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arXiv · 2108.01038

The SDP value of random 2CSPs

Amulya Musipatla·Ryan O'Donnell·Tselil Schramm·Xinyu Wu
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Abstract

We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over~$\{\pm 1\}^n$. For each model $\mathcal{M}$, we identify the "high-probability value"~$s^*_{\mathcal{M}}$ of the natural SDP relaxation (equivalently, the quantum value). That is, for all $\varepsilon > 0$ we show that the SDP optimum of a random $n$-variable instance is (when normalized by~$n$) in the range $(s^*_{\mathcal{M}}-\varepsilon, s^*_{\mathcal{M}}+\varepsilon)$ 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.

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Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, Xinyu Wu. 2021-08-02. The SDP value of random 2CSPs. https://arxiv.org/abs/2108.01038

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