Donald Bren School of Information and Computer Sciences

Maximum and minimum mean cycle problems are important problems with many applications in performance analysis of synchronous and asynchronous digital systems including rate analysis of embedded systems, in discrete-event systems, and in graph theory. Karp's algorithm is one of the fastest and commonest algorithms for both of these problems. We present this paper mainly in the context of the maximum mean cycle problem. We show that Karp's algorithm processes more vertices and arcs than needed to find the maximum cycle mean of a digraph. This observation motivated us to propose a new graph unfolding scheme that remedies this deficiency and leads to three faster algorithms with different characteristics. Asymptotic analysis tells us that our algorithms always run faster than Karp's algorithm. Experiments on benchmark graphs confirm this fact for most of the graphs. Like Karp's algorithm, they are also applicable to both the maximum and minimum mean cycle problems. Moreover, one of them is among the fastest to date.