Matching problems with delta-matroid constraints

Naonori Kakimura, Mizuyo Takamatsu

Research output: Contribution to journalArticle

Abstract

Given an undirected graph G = (V,E) and a delta-matroid (V,F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F. This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-matroid matching problem, where the given delta-matroid is a projection of a linear delta-matroid. We first show that it can be solved in polynomial time if the given linear delta-matroid is generic. This result enlarges a polynomially solvable class of matching problems with precedence constraints on vertices such as the 2-master/slave matching. In addition, we design a polynomial-time algorithm when the graph is bipartite and the delta-matroid is defined on one vertex side. This result is extended to the case where a linear matroid constraint is additionally imposed on the other vertex side.

Original languageEnglish
Pages (from-to)942-961
Number of pages20
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Constrained matching
  • Delta-matroid
  • Mixed matrix theory
  • Polynomial-time algorithm

ASJC Scopus subject areas

  • Mathematics(all)

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