An Experimental Study of Minimum Mean Cycle Algorithms

We present a comprehensive experimental study of ten leading algorithms for the minimum mean cycle problem. For most of these algorithms, there has not been a clear understanding of their performance in practice although theoretical bounds have been proved for their running times. Only an experimental study can shed light on whether changes in an algorithm that make its running time theoretically more e cient are worth the overhead in terms of their payo in practice. To this end, our experimental study provides a great deal of insight. In our evaluation, we programmed these algorithms uniformly and e ciently. We systematically compared them on a test suite composed of random graphs as well as benchmark circuits. Above all, our experimental results provide important insights into the individual performance as well as relative performance of these algorithms in practice. One of the most surprising results of this study is that Howard's algorithm, a well known algorithm to the stochastic control community but a relatively unknown algorithm to the graph theory community, is by far the fastest algorithm on our test suite although the only known bound on its running time is exponential. We also present two new, stronger bounds on its running time.