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### Paper:

TR16-079 | 2nd May 2016 11:07

#### Sum-of-squares hierarchy lower bounds for symmetric formulations

TR16-079
Authors: Adam Kurpisz, Samuli Lepp\"anen, Monaldo Mastrolilli
Publication: 17th May 2016 22:12
Keywords:

Abstract:

We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive semidefiniteness to the analysis of ``well-behaved'' univariate polynomial inequalities.

We illustrate the technique on two problems, one unconstrained and the other with constraints. More precisely, we give a short elementary proof of Grigoriev/Laurent lower bound for finding the integer cut polytope of the complete graph. We also show that the SoS hierarchy requires a non-constant number of rounds to improve the initial integrality gap of 2 for the \textsc{Min-Knapsack} linear program strengthened with cover inequalities.

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