Abstract
This paper presents a generic scheme for fractional packing in ideal clutters. Consider an ideal clutter with a nonnegative capacity function on its vertices. It follows from ideality that for any nonnegative capacity the total multiplicity of an optimal fractional packing is equal to the minimum capacity of a vertex cover. Our scheme finds an optimal packing using at most n edges with positive multiplicities, performing minimization for the clutter at most n times and minimization for its blocker at most n 2 times, where n denotes the cardinality of the vertex set. Applied to the clutter of dijoins (directed cut covers), the scheme provides the first combinatorial polynomial-time algorithm for fractional packing of dijoins.
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Preliminary version of this paper appeared in Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2007, pp. 1181–1186.
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Matsuoka, Y. Fractional packing in ideal clutters. Math. Program. 133, 159–169 (2012). https://doi.org/10.1007/s10107-010-0410-6
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DOI: https://doi.org/10.1007/s10107-010-0410-6