Principles of artificial intelligence
Principles of artificial intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Counting the number of solutions for instances of satisfiability
Theoretical Computer Science
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
On the hardness of approximate reasoning
Artificial Intelligence
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Backtrack programming techniques
Communications of the ACM
A machine program for theorem-proving
Communications of the ACM
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Introduction to Algorithms
Resolution versus Search: Two Strategies for SAT
Journal of Automated Reasoning
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Satisfiability, Branch-Width and Tseitin Tautologies
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Algorithms and Complexity Results for #SAT and Bayesian Inference
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Guiding Real-World SAT Solving with Dynamic Hypergraph Separator Decomposition
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Mixtures of deterministic-probabilistic networks and their AND/OR search space
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Unifying tree decompositions for reasoning in graphical models
Artificial Intelligence
AND/OR search spaces for graphical models
Artificial Intelligence
On probabilistic inference by weighted model counting
Artificial Intelligence
Dynamic Orderings for AND/OR Branch-and-Bound Search in Graphical Models
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Performing incremental Bayesian inference by dynamic model counting
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Using more reasoning to improve #SAT solving
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Best-first AND/OR search for graphical models
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Clause learning can effectively P-simulate general propositional resolution
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Exploiting causal independence using weighted model counting
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The good old Davis-Putnam procedure helps counting models
Journal of Artificial Intelligence Research
A dynamic approach to MPE and weighted MAX-SAT
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On the space-time trade-off in solving constraint satisfaction problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Compiling relational Bayesian networks for exact inference
International Journal of Approximate Reasoning
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Heuristics for fast exact model counting
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Encoding CNFs to empower component analysis
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
sharpSAT: counting models with advanced component caching and implicit BCP
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Exploiting decomposition on constraint problems with high tree-width
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Using sums-of-products for non-standard reasoning
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Inference in Bayes Nets (BAYES) is an important problem with numerous applications in probabilistic reasoning. Counting the number of satisfying assignments of a propositional formula (#SAT) is a closely related problem of fundamental theoretical importance. Both these problems, and others, are members of the class of sum-of-products (SUMPROD) problems. In this paper we show that standard backtracking search when augmented with a simple memoization scheme (caching) can solve any sum-of-products problem with time complexity that is at least as good any other state-of-the-art exact algorithm, and that it can also achieve the best known time-space tradeoff. Furthermore, backtracking's ability to utilize more flexible variable orderings allows us to prove that it can achieve an exponential speedup over other standard algorithms for SUMPROD on some instances. The ideas presented here have been utilized in a number of solvers that have been applied to various types of sum-of-product problem's. These system's have exploited the fact that backtracking can naturally exploit more of the problem's structure to achieve improved performance on a range of problem instances. Empirical evidence of this performance gain has appeared in published works describing these solvers, and we provide references to these works.