Lower bounds for the Chvátal-Gomory rank in the 0/1 cube

Authors:
Sebastian Pokutta;Gautier Stauffer
Affiliations:
Department of Mathematics, Friedrich-Alexander-University of Erlangen-Nürnberg, Am Weichselgarten 9, 91058 Erlangen, Germany;Institute of Mathematics, University of Bordeaux 1, 351, Cours de la Liberation, 33405 Talence, France
Venue:
Operations Research Letters
Year:
2011

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Abstract

We revisit the method of Chvatal, Cook, and Hartmann to establish lower bounds on the Chvatal-Gomory rank, and develop a simpler method. We provide new families of polytopes in the 0/1 cube with high rank, and we describe a deterministic family achieving a rank of at least (1+1/e)n-1n. Finally, we show how integrality gaps lead to lower bounds.