Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Using OBDDs to handle dynamic constraints
Information Processing Letters
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Checking satisfiability of a conjunction of BDDs
Proceedings of the 40th annual Design Automation Conference
Maintaining Generalized Arc Consistency on Ad-hoc n-ary Boolean Constraints
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A hybrid BDD and SAT finite domain constraint solver
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
Fast Set Bounds Propagation using BDDs
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Fast set bounds propagation using a BDD-SAT hybrid
Journal of Artificial Intelligence Research
MDD propagators with explanation
Constraints
Lazy explanations for constraint propagators
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
Explaining propagators for s-DNNF circuits
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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When BDDs are used for propagation in a constraint solver with nogood recording, it is necessary to find a small subset of a given set of variable assignments that is enough for a BDD to imply a new variable assignment. We show that the task of finding such a minimum subset is NP-complete by reduction from the hitting set problem. We present a new algorithm for finding such a minimal subset, which runs in time linear in the size of the BDD representation. In our experiments, the new method is up to ten times faster than the previous method, thereby reducing the solution time by even more than 80%. Due to linear time complexity the new method is able to scale well.