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Iwata–Takamatsu (2013) showed that the maximum degree of minors in mixed polynomial matrices for a specified order can be computed by combinatorial relaxation type algorithm. In this letter, based on their algorithm, we propose an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors. In our previous work, we dealt with a similar problem for rational matrices, where the efficiency derived from the discrete concavity of valuated bimatroids. We follow the same line of discussion; but, technical details are different due to special characteristics of mixed matrices.

Combinatorial relaxation algorithm for the entire sequence of the maximum degree of minors in mixed polynomial matrices