Cutting planes and the parameter cutwidth

Dantchev, Stefan and Martin, Barnaby (2011) Cutting planes and the parameter cutwidth. Theory of Computing Systems, 51 (1) . pp. 50-64. ISSN 1432-4350 (doi:10.1007/s00224-011-9373-0)

Abstract

We introduce the parameter cutwidth for the Cutting Planes (CP) system of Gomory and Chvátal. We provide linear lower bounds on cutwidth for two simple polytopes. Considering CP as a propositional refutation system, one can see that the cutwidth of a CNF contradiction F is always bound above by the Resolution width of F. We provide an example proving that the converse fails: there is an F which has constant cutwidth, but has Resolution width Ω(n). Following a standard method for converting an FO sentence ψ, without finite models, into a sequence of CNFs, F ψ,n , we provide a classification theorem for CP based on the sum cutwidth plus rank. Specifically, the cutwidth + rank of F ψ,n is bound by a constant c (depending on ψ only) if ψ has no (infinite) models. This result may be seen as a relative of various gap theorems extant in the literature.

Item Type: Article
Research Areas: A. > School of Science and Technology > Computer Science
A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 9641
Depositing User: Devika Mohan
Date Deposited: 20 Dec 2012 10:39
Last Modified: 24 Apr 2018 13:28
URI: https://eprints.mdx.ac.uk/id/eprint/9641

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