Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems

The goal of this paper is to identify the most efficient algorithms for the optimum mean cycle and optimum cost to time ratio problems and compare them with the popular ones in the CAD community. These problems have numerous important applications in CAD, graph theory, discrete event system theory, and manufacturing systems. In particular, they are fundamental to the performance analysis of digital systems such as synchronous, asynchronous, dataflow, and embedded real-time systems. For instance, algorithms for these problems are used to compute the cycle period of any cyclic digital system. Without loss of generality, we discuss these algorithms in the context of the minimum mean cycle problem (MCMP). We performed a comprehensive experimental study of ten leading algorithms for MCMP. We programmed these algorithms uniformly and efficiently. We systematically compared them on a test suite composed of random graphs as well as benchmark circuits. Above all, our results provide important insight into the performance of these algorithms in practice. One of the most surprising results of this paper is that Howard's algorithm, known primarily in the stochastic control community, is by far the fastest algorithm on our test suite although the only known bound on its running time is exponential. We provide two stronger bounds on its running time.