Cardinality Networks: a theoretical and empirical study

@article{Ach2010CardinalityNA,
  title={Cardinality Networks: a theoretical and empirical study},
  author={Roberto Javier As{\'i}n Ach{\'a} and Robert Nieuwenhuis and Albert Oliveras and Enric Rodr{\'i}guez-Carbonell},
  journal={Constraints},
  year={2010},
  volume={16},
  pages={195-221}
}
We introduce Cardinality Networks, a new CNF encoding of cardinality constraints. It improves upon the previously existing encodings such as the sorting networks of Eén and Sörensson (JSAT 2:1–26, 2006) in that it requires much less clauses and auxiliary variables, while arc consistency is still preserved: e.g., for a constraint x 1 + ... + x n  ≤ k, as soon as k variables among the x i ’s become true, unit propagation sets all other x i ’s to false. Our encoding also still admits incremental… CONTINUE READING
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