文章基本信息

标题：Tractable Constraint Satisfaction Problems on a 3-element set
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作者：Andrei Bulatov
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2002
卷号：2002
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：The Constraint Satisfaction Problem (CSP) provides a common framework for many combinatorial problems. The general CSP is known to be NP-complete; however, certain restrictions on a possible form of constraints may affect the complexity, and lead to tractable problem classes. There is, therefore, a fundamental research direction, aiming to separate those subclasses of the CSP which are tractable, and those which remain NP-complete. Schaefer gave an exhaustive solution of this problem for the CSP on a 2-element domain. In this paper we generalise this result to a classification of the complexity of CSPs on a 3-element domain. The main result states that every subclass of the CSP is either tractable and the criterion separating them is that conjectured earlier. We also exhibit a polynomial time algorithm which, for a given set of allowed constraints, outputs if this set gives rise to a tractable problem class. To obtain the main result and the algorithm we extensively use the algebraic technique for the CSP developed by Jeavons and coauthors.
关键词：algebra , complexity , constraint satisfaction problem