Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
On the hardness of approximate reasoning
Artificial Intelligence
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Algorithms and Complexity Results for #SAT and Bayesian Inference
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
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
Constraint satisfaction with bounded treewidth revisited
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Fast Counting with Bounded Treewidth
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width
Graph-Theoretic Concepts in Computer Science
Belief Revision with Bounded Treewidth
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Volume Computation for Boolean Combination of Linear Arithmetic Constraints
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Algorithms for propositional model counting
Journal of Discrete Algorithms
Constraint satisfaction with bounded treewidth revisited
Journal of Computer and System Sciences
Answer-set programming with bounded treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Tractable database design and datalog abduction through bounded treewidth
Information Systems
Complexity and algorithms for well-structured k-SAT instances
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Tree-width in Algebraic Complexity
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
On the expressive power of CNF formulas of bounded tree- and clique-width
Discrete Applied Mathematics
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We present algorithms for the propositional model counting problem #SAT. The algorithms are based on tree-decompositions of graphs associated with the given CNF formula, in particular primal, dual, and incidence graphs. We describe the algorithms in a coherent fashion that admits a direct comparison of their algorithmic advantages. We analyze and discuss several aspects of the algorithms including worst-case time and space requirements and simplicity of implementation. The algorithms are described in sufficient detail for making an implementation reasonably easy.