High Degree Sum of Squares Proofs, Bienstock-Zuckerberg Hierarchy and CG Cuts

  • Monaldo MastrolilliEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)


Chvátal-Gomory (CG) cuts captures useful and efficient linear programs that the bounded degree Lasserre/Sum-of-Squares (\({\textsc {sos}}\)) hierarchy fails to capture. We present an augmented version of the \({\textsc {sos}}\) hierarchy for 0/1 integer problems that implies the Bienstock-Zuckerberg hierarchy by using high degree polynomials (when expressed in the standard monomial basis). It follows that for a class of polytopes (e.g. set covering and packing problems), the \({\textsc {sos}}\) approach can optimize, up to an arbitrarily small error, over the polytope resulting from any constant rounds of CG cuts in polynomial time.


Packing Problem Valid Inequality Symmetric Polynomial Invariant Polynomial High Degree Polynomial 
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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IDSIAMannoSwitzerland

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