A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Arc and path consistence revisited
Artificial Intelligence
Tree clustering for constraint networks (research note)
Artificial Intelligence
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Using constraint metaknowledge to reduce arc consistency computation
Artificial Intelligence
Discrete Mathematics
A comparison of structural CSP decomposition methods
Artificial Intelligence
A Constraint Programming Approach to the Stable Marriage Problem
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
The complexity of digraph homomorphisms: local tournaments, injective homomorphisms and polymorphisms
Parameterized Complexity
Hybrid tractability of valued constraint problems
Artificial Intelligence
Constraint satisfaction problems: convexity makes all different constraints tractable
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
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The ALLDIFFERENT constraint was one of the first global constraints [17] and it enforces the conjunction of one binary constraint, the not-equal constraint, for every pair of variables. By looking at the set of all pairwise not-equal relations at the same time, AllDifferent offers greater filtering power. The natural question arises whether we can generally leverage the knowledge that sets of pairs of variables all share the same relation. This paper studies exactly this question. We study in particular special constraint graphs like cliques, complete bipartite graphs, and directed acyclic graphs, whereby we always assume that the same constraint is enforced on all edges in the graph. In particular, we study whether there exists a tractable GAC propagator for these global Same-Relation constraints and show that AllDifferent is a huge exception: most Same-Relation Constraints pose NP-hard filtering problems. We present algorithms, based on AC-4 and AC-6, for one family of Same-Relation Constraints, which do not achieve GAC propagation but outperform propagating each constraint individually in both theory and practice.