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A Cardinality Solver: More Expressive Constraints for Free

(Poster Presentation)
  • Mark H. Liffiton
  • Jordyn C. Maglalang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7317)

Abstract

Despite the semantic simplicity of cardinality constraints, the CNF encodings typically used to solve them invariably turn one constraint into a large number of CNF clauses and/or auxiliary variables. This incurs a significant cost, both in space complexity and in runtime, that could be avoided by reasoning about cardinality constraints directly within a solver. Adding a single, native cardinality constraint instead of numerous clauses and/or auxiliary variables avoids any space overhead and simplifies the solver’s procedures for reasoning about that constraint. Inspired by the simple observation that clauses are cardinality constraints themselves, and thus cardinality constraints generalize clauses, this work seeks to answer the question: How much of the research on developing efficient CNF SAT solvers can be applied to solving cardinality constraints?

Keywords

Space Complexity Auxiliary Variable Cardinality Constraint Space Overhead Semantic Simplicity 
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.

References

  1. 1.
    Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16, 195–221 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dixon, H.E.: Automating Psuedo-Boolean Inference within a DPLL Framework. Ph.D. thesis, University of Oregon (2004)Google Scholar
  3. 3.
    Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Marques-Silva, J., Lynce, I.: Towards Robust CNF Encodings of Cardinality Constraints. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 483–497. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mark H. Liffiton
    • 1
  • Jordyn C. Maglalang
    • 1
  1. 1.Illinois Wesleyan UniversityBloomingtonUSA

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