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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.79
URN: urn:nbn:de:0030-drops-62064
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6206/
Brown-Cohen, Jonah ;
Raghavendra, Prasad
Correlation Decay and Tractability of CSPs
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: |
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Constraint Satisfaction, Polymorphisms, Linear Equations, Correlation Decay |
Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
Issue Date: |
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2016 |
Date of publication: |
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23.08.2016 |