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Approximate fixed-rank closures of covering problems

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Abstract

Consider a 0/1 integer program min{c T x :Ax≥b, x ∈ {0,1}n} where A is nonnegative. We show that if the number of minimal covers of Ax≥b is polynomially bounded, then for any ε>0 and any fixed q, there is a polynomially large lift-and-project relaxation whose value is at least (1−ε) times the value of the rank ≤q relaxation. A special case of this result is that given by set-covering problems, or, generally, problems where the coefficients in A and b are bounded.

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Authors and Affiliations

  1. Department of IEOR, Columbia University, 500W, 120th St., New York, NY, 10027, USA

    Daniel Bienstock & Mark Zuckerberg

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  1. Daniel Bienstock
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  2. Mark Zuckerberg
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Correspondence to Daniel Bienstock.

Additional information

This research was partially funded by NSF awards ITR:CCR-0213848 and DMI-0200221

formerly: Set covering problems and Chvátal-Gomory cuts

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Bienstock, D., Zuckerberg, M. Approximate fixed-rank closures of covering problems. Math. Program. 105, 9–27 (2006). https://doi.org/10.1007/s10107-005-0598-z

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  • DOI: https://doi.org/10.1007/s10107-005-0598-z

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