Strengthened Semidefinite Programming Relaxations for the Max-Cut Problem

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Abstract

In this paper we summarize recent results on finding tight semidefinite programming relaxations for the Max-Cut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of Max-Cut and in particular we make no assumptions on the edge weights. We present two strengthenings of the well-known semidefinite programming relaxation of Max-Cut studied by Goemans and Williamson. Preliminary numerical results comparing the relaxations on several interesting instances of Max-Cut are also presented.