Using Community Structure to Detect Relevant Learnt Clauses

  • Carlos Ansótegui
  • Jesús Giráldez-Cru
  • Jordi Levy
  • Laurent Simon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9340)

Abstract

Nowadays, Conflict-Driven Clause Learning (CDCL) techniques are one of the key components of modern SAT solvers specialized in industrial instances. Last years, one of the focuses has been put on strategies to select which learnt clauses are removed during the search. Originally, one need for removing clauses was motivated by the finiteness of memory. Recently, it has been shown that more aggressive clause deletion policies may improve solvers performance, even when memory is sufficient. Also, the utility of learnt clauses has been related to the modular structure of industrial SAT instances.

In this paper, we show that augmenting SAT instances with learnt clauses does not always make them easier for the SAT solver. In fact, it makes worse the solver performance in many cases. However, we identify a set of highly useful learnt clauses, and we show that augmenting SAT instances with this set of clauses contributes to improve the solver performance in many cases, especially in satisfiable formulas. These clauses are related to the community structure of the formula, and they can be computed in a fast preprocessing step. This would suggest that the community structure may play an important role in clause deletion policies.

References

  1. 1.
    Ansótegui, C., Giráldez-Cru, J., Levy, J.: The community structure of SAT formulas. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 410–423. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  2. 2.
    Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proc. of IJCAI 2009, pp. 399–404 (2009)Google Scholar
  3. 3.
    Biere, A.: Lingeling essentials, A tutorial on design and implementation aspects of the the SAT solver Lingeling. In: Proc. of POS 2014 (2014)Google Scholar
  4. 4.
    Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008(10), P10008 (2008)CrossRefGoogle Scholar
  5. 5.
    Brandes, U., Delling, D., Gaertler, M., Görke, R., Hoefer, M., Nikoloski, Z., Wagner, D.: On modularity clustering. IEEE Trans. on Knowledge and Data Engineering 20(2), 172–188 (2008)CrossRefMATHGoogle Scholar
  6. 6.
    Chen, J.: A bit-encoding phase selection strategy for satisfiability solvers. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds.) TAMC 2014. LNCS, vol. 8402, pp. 158–167. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Gomes, C.P., Selman, B., Kautz, H.A.: Boosting combinatorial search through randomization. In: Proc. of the Fifteenth National Conf. on Artificial Intelligence, AAAI 1998, pp. 431–437 (1998)Google Scholar
  9. 9.
    Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 355–370. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  10. 10.
    Katebi, H., Sakallah, K.A., Marques-Silva, J.P.: Empirical study of the anatomy of modern sat solvers. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 343–356. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  11. 11.
    Katsirelos, G., Simon, L.: Eigenvector centrality in industrial SAT instances. In: Milano, M. (ed.) CP 2012. LNCS, pp. 348–356. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  12. 12.
    Martins, R., Manquinho, V., Lynce, I.: Community-based partitioning for MaxSAT solving. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 182–191. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  13. 13.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proc. of DAC 2001, pp. 530–535 (2001)Google Scholar
  14. 14.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)CrossRefGoogle Scholar
  15. 15.
    Newsham, Z., Ganesh, V., Fischmeister, S., Audemard, G., Simon, L.: Impact of community structure on SAT solver performance. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 252–268. Springer, Heidelberg (2014) Google Scholar
  16. 16.
    Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  17. 17.
    Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers 48(5), 506–521 (1999)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Simon, L.: Post mortem analysis of SAT solver proofs. In: Proc. of POS 2014, pp. 26–40 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Carlos Ansótegui
    • 1
  • Jesús Giráldez-Cru
    • 2
  • Jordi Levy
    • 2
  • Laurent Simon
    • 3
  1. 1.DIEIUniversitat de LleidaLleidaSpain
  2. 2.Artificial Intelligence Research InstituteSpanish National Research Council (IIIA-CSIC)BarcelonaSpain
  3. 3.LaBRIUniversité de BordeauxTalenceFrance

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