Empirical analysis of algorithms for the shortest negative cost cycle problem

Abstract

In this paper, we empirically profile three algorithms for the Shortest Negative Cost Cycle (SNCC) problem. In this problem, we are given a directed, weighted graph G=〈V,E,c〉, and the goal is to identify a negative cost cycle with the fewest number of edges. The SNCC problem finds applications in a number of domains ranging from program verification to certifying algorithm design. The first polynomial time algorithm for this problem was proposed in Subramani (2009). Since then, several additional techniques, including a randomized approach, have been proposed for the SNCC problem. Our goal in this paper is to analyze three algorithmic paradigms for this problem from the empirical perspective. Towards this end, we profile these algorithmic approaches over a wide range of inputs. Our results indicated that the randomized algorithm is the algorithm of choice over a number of graph classes.