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)
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
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
A Refutation Approach to Neighborhood Interchangeability in CSPs
AI '08 Proceedings of the 21st Australasian Joint Conference on Artificial Intelligence: Advances in Artificial Intelligence
Encoding Table Constraints in CLP(FD) Based on Pair-Wise AC
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
Type Parametric Compilation of Algebraic Constraints
EPIA '09 Proceedings of the 14th Portuguese Conference on Artificial Intelligence: Progress in Artificial Intelligence
Domain consistency with forbidden values
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A systematic approach to MDD-based constraint programming
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Fast set bounds propagation using a BDD-SAT hybrid
Journal of Artificial Intelligence Research
Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism
Journal of Experimental Algorithmics (JEA)
MDD propagators with explanation
Constraints
Dealing with Satisfiability and n-ary CSPs in a Logical Framework
Journal of Automated Reasoning
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
An automaton Constraint for Local Search
Fundamenta Informaticae - RCRA 2009 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Domain consistency with forbidden values
Constraints
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In many real-life problems, constraints are explicitly defined as a set of solutions. This ad hoc (table) representation uses exponential memory and makes support checking (for enforcing GAC) difficult. In this paper, we address both problems simultaneously by representing an ad hoc constraint with a multi-valued decision diagram (MDD), a memory efficient data structure that supports fast support search. We explain how to convert a table constraint into an MDD constraint and how to maintain GAC on the MDD constraint. Thanks to a sparse set data structure, our MDD-based GAC algorithm, mddc, achieves full incrementality in constant time. Our experiments on structured problems, car sequencing and still-life, show that mddcis a fast GAC algorithm for ad hoc constraints. It can replace a Boolean sequence constraint [1], and scales up well for structural MDD constraints with 208 variables and 340984 nodes. We also show why it is possible for mddcto be faster than the state-of-the-art generic GAC algorithms in [2,3,4]. Its efficiency on non-structural ad hoc constraints is justified empirically.