Matchings, hypergraphs, association schemes, and semidefinite optimization

08/19/2020

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by   Yu Hin Au, et al.

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We utilize association schemes to analyze the quality of semidefinite programming (SDP) based convex relaxations of integral packing and covering polyhedra determined by matchings in hypergraphs. As a by-product of our approach, we obtain bounds on the clique and stability numbers of some regular graphs reminiscent of classical bounds by Delsarte and Hoffman. We determine exactly or provide bounds on the performance of Lovász-Schrijver SDP hierarchy, and illustrate the usefulness of obtaining commutative subschemes from non-commutative schemes via contraction in this context.