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.ICALP.2016.79
URN: urn:nbn:de:0030-drops-62064
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6206/
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Brown-Cohen, Jonah ; Raghavendra, Prasad

Correlation Decay and Tractability of CSPs

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Abstract

The algebraic dichotomy conjecture of Bulatov, Krokhin and Jeavons yields an elegant characterization of the complexity of constraint satisfaction problems. Roughly speaking, the characterization asserts that a CSP L is tractable if and only if there exist certain non-trivial operations known as polymorphisms to combine solutions to L to create new ones.

In this work, we study the dynamical system associated with repeated applications of a polymorphism to a distribution over assignments. Specifically, we exhibit a correlation decay phenomenon that makes two variables or groups of variables that are not perfectly correlated become independent after repeated applications of a polymorphism.

We show that this correlation decay phenomenon can be utilized in designing algorithms for CSPs by exhibiting two applications:

1. A simple randomized algorithm to solve linear equations over a prime field, whose analysis crucially relies on correlation decay.

2. A sufficient condition for the simple linear programming relaxation for a 2-CSP to be sound (have no integrality gap) on a given instance.

BibTeX - Entry

@InProceedings{browncohen_et_al:LIPIcs:2016:6206,
  author =	{Jonah Brown-Cohen and Prasad Raghavendra},
  title =	{{Correlation Decay and Tractability of CSPs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6206},
  URN =		{urn:nbn:de:0030-drops-62064},
  doi =		{10.4230/LIPIcs.ICALP.2016.79},
  annote =	{Keywords: Constraint Satisfaction, Polymorphisms, Linear Equations, Correlation Decay}
}

Keywords: Constraint Satisfaction, Polymorphisms, Linear Equations, Correlation Decay
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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