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Combinatorial Relaxation Algorithm for the Entire Sequence of the Maximum Degree of Minors

Abstract

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.

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Acknowledgments

Thanks are due to Kazuo Murota and Takayasu Matsuo for helpful comments on the manuscript. The author would also like to thank the anonymous referee for essential comments. This work is partly supported by JSPS KAKENHI Grant Numbers 25287030, 26280004.

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Correspondence to Shun Sato.

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Sato, S. Combinatorial Relaxation Algorithm for the Entire Sequence of the Maximum Degree of Minors. Algorithmica 77, 815–835 (2017). https://doi.org/10.1007/s00453-015-0109-4

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Keywords

  • Combinatorial relaxation
  • Degree of minor
  • Valuated bimatroid
  • Discrete concavity

Mathematics Subject Classification

  • 90C27