This paper presents an efficient “combinatorial relaxation” algorithm for computing the entire sequence of the maximum degree of minors in rational function matrices, whereas the previous algorithms find them separately for a specified order k. The efficiency of the algorithm is based on the discrete concavity related to valuated bimatroids.

@article{Sato2015CombinatorialRA,
title={Combinatorial Relaxation Algorithm for the Entire Sequence of the Maximum Degree of Minors},
author={Shun Sato},
journal={Algorithmica},
year={2015},
volume={77},
pages={815-835}
}