A fast, simpler algorithm for the matroid parity problem

Authors:
James B. Orlin
Affiliations:
MIT Sloan School of Management, Cambridge, MA
Venue:
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Year:
2008

Citing 4
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Abstract

Consider a matrix with m rows and n pairs of columns. The linear matroid parity problem (LMPP) is to determine a maximum number of pairs of columns that are linearly independent. We show how to solve the linear matroid parity problem as a sequence of matroid intersection problems. The algorithm runs in O(m3n). Our algorithm is comparable to the best running time for the LMPP, and is far simpler and faster than the algorithm of Orlin and Vande Vate [10], who also solved the LMPP as a sequence of matroid intersection problems. In addition, the algorithm may be viewed naturally as an extension of the blossom algorithm for nonbipartite matchings.