Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
An introduction to variational methods for graphical models
Learning in graphical models
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Using expectation maximization to find likely assignments for solving CSP's
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Backbone fragility and the local search cost peak
Journal of Artificial Intelligence Research
A backbone-search heuristic for efficient solving of hard 3-SAT formulae
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Iterative join-graph propagation
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
VARSAT: Integrating Novel Probabilistic Inference Techniques with DPLL Search
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
On Computing Backbones of Propositional Theories
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Reasoning over biological networks using maximum satisfiability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
On the interpolation between product-based message passing heuristics for SAT
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Algorithm runtime prediction: Methods & evaluation
Artificial Intelligence
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Backbone variables have the same assignment in all solutions to a given constraint satisfaction problem; more generally, biasrepresents the proportion of solutions that assign a variable a particular value. Intuitively such constructs would seem important to efficient search, but their study to date has been from a mostly conceptual perspective, in terms of indicating problem hardness or motivating and interpreting heuristics. Here we summarize a two-phase project where we first measure the ability of both existing and novel probabilistic message-passing techniques to directly estimate bias and identify backbones for the Boolean Satisfiability (SAT) Problem. We confirm that methods like Belief Propagation and Survey Propagation---plus Expectation Maximization-based variants---do produce good estimates with distinctive properties. The second phase demonstrates the use of bias estimation within a modern SAT solver, exhibiting a correlation between accurate, stable, estimates and successful backtracking search. The same process also yields a family of search heuristics that can dramatically improve search efficiency for the hard random problems considered.