A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
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
Specific Filtering Algorithms for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
On global warming: Flow-based soft global constraints
Journal of Heuristics
Filtering Algorithms for the NValue Constraint
Constraints
A constraint seeker: finding and ranking global constraints from examples
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Soft constraints of difference and equality
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
Many combinatorial problems encountered in practice involve constraints that require that a set of variables take distinct or equal values. The ALLDIFFERENT constraint, in particular, ensures that all variables take distinct values. Two soft variants of this constraint were proposed in [4], defined either with respect to a so-called variable or graph-based cost function. When requiring similarity, as opposed to diversity, one can consider the dual definition either for the cost or for the basic constraint itself, that is, ALLEQUAL in our case. Six cost functions can be defined by exploring every combination of these definitions. It is therefore natural to study the complexity of achieving arc consistency and bounds consistency on them. From our earlier work on this topic an open problem remained, namely achieving bounds consistency on the maximisation of the SOFTALLDIFF constraint when considering the graph-based cost. In this paper we resolve this problem. Therefore, we give a complete taxonomy of constraints of equality and difference, based on the alternative objective functions used for the soft variants.