The SDP value of random 2CSPs

08/02/2021

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by   Amulya Musipatla, et al.

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We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over {± 1}^n. For each model ℳ, we identify the "high-probability value" s^*_ℳ of the natural SDP relaxation (equivalently, the quantum value). That is, for all ε > 0 we show that the SDP optimum of a random n-variable instance is (when normalized by n) in the range (s^*_ℳ-ε, s^*_ℳ+ε) with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.