Solving max-plus linear systems by level sparsification

In this study, an algorithm for solving max-plus linear systems is discussed. Such a system is applied to many problems, such as control and scheduling, and is equivalent to the mean-payoff game. To reduce the computational time required to solve max-plus linear systems, we improve the alternating method, which is a well-known algorithm for the problem. In max-plus arithmetics, small numbers rarely contribute to the results. Based on this observation, our method, called level sparsification, selects some large entries of matrices as active ones and ignore other entries by replacing with a fixed value. Depending on the number of selected entries, we propose two types of sparsification and experiment with the performance compared to the original alternating method.