Advertisement

Abstract

Counting-based search, a branching heuristic used in constraint programming, relies on computing the proportion of solutions to a constraint in which a given variable-value assignment appears in order to build an integrated variable- and value-selection heuristic to solve constraint satisfaction problems. The information it collects has led to very effective search guidance in many contexts. However, depending on the constraint, computing such information can carry a high computational cost. This paper presents several contributions to accelerate counting-based search, with supporting empirical evidence that solutions can thus be obtained orders of magnitude faster.

References

  1. 1.
    Brockbank, S., Pesant, G., Rousseau, L.-M.: Counting spanning trees to guide search in constrained spanning tree problems. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 175–183. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40627-0_16CrossRefGoogle Scholar
  2. 2.
    Chaiken, S., Kleitman, D.J.: Matrix tree theorems. J. Comb. Theory Ser. A 24(3), 377–381 (1978)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Choi, J., Dongarra, J.J., Ostrouchov, L.S., Petitet, A.P., Walker, D.W., Whaley, R.C.: Design and implementation of the ScaLAPACK LU, QR, and Cholesky factorization routines. Sci. Program. 5(3), 173–184 (1996)Google Scholar
  4. 4.
    Delaite, A., Pesant, G.: Counting weighted spanning trees to solve constrained minimum spanning tree problems. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 176–184. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-59776-8_14CrossRefGoogle Scholar
  5. 5.
    Gagnon, S.: Gecode extension for counting-based search (2017). https://github.com/SaGagnon/gecode-5-extension
  6. 6.
    Gecode Team: Gecode: generic constraint development environment (2017). http://www.gecode.org
  7. 7.
    Gomes, C., Shmoys, D.: Completing quasigroups or Latin squares: a structured graph coloring problem. In: Computational Symposium on Graph Coloring and Generalizations, January 2002Google Scholar
  8. 8.
    Haythorpe, M.: FHCP challenge set (2015). http://fhcp.edu.au/fhcpcs
  9. 9.
    Pesant, G.: Counting-based search for constraint optimization problems. In: Schuurmans, D., Wellman, M.P. (eds.) AAAI, pp. 3441–3448. AAAI Press (2016)Google Scholar
  10. 10.
    Pesant, G., Quimper, C.G., Zanarini, A.: Counting-based search: branching heuristics for constraint satisfaction problems. J. Artif. Int. Res. 43(1), 173–210 (2012)MathSciNetMATHGoogle Scholar
  11. 11.
    Valiant, L.G.: The complexity of computing the permanent. Theoret. Comput. Sci. 8(2), 189–201 (1979)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zanarini, A., Pesant, G.: Solution counting algorithms for constraint-centered search heuristics. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 743–757. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74970-7_52CrossRefMATHGoogle Scholar
  13. 13.
    Zanarini, A., Pesant, G.: More robust counting-based search heuristics with alldifferent constraints. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 354–368. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13520-0_38CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Polytechnique MontréalMontrealCanada

Personalised recommendations