Go to the corresponding LIPIcs Volume Portal |
Brown-Cohen, Jonah ;
Raghavendra, Prasad
Correlation Decay and Tractability of CSPs
pdf-format:
LIPIcs-ICALP-2016-79.pdf (0.5 MB)
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