Matching problems with delta-matroid constraints

Naonori Kakimura, Mizuyo Takamatsu

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

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 languageEnglish
Title of host publicationTheory of Computing 2012 - Proceedings of the Eighteenth Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2012
Pages83-92
Number of pages10
Volume128
Publication statusPublished - 2012
Externally publishedYes
EventTheory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012 - Melbourne, VIC, Australia
Duration: 2012 Jan 312012 Feb 3

Other

OtherTheory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012
CountryAustralia
CityMelbourne, VIC
Period12/1/3112/2/3

Fingerprint

Directed graphs
Polynomials

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

Kakimura, N., & Takamatsu, M. (2012). Matching problems with delta-matroid constraints. In 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.

Theory of Computing 2012 - Proceedings of the Eighteenth Computing: The Australasian Theory Symposium, CATS 2012. Vol. 128 2012. p. 83-92.

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

Kakimura, N & Takamatsu, M 2012, Matching problems with delta-matroid constraints. in 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.
Kakimura N, Takamatsu M. Matching problems with delta-matroid constraints. In Theory of Computing 2012 - Proceedings of the Eighteenth Computing: The Australasian Theory Symposium, CATS 2012. Vol. 128. 2012. p. 83-92
Kakimura, Naonori ; Takamatsu, Mizuyo. / Matching problems with delta-matroid constraints. Theory of Computing 2012 - Proceedings of the Eighteenth Computing: The Australasian Theory Symposium, CATS 2012. Vol. 128 2012. pp. 83-92
@inproceedings{eae6e7a079104d7a866eb4695ae3b18d,
title = "Matching problems with delta-matroid constraints",
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.",
keywords = "Constrained matching, Delta-matroid, Mixed matrix theory, Polynomial-time algorithm",
author = "Naonori Kakimura and Mizuyo Takamatsu",
year = "2012",
language = "English",
isbn = "9781921770098",
volume = "128",
pages = "83--92",
booktitle = "Theory of Computing 2012 - Proceedings of the Eighteenth Computing",

}

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 -