License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.97
URN: urn:nbn:de:0030-drops-164381
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Musipatla, Amulya ; O'Donnell, Ryan ; Schramm, Tselil ; Wu, Xinyu

The SDP Value of Random 2CSPs

LIPIcs-ICALP-2022-97.pdf (0.8 MB)


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.

BibTeX - Entry

  author =	{Musipatla, Amulya and O'Donnell, Ryan and Schramm, Tselil and Wu, Xinyu},
  title =	{{The SDP Value of Random 2CSPs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{97:1--97:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-164381},
  doi =		{10.4230/LIPIcs.ICALP.2022.97},
  annote =	{Keywords: Random constraint satisfaction problems}

Keywords: Random constraint satisfaction problems
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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