Smaller Selection Networks for Cardinality Constraints Encoding
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.
KeywordsUnit Propagation Large Element Boolean Variable Selection Network Cardinality Constraint
Unable to display preview. Download preview PDF.
- 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.Codish, M., Zazon-Ivry, M.: Pairwise networks are superior for selection. http://www.cs.bgu.ac.il/~mcodish/Papers/Sources/pairwiseSelection.pdf
- 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.Parberry, I.: Parallel complexity theory. Pitman, Research notes in theoretical computer science (1987)Google Scholar