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标题：Correlation Decay and Tractability of CSPs
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作者：Jonah Brown-Cohen ; Prasad Raghavendra
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：55
页码：79:1-79:13
DOI：10.4230/LIPIcs.ICALP.2016.79
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Constraint Satisfaction; Polymorphisms; Linear Equations; Correlation Decay