Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, February 09, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Stefan Weltge (IFOR)

Polytopes in the 0/1-Cube with Bounded Chvátal-Gomory Rank

The Chvátal-Gomory procedure is a classical proof technique to obtain valid linear inequalities for a set of integer points S, where the input is a description (by means of linear inequalities) of any polytope R whose set of integer points is S. In this work, we focus on the natural case where S is contained in \{0,1\}^n and R is contained in [0,1]^n. We prove that R has bounded CG-rank provided that S has bounded pitch and bounded gap, where the pitch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the facet coefficients of conv(S). Furthermore, we illustrate how our result generalizes a recent theorem of Cornuéjols and Lee (IPCO 2016). This is joint work with Yohann Benchetrit, Samuel Fiorini and Tony Huynh.

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