Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Decomposable negation normal form
Journal of the ACM (JACM)
Using Recursive Decomposition to Construct Elimination Orders, Jointrees, and Dtrees
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Constraint Processing
Theory of Relational Databases
Theory of Relational Databases
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Management of probabilistic data: foundations and challenges
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Visualizing SAT Instances and Runs of the DPLL Algorithm
Journal of Automated Reasoning
The boundary between privacy and utility in data publishing
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
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Many reasoning problems in logic and constraint satisfaction have been shown to be exponential only in the treewidth of their interaction graph: a graph which captures the structural interactions among variables in a problem. It has long been observed in both logic and constraint satisfaction, however, that problems may be easy even when their treewidth is quite high. To bridge some of the gap between theoretical bounds and actual runtime, we propose a complexity parameter, called functional treewidth, which refines treewidth by being sensitive to non–structural aspects of a problem: functional dependencies in particular. This measure dominates treewidth and can be used to bound the size of CNF compilations, which permit a variety of queries in polytime, including clausal implication, existential quantification, and model counting. We present empirical results which show how the new measure can predict the complexity of certain benchmarks, that would have been considered quite difficult based on treewidth alone.