Cutting Planes and the Parameter Cutwidth

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Cutting Planes and the Parameter Cutwidth
We introduce the parameter cutwidth for the Cutting Planes (CP) system of Gomory and Chv´atal. 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, Fψ,n, we provide a classification theorem for CP based on the sum cutwidth plus rank. Specifically, the cutwidth+rank of Fψ,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.
Stefan S. Dantchev, Barnaby Martin
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CIE
Authors Stefan S. Dantchev, Barnaby Martin
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