Cardinality Networks and Their Applications

  • Roberto Asín
  • Robert Nieuwenhuis
  • Albert Oliveras
  • Enric Rodríguez-Carbonell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5584)


We introduce Cardinality Networks, a new CNF encoding of cardinality constraints. It improves upon the previously existing encodings such as the sorting networks of [ES06] 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 strengthening: this constraint for any smaller k is obtained without adding any new clauses, by setting a single variable to false.

Here we give precise recursive definitions of the clause sets that are needed and give detailed proofs of the required properties. We demonstrate the practical impact of this new encoding by careful experiments comparing it with previous encodings on real-world instances.


Auxiliary Variable Unit Propagation Cardinality Constraint Sorting Network Incremental Strengthen 
These 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Roberto Asín
  • Robert Nieuwenhuis
  • Albert Oliveras
  • Enric Rodríguez-Carbonell

There are no affiliations available

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