TY - GEN

T1 - Matching problems with delta-matroid constraints

AU - Kakimura, Naonori

AU - Takamatsu, Mizuyo

PY - 2012/7/24

Y1 - 2012/7/24

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

T3 - Conferences in Research and Practice in Information Technology Series

SP - 83

EP - 92

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

T2 - Theory of Computing 2012 - 18th Computing: The Australasian Theory Symposium, CATS 2012

Y2 - 31 January 2012 through 3 February 2012

ER -