Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
Global Constraints for Lexicographic Orderings
CP '02 Proceedings of the 8th 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
Solving set constraint satisfaction problems using ROBDDs
Journal of Artificial Intelligence Research
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The "Not-Too-Heavy Spanning Tree" Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Length-Lex Bounds Consistency for Knapsack Constraints
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Length-lex bound consistency for knapsack constraints
Proceedings of the 2009 ACM symposium on Applied Computing
Bound consistency for binary length-lex set constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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
Exponential propagation for set variables
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
Constraint reasoning and Kernel clustering for pattern decomposition with scaling
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Checking and filtering global set constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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
Extending the TOY system with the ECLiPSe solver over sets of integers
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
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Combinatorial design problems arise in many application areas and are naturally modelled in terms of set variables and constraints. Traditionally, the domain of a set variable is specified by two sets (R,E) and denotes all sets containing R and disjoint from E. This representation has inherent difficulties in handling cardinality and lexicographic constraints so important in combinatorial design. This paper takes a dual view of set variables. It proposes a representation that encodes directly cardinality and lexicographic information, by totally ordering a set domain with a length-lex ordering. The solver can then enforce bound-consistency on all unary constraints in time Õ(k) where k is the set cardinality. In analogy with finite-domain solvers, non-unary constraints can be viewed as inference rules generating new unary constraints. The resulting set solver achieves a pruning (at least) comparable to the hybrid domain of Sadler and Gervet at a fraction of the computational cost.