Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)
Asín, R., Nieuwenhuis, R.: Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research 218(1), 71–91 (2014)
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)
Codish, M., Zazon-Ivry, M.: Pairwise networks are superior for selection. http://www.cs.bgu.ac.il/~mcodish/Papers/Sources/pairwiseSelection.pdf
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)
Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into sat. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–26 (2006)
Knuth, D.E.: The Art of Computer Programming, Sorting and Searching, vol. 3, 2nd edn. Addison Wesley Longman Publishing Co. Inc., Redwood City (1998)
Parberry, I.: Parallel complexity theory. Pitman, Research notes in theoretical computer science (1987)
Parberry, I.: The pairwise sorting network. Parallel Processing Letters 2, 205–211 (1992)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Karpiński, M., Piotrów, M. (2015). Smaller Selection Networks for Cardinality Constraints Encoding. In: Pesant, G. (eds) Principles and Practice of Constraint Programming. CP 2015. Lecture Notes in Computer Science(), vol 9255. Springer, Cham. https://doi.org/10.1007/978-3-319-23219-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-23219-5_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23218-8
Online ISBN: 978-3-319-23219-5
eBook Packages: Computer ScienceComputer Science (R0)