Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Node and arc consistency in weighted CSP
Eighteenth national conference on Artificial intelligence
Constraint Processing
Arc consistency for soft constraints
Artificial Intelligence
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
A Soft Approach to Multi-objective Optimization
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Bipolar preference problems: framework, properties and solving techniques
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Expert Systems with Applications: An International Journal
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We extend algorithms for arc consistency proposed in the literature in order to deal with (absorptive) semirings that are not invertible. As a consequence, these consistency algorithms can be used as a pre-processing procedure in soft Constraint Satisfaction Problems (CSPs) defined over a larger class of semirings: among other instances, for those semirings obtained as the cartesian product of any family of semirings. The main application is that the new arc consistency algorithm can be used for multi-criteria soft CSPs. To reach this objective, we first show that any semiring can be transformed into a new one where the + operator is instantiated with the Least Common Divisor (LCD) between the elements of the original semiring. The LCD value corresponds to the amount we can "safely move" from the binary constraint to the unary one in the arc consistency algorithm (when the × operator of the semiring is not idempotent). We then propose an arc consistency algorithm which takes advantage of this LCD operator.