Abstract
According to the present state of the theory of the matroid matching problem, the existence of a good characterization to the size of a maximum matching depends on the behavior of certain substructures, called double circuits. In this paper we prove that if a polymatroid has no double circuits at all, then a partition-type min-max formula characterizes the size of a maximum matching. We provide applications of this result to parity constrained orientations and to a rigidity problem.
A polynomial time algorithm is constructed by generalizing the principle of shrinking blossoms used in Edmonds’ matching algorithm [2].
Research is supported by OTKA grants K60802, T037547 and TS049788, by European MCRTN Adonet, Contract Grant No. 504438.
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Makai, M., Pap, G., Szabó, J. (2007). Matching Problems in Polymatroids Without Double Circuits. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_14
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DOI: https://doi.org/10.1007/978-3-540-72792-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72791-0
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