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

Akira Onozawa, Masayuki Inoue, Shin'ichi Oishi, Kazuo Horiuchi

Research output: Contribution to journalConference article

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
Pages (from-to)815-818
Number of pages4
JournalProceedings - IEEE International Symposium on Circuits and Systems
Publication statusPublished - 1985 Dec 1

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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