Cutting Planes and the Parameter Cutwidth

Dantchev, Stefan; Martin, Barnaby

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) iff ψ has no (infinite) models. This result may be seen as a relative of various gap theorems extant in the literature.

Citation

Dantchev, S., & Martin, B. (2012). Cutting Planes and the Parameter Cutwidth. Theory of Computing Systems, 51(1), 50-64. https://doi.org/10.1007/s00224-011-9373-0

• Journal Article Type: Article
• Publication Date: 2012-07
• Deposit Date: Dec 15, 2009
• Journal: Theory of Computing Systems
• Print ISSN: 1432-4350
• Electronic ISSN: 1433-0490
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 1
• Pages: 50-64
• DOI: https://doi.org/10.1007/s00224-011-9373-0
• Public URL: https://durham-repository.worktribe.com/output/1524210