REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM.

Akira Onozawa, Masayuki Inoue, Shinichi Oishi, Kazuo Horiuchi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.

    Original languageEnglish
    Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
    PublisherIEEE
    Pages815-818
    Number of pages4
    Publication statusPublished - 1985

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Electronic, Optical and Magnetic Materials

    Cite this

    Onozawa, A., Inoue, M., Oishi, S., & Horiuchi, K. (1985). REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM. In Proceedings - IEEE International Symposium on Circuits and Systems (pp. 815-818). IEEE.

    REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM. / Onozawa, Akira; Inoue, Masayuki; Oishi, Shinichi; Horiuchi, Kazuo.

    Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, 1985. p. 815-818.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Onozawa, A, Inoue, M, Oishi, S & Horiuchi, K 1985, REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM. in Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, pp. 815-818.
    Onozawa A, Inoue M, Oishi S, Horiuchi K. REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM. In Proceedings - IEEE International Symposium on Circuits and Systems. IEEE. 1985. p. 815-818
    Onozawa, Akira ; Inoue, Masayuki ; Oishi, Shinichi ; Horiuchi, Kazuo. / REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM. Proceedings - IEEE International Symposium on Circuits and Systems. IEEE, 1985. pp. 815-818
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    abstract = "The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.",
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