Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Accelerating filtering techniques for numeric CSPs
Artificial Intelligence
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
Solving the Kirkman's Schoolgirl Problem in a Few Seconds
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Cardinal: A Finite Sets Constraint Solver
Constraints
Length-Lex Bounds Consistency for Knapsack Constraints
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Edge Finding for Cumulative Scheduling
INFORMS Journal on Computing
The complexity of global constraints
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Length-lex ordering for set CSPs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Bound consistency for binary length-lex set constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Solving set constraint satisfaction problems using ROBDDs
Journal of Artificial Intelligence Research
Filtering atmost1 on pairs of set variables
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
On decomposing Knapsack constraints for length-lex bounds consistency
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Evaluation of length-lex set variables
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Fast set bounds propagation using a BDD-SAT hybrid
Journal of Artificial Intelligence Research
Boosting set constraint propagation for network design
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Checking and filtering global set constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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Research on constraint propagation has primarily focused on designing polynomial-time propagators sometimes at the cost of a weaker filtering. Interestingly, the evolution of constraint programming over sets have been diametrically different. The domain representations are becoming increasingly expensive computationally and theoretical results appear to question the wisdom of these research directions. This paper explores this apparent contradiction by pursuing even more complexity in the domain representation and the filtering algorithms. It shows that the product of the length-lex and subset-bound domains improves filtering and produces orders of magnitude improvements over existing approaches on standard benchmarks. Moreover, the paper proposes exponential-time algorithms for NP-hard intersection constraints and demonstrates that they bring significant performance improvements and speeds up constraint propagation considerably.