A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Pruning for the Minimum Constraint Family and for the Number of Distinct Values Constraint Family
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Range-Based Algorithm for Max-CSP
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
ICCBR '01 Proceedings of the 4th International Conference on Case-Based Reasoning: Case-Based Reasoning Research and Development
Specific Filtering Algorithms for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Meta-constraints on violations for over constrained problems
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Graphs and Hypergraphs
On global warming: Flow-based soft global constraints
Journal of Heuristics
Filtering Algorithms for the NValue Constraint
Constraints
Machine Learning: ECML 2005: 16th European Conference on Machine Learning, Porto, Portugal, October 3-7, 2005, Proceedings (Lecture Notes in Computer Science ... / Lecture Notes in Artificial Intelligence)
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
A Soft Constraint of Equality: Complexity and Approximability
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Finding diverse and similar solutions in constraint programming
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
The Consistent Vehicle Routing Problem
Manufacturing & Service Operations Management
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
ExpertClerk: navigating shoppers' buying process with the combination of asking and proposing
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
Reasoning about optimal collections of solutions
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Constraints of difference and equality: a complete taxonomic characterisation
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Constraint-based local search for the automatic generation of architectural tests
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
A SAT-based version space algorithm for acquiring constraint satisfaction problems
ECML'05 Proceedings of the 16th European conference on Machine Learning
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In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known ALLDIFFERENT and ALLEQUAL constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 1/2 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.