Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
Enhancing set constraint solvers with lexicographic bounds
Journal of Heuristics
Length-lex ordering for set CSPs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Length-lex bound consistency for knapsack constraints
Proceedings of the 2009 ACM symposium on Applied Computing
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
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
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The length-lex representation has been recently proposed for representing sets in Constraint Satisfaction Problems. The length-lex representation directly captures cardinality information, provides a total ordering for sets, and allows bound consistency on unary constraints to be enforced in time Õ(c), where c is the cardinality of the set. However, no algorithms were given to enforce bound consistency on binary constraints. This paper addresses this open issue. It presents algorithms to enforce bound consistency on disjointness and cardinality constraints in time O(c3). Moreover, it presents a generic bound-consistency algorithm for any binary constraint S which requires Õ(c2) calls to a feasibility subroutine for S.