On the complexity of cutting-plane proofs

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Abstract

As introduced by Chvátal, cutting planes provide a canonical way of proving that every integral solution of a given system of linear inequalities satisfies another specified inequality. In this note we make several observations on the complexity of such proofs in general and when restricted to proving the unsatisfiability of formulae in the propositional calculus.

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Supported by a grant from the Alexander von Humbolt Stiftung and by the Institut für Ökonometrie und Operations Research of the University of Bonn, W. Germany.

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Supported by the joint research project “Algorithmic Aspects of Combinatorial Optimization” of the Hungarian Academy of Sciences (Magyar Tudományos Akadémia) and the German Research Association (Deutsche Forschungsgemeinschaft) and SFB 303 (DFG).