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• W2143937162 abstract "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.KeywordsConstraint Satisfaction ProblemUnary ConstraintGlobal ConstraintComplete Bipartite GraphSatisfying AssignmentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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• W2143937162 date "2009-01-01" @default.
• W2143937162 modified "2023-09-28" @default.
• W2143937162 title "Same-Relation Constraints" @default.
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• W2143937162 doi "https://doi.org/10.1007/978-3-642-04244-7_38" @default.
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