License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.49
URN: urn:nbn:de:0030-drops-101420
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10142/
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Kothari, Pravesh K. ; O'Donnell, Ryan ; Schramm, Tselil

SOS Lower Bounds with Hard Constraints: Think Global, Act Local

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Abstract

Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a "cardinality constraint", as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value beta, it did not necessarily actually "satisfy" the constraint "objective = beta". In this paper we show how to remedy both deficiencies in the case of random CSPs, by translating global constraints into local constraints. Using these ideas, we also show that degree-Omega(sqrt{n}) SOS does not provide a (4/3 - epsilon)-approximation for Min-Bisection, and degree-Omega(n) SOS does not provide a (11/12 + epsilon)-approximation for Max-Bisection or a (5/4 - epsilon)-approximation for Min-Bisection. No prior SOS lower bounds for these problems were known.

BibTeX - Entry

@InProceedings{kothari_et_al:LIPIcs:2018:10142,
  author =	{Pravesh K. Kothari and Ryan O'Donnell and Tselil Schramm},
  title =	{{SOS Lower Bounds with Hard Constraints: Think Global, Act Local}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{49:1--49:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10142},
  URN =		{urn:nbn:de:0030-drops-101420},
  doi =		{10.4230/LIPIcs.ITCS.2019.49},
  annote =	{Keywords: sum-of-squares hierarchy, random constraint satisfaction problems}
}

Keywords: sum-of-squares hierarchy, random constraint satisfaction problems
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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