An augmenting path algorithm for linear matroid parity

Linear matroid parity generalizes matroid intersection and graph matching (and hence network flow, degree-constrained subgraphs, etc.). A polynomial algorithm was given by Lovász. This paper presents an algorithm that uses timeO(mn3), wherem is the number of elements andn is the rank. (The time isO(mn2.5) using fast matrix multiplication; both bounds assume the uniform cost model). For graphic matroids the time isO(mn2). The algorithm is based on the method of augmenting paths used in the algorithms for all subcases of the problem.

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