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Proving integrality gaps without knowing the linear program. (English) Zbl 1213.68306

Summary: Proving integrality gaps for linear relaxations of NP optimization problems is a difficult task and usually undertaken on a case-by-case basis. We initiate a more systematic approach. We prove an integrality gap of \(2 -o(1)\) for three families of linear relaxations for VERTEX COVER, and our methods seem relevant to other problems as well.

MSC:

68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
90C05 Linear programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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