comprehensive empirical analysis of the Vertex Contraction (VC) algorithm for the problem of checking whether a directed graph with positive and negative costs on its edges has a negative cost cycle (NCCD). VC is a greedy algorithm, first presented in [SK05], for NCCD and is the only known greedy strategy for this problem. In [SK05] we compared a naive implementation of VC with the "standard" Bellman-Ford (BF) algorithm for the same problem. We observed that our algorithm performed an order of magnitude better than the BF algorithm on a range of randomly generated inputs, thereby conclusively demonstrating the superiority of our approach. This paper continues the study of contrasting greedy and dynamic programming approaches, by comparing VC with a number of sophisticated implementations of the BF algorithm. © Springer-Verlag Berlin Heidelberg 2005.