Sum-of-squares rank upper bounds for matching problems

Adam Kurpisz (), Samuli Leppänen () and Monaldo Mastrolilli ()
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Adam Kurpisz: IDSIA
Samuli Leppänen: IDSIA
Monaldo Mastrolilli: IDSIA

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 8, 844 pages

Abstract: Abstract The matching problem is one of the most studied combinatorial optimization problems in the context of extended formulations and convex relaxations. In this paper we provide upper bounds for the rank of the sum-of-squares/Lasserre hierarchy for a family of matching problems. In particular, we show that when the problem formulation is strengthened by incorporating the objective function in the constraints, the hierarchy requires at most $$\left\lceil \frac{k}{2} \right\rceil $$ k 2 levels to refute the existence of a perfect matching in an odd clique of size $$2k+1$$ 2 k + 1 .

Keywords: Sum-of-squares hierarchy; Integrality gap; Matching problem; 90C05; 90C22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0169-2

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