A fast, simpler algorithm for the matroid parity problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
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The matroid parity problem is a generalization of matroid intersection and general graph matching (and hence network flow, degree-constrained subgraphs, etc.). A polynomial algorithm for linear matroids was presented by Lovasz. This paper presents an algorithm that uses time 0(mn/sup 3/), where m is the number of elements and n is the rank; for the spanning tree parity problem the time 0(mn/sup 2/). The algorithm is based on the method of augmenting paths used in the algorithms for all subcases of the problem.