Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems
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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 most common algorithms for these problems. We present this paper mainly in the context of the maximum mean cycle problem. We show that Karp's algorithm processes more nodes 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 two faster algorithms with different characteristics. Theoretical analysis tells us that our algorithms always run faster than Karp's algorithm and that they are among the fastest to date. Experiments on small benchmark graphs confirm this fact for most of the graphs. These algorithms have been used in building a framework for analysis of timing constraints for embedded systems