A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
A fast algorithm for the bound consistency of alldiff constraints
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A linear-time algorithm for a special case of disjoint set union
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Fast Optimal Instruction Scheduling for Single-Issue Processors with Arbitrary Latencies
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Network Flow Problems in Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Simultaneous matchings: Hardness and approximation
Journal of Computer and System Sciences
The alldifferent constraint with precedences
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Soft constraints of difference and equality
Journal of Artificial Intelligence Research
Algorithms and constraint programming
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Multiconsistency and robustness with global constraints
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Finite domain bounds consistency revisited
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
GCC-like restrictions on the same constraint
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
ILP'11 Proceedings of the 21st international conference on Inductive Logic Programming
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
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We present narrowing algorithms for the sortedness and the alldifferent constraint which achieve bound-consistency. The algorithm for the sortedness constraint takes as input 2n intervals X1, ... , Xn, Y1, ... , Yn from a linearly ordered set D. Let S denote the set of all tuples t ∈ X1 × ... × Xn × Y1 × ... × Yn such that the last n components of t are obtained by sorting the first n components. Our algorithm determines whether S is non-empty and if so reduces the intervals to bound-consistency. The running time of the algorithm is asymptotically the same as for sorting the interval endpoints. In problems where this is faster than O(n log n), this improves upon previous results. The algorithm for the alldifferent constraint takes as input n integer intervals Z1, ... , Zn. Let T denote all tuples t ∈ Z1 × ... × Zn where all components are pairwise different. The algorithm checks whether T is non-empty and if so reduces the ranges to bound-consistency. The running time is also asymptotically the same as for sorting the interval endpoints. When the constraint is for example a permutation constraint, i.e. Zi ⊆ [1; n] for all i, the running time is linear. This also improves upon previous results.