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Packing in generalized kernel systems: a framework that generalizes packing of branchings

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Abstract

We study a framework, which we call a generalized kernel system, introduced by Frank. We prove some integral and fractional packing theorems in this framework which, in particular, imply an improvement over the best known upper bounds on the size of the packing, one due to Gabow and Manu, for packing arborescences from a given root, and another, due to Schrijver, for packing branchings from given root-sets in a digraph.

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Acknowledgments

We thank the referees for suggestions that improved the presentation of this paper. We also thank the partial support received from CNPq (Proc. 551561/2009-2, Proc. 303987/2010-3).

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  1. Department of Computer Science, University of São Paulo, São Paulo, Brazil

    Mario Leston-Rey & Yoshiko Wakabayashi

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  1. Mario Leston-Rey
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  2. Yoshiko Wakabayashi
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Correspondence to Mario Leston-Rey.

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Leston-Rey, M., Wakabayashi, Y. Packing in generalized kernel systems: a framework that generalizes packing of branchings. Math. Program. 149, 209–251 (2015). https://doi.org/10.1007/s10107-014-0746-4

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  • DOI: https://doi.org/10.1007/s10107-014-0746-4

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