An augmenting path algorithm for linear matroid parity
Combinatorica
Greedy algorithm and symmetric matroids
Mathematical Programming: Series A and B
Discrete Mathematics
Solving the linear matroid parity problem as a sequence of matroid intersection problems
Mathematical Programming: Series A and B
Delta-Matroids, Jump Systems, and Bisubmodular Polyhedra
SIAM Journal on Discrete Mathematics
Alternating cycles and paths in edge-coloured multigraphs: a survey
Proceedings of an international symposium on Graphs and combinatorics
A Min-Max Theorem for a Constrained Matching Problem
SIAM Journal on Discrete Mathematics
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
The linear delta-matroid parity problem
Journal of Combinatorial Theory Series B
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
Polynomial-Time Algorithms for Linear and Convex Optimization on Jump Systems
SIAM Journal on Discrete Mathematics
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Optimal matching forests and valuated delta-matroids
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
On tree-constrained matchings and generalizations
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A constrained independent set problem for matroids
Operations Research Letters
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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) ε 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.