Smaller Selection Networks for Cardinality Constraints Encoding

  • Michał Karpiński
  • Marek Piotrów
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9255)


Selection comparator networks have been studied for many years. Recently, they have been successfully applied to encode cardinality constraints for SAT-solvers. To decrease the size of generated formula there is a need for constructions of selection networks that can be efficiently generated and produce networks of small sizes for the practical range of their two parameters: n – the number of inputs (Boolean variables) and k – the number of selected items (a cardinality bound). In this paper we give and analyze a new construction of smaller selection networks that are based on the pairwise selection networks introduced by Codish and Zazon-Ivry. We prove also that standard encodings of cardinality constraints with selection networks preserve arc-consistency.


Unit Propagation Large Element Boolean Variable Selection Network Cardinality Constraint 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks and their applications. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 167–180. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  2. 2.
    Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Asín, R., Nieuwenhuis, R.: Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research 218(1), 71–91 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Batcher, K.E.: Sorting networks and their applications. In: Proc. of the April 30-May 2, 1968, Spring Joint Computer Conference, AFIPS 1968 (Spring), pp. 307–314. ACM, New York (1968)Google Scholar
  5. 5.
    Codish, M., Zazon-Ivry, M.: Pairwise networks are superior for selection.
  6. 6.
    Codish, M., Zazon-Ivry, M.: Pairwise cardinality networks. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 154–172. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  7. 7.
    Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into sat. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–26 (2006)zbMATHGoogle Scholar
  8. 8.
    Knuth, D.E.: The Art of Computer Programming, Sorting and Searching, vol. 3, 2nd edn. Addison Wesley Longman Publishing Co. Inc., Redwood City (1998) Google Scholar
  9. 9.
    Parberry, I.: Parallel complexity theory. Pitman, Research notes in theoretical computer science (1987)Google Scholar
  10. 10.
    Parberry, I.: The pairwise sorting network. Parallel Processing Letters 2, 205–211 (1992)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Why Cumulative decomposition is not as bad as it sounds. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 746–761. Springer, Heidelberg (2009) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocłAwPoland

Personalised recommendations