Several notes on the power of Gomory-Chvátal cuts

Edward A. Hirsch; Arist Kojevnikov

doi:10.1016/j.apal.2005.12.006

Several notes on the power of Gomory-Chvátal cuts

Edward A. Hirsch
, Arist Kojevnikov

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove that the Cutting Plane proof system based on Gomory-Chvátal cuts polynomially simulates the lift-and-project system with integer coefficients written in unary. The restriction on the coefficients can be omitted when using Krajíček's cut-free Gentzen-style extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and with any coefficients).

Original language	English
Pages (from-to)	429-436
Number of pages	8
Journal	Annals of Pure and Applied Logic
Volume	141
Issue number	3
DOIs	https://doi.org/10.1016/j.apal.2005.12.006
State	Published - Sep 2006
Externally published	Yes

Keywords

Integer programming
Propositional proof complexity

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10.1016/j.apal.2005.12.006

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abstract = "We prove that the Cutting Plane proof system based on Gomory-Chv{\'a}tal cuts polynomially simulates the lift-and-project system with integer coefficients written in unary. The restriction on the coefficients can be omitted when using Kraj{\'i}{\v c}ek's cut-free Gentzen-style extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and with any coefficients).",

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AU - Kojevnikov, Arist

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AB - We prove that the Cutting Plane proof system based on Gomory-Chvátal cuts polynomially simulates the lift-and-project system with integer coefficients written in unary. The restriction on the coefficients can be omitted when using Krajíček's cut-free Gentzen-style extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and with any coefficients).

KW - Integer programming

KW - Propositional proof complexity

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 3

ER -

Several notes on the power of Gomory-Chvátal cuts

Abstract

Keywords

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