### Abstract

Given an undirected graph G = (V, E) and a directed graph D = (V, A), the master/slave matching problem is to find a matching of maximum cardinality in G such that for each arc (u; v) ∈ A with u being matched, v is also matched. This problem is known to be NP-hard in general, but polynomially solvable in a special case where the maximum size of a connected component of D is at most two. This paper investigates the master/slave matching problem in terms of delta-matroids, which is a generalization of matroids. We first observe that the above polynomially solvable constraint can be interpreted as delta-matroids. We then introduce a new class of matching problem with delta-matroid constraints, which can be solved in polynomial time. In addition, we discuss our problem with additional constraints such as capacity constraints.

Original language | English |
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Title of host publication | Theory of Computing 2012 - Proceedings of the Eighteenth Computing |

Subtitle of host publication | The Australasian Theory Symposium, CATS 2012 |

Pages | 83-92 |

Number of pages | 10 |

Volume | 128 |

Publication status | Published - 2012 |

Externally published | Yes |

Event | Theory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012 - Melbourne, VIC, Australia Duration: 2012 Jan 31 → 2012 Feb 3 |

### Other

Other | Theory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012 |
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Country | Australia |

City | Melbourne, VIC |

Period | 12/1/31 → 12/2/3 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications
- Hardware and Architecture
- Information Systems
- Software

### Cite this

*Theory of Computing 2012 - Proceedings of the Eighteenth Computing: The Australasian Theory Symposium, CATS 2012*(Vol. 128, pp. 83-92)

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Theory of Computing 2012 - Proceedings of the Eighteenth Computing: The Australasian Theory Symposium, CATS 2012.*vol. 128, pp. 83-92, Theory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012, Melbourne, VIC, Australia, 12/1/31.

}

TY - GEN

T1 - Matching problems with delta-matroid constraints

AU - Kakimura, Naonori

AU - Takamatsu, Mizuyo

PY - 2012

Y1 - 2012

N2 - Given an undirected graph G = (V, E) and a directed graph D = (V, A), the master/slave matching problem is to find a matching of maximum cardinality in G such that for each arc (u; v) ∈ A with u being matched, v is also matched. This problem is known to be NP-hard in general, but polynomially solvable in a special case where the maximum size of a connected component of D is at most two. This paper investigates the master/slave matching problem in terms of delta-matroids, which is a generalization of matroids. We first observe that the above polynomially solvable constraint can be interpreted as delta-matroids. We then introduce a new class of matching problem with delta-matroid constraints, which can be solved in polynomial time. In addition, we discuss our problem with additional constraints such as capacity constraints.

AB - Given an undirected graph G = (V, E) and a directed graph D = (V, A), the master/slave matching problem is to find a matching of maximum cardinality in G such that for each arc (u; v) ∈ A with u being matched, v is also matched. This problem is known to be NP-hard in general, but polynomially solvable in a special case where the maximum size of a connected component of D is at most two. This paper investigates the master/slave matching problem in terms of delta-matroids, which is a generalization of matroids. We first observe that the above polynomially solvable constraint can be interpreted as delta-matroids. We then introduce a new class of matching problem with delta-matroid constraints, which can be solved in polynomial time. In addition, we discuss our problem with additional constraints such as capacity constraints.

KW - Constrained matching

KW - Delta-matroid

KW - Mixed matrix theory

KW - Polynomial-time algorithm

UR - http://www.scopus.com/inward/record.url?scp=84863993737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863993737&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84863993737

SN - 9781921770098

VL - 128

SP - 83

EP - 92

BT - Theory of Computing 2012 - Proceedings of the Eighteenth Computing

ER -