Abstract
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(mn 3), wherem is the number of elements andn is the rank. (The time isO(mn 2.5) using fast matrix multiplication; both bounds assume the uniform cost model). For graphic matroids the time isO(mn 2). The algorithm is based on the method of augmenting paths used in the algorithms for all subcases of the problem.
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First author was supported in part by the National Science Foundation under grants MCS 78-18909, MCS-8302648, and DCR-8511991. The research was done while the second author was at the University of Denver and at the University of Colorado at Boulder.