The SDP Value of Random 2CSPs

Authors Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, Xinyu Wu

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Amulya Musipatla
  • Carnegie Mellon University, Pittsburgh, PA, USA
Ryan O'Donnell
  • Carnegie Mellon University, Pittsburgh, PA, USA
Tselil Schramm
  • Stanford University, CA, USA
Xinyu Wu
  • Carnegie Mellon University, Pittsburgh, PA, USA

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Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu. The SDP Value of Random 2CSPs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 97:1-97:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

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ACM Subject Classification
  • Theory of computation → Random network models
  • Theory of computation → Approximation algorithms analysis
  • Random constraint satisfaction problems


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