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Clean clutters and dyadic fractional packings

Abdi, Ahmad ORCID: 0000-0002-3008-4167, Cornuéjols, Gérard, Guenin, Bertrand and Tunçel, Levent (2022) Clean clutters and dyadic fractional packings. SIAM Journal on Discrete Mathematics. ISSN 0895-4801

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A vector is dyadic if each of its entries is a dyadic rational number, i.e., an integer multiple of 1 2k for some nonnegative integer k. We prove that every clean clutter with a covering number of at least two has a dyadic fractional packing of value two. This result is best possible for there exist clean clutters with a covering number of three and no dyadic fractional packing of value three. Examples of clean clutters include ideal clutters, binary clutters, and clutters without an intersecting minor. Our proof is constructive and leads naturally to an albeit exponential algorithm. We improve the running time to quasi-polynomial in the rank of the input, and to polynomial in the binary case

Item Type: Article
Additional Information: © 2022 Ahmad Abdi
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 21 Dec 2021 14:24
Last Modified: 15 Sep 2023 16:59

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