Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
An efficient representation for sparse sets
ACM Letters on Programming Languages and Systems (LOPLAS)
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Enforcing Arc Consistency on Global Constraints by Solving Subproblems on the Fly
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Partition search for non-binary constraint satisfaction
Information Sciences: an International Journal
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 fast arc consistency algorithm for n-ary constraints
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Data structures for generalised arc consistency for extensional constraints
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
A simple model to generate hard satisfiable instances
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
An optimal coarse-grained arc consistency algorithm
Artificial Intelligence
A compression algorithm for large arity extensional constraints
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Generalized arc consistency for positive table constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Revisiting the sequence constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Generating special-purpose stateless propagators for arbitrary constraints
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism
Journal of Experimental Algorithmics (JEA)
Space-Time tradeoffs for the regular constraint
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
An optimal filtering algorithm for table constraints
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Domain consistency with forbidden values
Constraints
Short and long supports for constraint propagation
Journal of Artificial Intelligence Research
Extending simple tabular reduction with short supports
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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A table constraint is explicitly represented as its set of solutions or non-solutions. This ad hoc (or extensional) representation may require space exponential to the arity of the constraint, making enforcing GAC expensive. In this paper, we address the space and time inefficiencies simultaneously by presenting the mddc constraint. mddc is a global constraint that represents its (non-)solutions with a multi-valued decision diagram (MDD). The MDD-based representation has the advantage that it can be exponentially smaller than a table. The associated GAC algorithm (called mddc) has time complexity linear to the size of the MDD, and achieves full incrementality in constant time. In addition, we show how to convert a positive or negative table constraint into an mddc constraint in time linear to the size of the table. Our experiments on structured problems, car sequencing and still-life, show that mddc is also a fast GAC algorithm for some global constraints such as sequence and regular. We also show that mddc is faster than the state-of-the-art generic GAC algorithms in Gent et al. (2007), Lecoutre and Szymanek (2006), Lhomme and Régin (2005) for table constraint.