Abstract
We introduce the reverse Chvátal-Gomory rank r *(P) of an integral polyhedron P, defined as the supremum of the Chvátal-Gomory ranks of all rational polyhedra whose integer hull is P. A well-known example in dimension two shows that there exist integral polytopes P with r *(P) = + ∞. We provide a geometric characterization of polyhedra with this property in general dimension, and investigate upper bounds on r *(P) when this value is finite. We also sketch possible extensions, in particular to the reverse split rank.
This work was supported by the Progetto di Eccellenza 2008–2009 of the Fondazione Cassa di Risparmio di Padova e Rovigo.
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Conforti, M., Del Pia, A., Di Summa, M., Faenza, Y., Grappe, R. (2013). Reverse Chvátal-Gomory Rank. In: Goemans, M., Correa, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36694-9_12
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DOI: https://doi.org/10.1007/978-3-642-36694-9_12
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