A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
Syntactic Characterization of Tree Database Schemas
Journal of the ACM (JACM)
Conjunctive query containment revisited
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
Encyclopedia of Artificial Intelligence
Encyclopedia of Artificial Intelligence
Theoretical Computer Science
Binary vs. non-binary constraints
Artificial Intelligence
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Generalized hypertree decompositions: np-hardness and tractable variants
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Approximating fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A new method for solving constraint satisfaction problems
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
Constraint satisfaction with bounded treewidth revisited
Journal of Computer and System Sciences
Parameterized Complexity
On the complexity of core, kernel, and bargaining set
Artificial Intelligence
Large hinge width on sparse random hypergraphs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
Parameterized complexity results for exact bayesian network structure learning
Journal of Artificial Intelligence Research
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The Constraint Satisfaction Problem (CSP) is a central issue of research in Artificial Intelligence. Due to its intractability, many efforts have been made in order to identify tractable classes of CSP instances, and in fact deep and useful results have already been achieved. In particular, this paper focuses on structural decomposition methods, which are essentially meant to look for near-acyclicity properties of the graphs or hypergraphs that encode the structure of the constraints interactions. In general, constraint scopes comprise an arbitrary number of variables, and thus this structure may be naturally encoded via hypergraphs. However, in many practical applications, decomposition methods are applied over suitable graph representations of the (possibly non-binary) CSP instances at hand. Despite the great interest in such binary approaches, a formal analysis of their power, in terms of their ability of identifying islands of tractability, was missing in the literature. The aim of this paper is precisely to fill this gap, by studying the relationships among binary structural methods, and by providing a clear picture of the tractable fragments of CSP that can be specified with respect to each of these decomposition approaches, when they are applied to binary representations of non-binary CSP instances. In particular, various long-standing questions about primal, dual and incidence graph encodings are answered. The picture is then completed by comparing methods on binary encodings with methods specifically conceived for non-binary constraints.