Matching problems with delta-matroid constraints

Naonori Kakimura, Mizuyo Takamatsu

研究成果: Article

抄録

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.

元の言語English
ページ(範囲)942-961
ページ数20
ジャーナルSIAM Journal on Discrete Mathematics
28
発行部数2
DOI
出版物ステータスPublished - 2014
外部発表Yes

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Matching Problem
Matroid
Polynomial time
Precedence Constraints
Vertex of a graph
Undirected Graph
Polynomial-time Algorithm
Cardinality
Projection

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

Matching problems with delta-matroid constraints. / Kakimura, Naonori; Takamatsu, Mizuyo.

:: SIAM Journal on Discrete Mathematics, 巻 28, 番号 2, 2014, p. 942-961.

研究成果: Article

Kakimura, Naonori ; Takamatsu, Mizuyo. / Matching problems with delta-matroid constraints. :: SIAM Journal on Discrete Mathematics. 2014 ; 巻 28, 番号 2. pp. 942-961.
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