A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
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Artificial Intelligence
A comparison of structural CSP decomposition methods
Artificial Intelligence
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
Constraint Processing
Reducing Redundancy in the Hypertree Decomposition Scheme
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Treewidth: A Useful Marker of Empirical Hardness in Quantified Boolean Logic Encodings
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Uniform Constraint Satisfaction Problems and Database Theory
Complexity of Constraints
Tree Projections: Game Characterization and Computational Aspects
Graph Theory, Computational Intelligence and Thought
An Empirical Study of QBF Encodings: from Treewidth Estimation to Useful Preprocessing
Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Theoretical Computer Science
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Hypertree decomposition has been shown to be the most general CSP decomposition method. However, so far the exact methods are not able to find optimal hypertree decompositions of realistic instances. We present a backtracking procedure which, along with isomorphic component detection, results in optimal hypertree decompositions. We also make the procedure generic; variations of which results in two new tractable decompositions: hyperspread and connected hypertree. We show that the hyperspread width is bounded by both the hypertree width and the spread cut width, which solves a recently stated open problem. In our experiments on several realistic instances, our methods find many optimal decompositions, while the previous methods can find at most one.