Ideal clutters that do not pack

Abdi, Ahmad ORCID: 0000-0002-3008-4167, Pashkovich, Kanstantsin and Cornuéjols, Gérard (2018) Ideal clutters that do not pack. Mathematics of Operations Research, 43 (2). pp. 533-553. ISSN 0364-765X

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Abstract

For a clutter over ground set E, a pair of distinct elements e, f ∈ E are coexclusive if every minimal cover contains at most one of them. An identification of is another clutter obtained after identifying coexclusive elements of . If a clutter is nonpacking, then so is any identification of it. Inspired by this observation, and impelled by the lack of a qualitative characterization for ideal minimally nonpacking (mnp) clutters, we reduce ideal mnp clutters even further by taking their identifications. In doing so, we reveal chains of ideal mnp clutters, demonstrate the centrality of mnp clutters with covering number two, as well as provide a qualitative characterization of irreducible ideal mnp clutters with covering number two. At the core of this characterization lies a class of objects, called marginal cuboids, that naturally give rise to ideal nonpacking clutters with covering number two. We present an explicit class of marginal cuboids, and show that the corresponding clutters have one of Q 6 , Q 2, 1 , Q 10 as a minor, where Q 6 , Q 2, 1 are known ideal mnp clutters, and Q 10 is a new ideal mnp clutter.

Item Type:	Article
Official URL:	https://pubsonline.informs.org/journal/moor
Additional Information:	© 2017 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	30 Oct 2019 14:51
Last Modified:	15 Nov 2024 00:42
URI:	http://eprints.lse.ac.uk/id/eprint/101837

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