Advertisement

Abstract

Symmetry occurs naturally in many computational problems. The use of symmetry breaking techniques for solving search problems reduces the search space and therefore is expected to reduce the search time. Recent advances in breaking symmetries in SAT models are mainly focused on the identification of permutable variables via graph automorphism. These symmetries are denoted as instance-dependent, and although shown to be effective for different problem instances, the advantages of their generalised use in SAT are far from clear. Indeed, in many cases symmetry breaking predicates can introduce significant computational overhead, rendering ineffective the use of symmetry breaking. In contrast, in other domains, symmetry breaking is usually achieved by identifying instance-independent symmetries, often with promising experimental results. This paper studies the use of instance-independent symmetry breaking predicates in SAT. A concrete application is considered, and techniques for symmetry breaking in matrix models from CP are used. Our results indicate that instance-independent symmetry breaking predicates for matrix models can be significantly more effective than instance-dependent symmetry breaking predicates.

Keywords

Symmetry Breaking Matrix Model Problem Instance Constraint Programming SHIPs Model 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aloul, F.A., et al.: Solving difficult instances in the presence of symmetry. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 22(9), 1117–1137 (2003)CrossRefGoogle Scholar
  2. 2.
    Crawford, J.M., et al.: Symmetry-breaking predicates for search problems. In: Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (1996)Google Scholar
  3. 3.
    Frisch, A.M., et al.: Breaking Row and Column Symmetries in Matrix Models. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, Springer, Heidelberg (2002)Google Scholar
  4. 4.
    Lynce, I., Marques-Silva, J.: Efficient haplotype inference with Boolean satisfiability. In: National Conference on Artificial Intelligence (AAAI) (2006)Google Scholar
  5. 5.
    Marques-Silva, J., Lynce, I.: SAT in Bioinformatics: Making the Case with Haplotype Inference. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 136–141. Springer, Heidelberg (2006)Google Scholar
  6. 6.
    Prestwich, S.: First-solution search with symmetry breaking and implied constraints. In: CP Workshop on Modelling and Problem Formulation (2001)Google Scholar
  7. 7.
    Ramani, A., et al.: Breaking instance-independent symmetries in exact graph coloring. Journal of Artificial Intelligence Research 26, 289–322 (2006)MathSciNetGoogle Scholar
  8. 8.
    Shlyakhter, I.: Generating effective symmetry-breaking predicates for search problems. In: LICS Workshop on Theory and Applications of Satisfiability Testing (2001)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Inês Lynce
    • 1
  • Joao Marques-Silva
    • 2
  1. 1.IST/INESC-ID, Technical University of LisbonPortugal
  2. 2.School of Electronics and Computer Science, University of SouthamptonUK

Personalised recommendations