From Sequential to Parallel Local Search for SAT

  • Alejandro Arbelaez
  • Philippe Codognet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7832)


In the domain of propositional Satisfiability Problem (SAT), parallel portfolio-based algorithms have become a standard methodology for both complete and incomplete solvers. In this methodology several algorithms explore the search space in parallel, either independently or cooperatively with some communication between the solvers. We conducted a study of the scalability of several SAT solvers in different application domains (crafted, verification, quasigroups and random instances) when drastically increasing the number of cores in the portfolio, up to 512 cores. Our experiments show that on different problem families the behaviors of different solvers vary greatly. We present an empirical study that suggests that the best sequential solver is not necessary the one with the overall best parallel speedup.


Local Search Local Search Algorithm Random Instance Parallel Local Core Increase 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cook, S.A.: The Complexity of Theorem-Proving Procedures. In: Third Annual ACM Symposium on Theory of Computing, STOC 1971, pp. 151–158. ACM (1971)Google Scholar
  2. 2.
    Chrabakh, W., Wolski, R.: GridSAT: A System for Solving Satisfiability Problems Using a Computational Grid. Parallel Computing 32(9), 660–687 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: A Parallel SAT Solver. Journal on Satisfiability, Boolean Modeling and Computation, JSAT 6(4), 245–262 (2009)zbMATHGoogle Scholar
  4. 4.
    Arbelaez, A., Hamadi, Y.: Improving Parallel Local Search for SAT. In: Coello Coello, C.A. (ed.) LION 2011. LNCS, vol. 6683, pp. 46–60. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Hoos, H., Stützle, T.: Stochastic Local Search: Foundations & Applications. Morgan Kaufmann Publishers Inc., San Francisco (2004)Google Scholar
  6. 6.
    Selman, B., Kautz, H.A., Cohen, B.: Noise Strategies for Improving Local Search. In: AAAI 1994, vol. 1, pp. 337–343 (July 1994)Google Scholar
  7. 7.
    McAllester, D.A., Selman, B., Kautz, H.A.: Evidence for Invariants in Local Search. In: AAAI 1997, pp. 321–326 (1997)Google Scholar
  8. 8.
    Thornton, J., Pham, D.N., Bain, S., Ferreira Jr., V.: Additive versus Multiplicative Clause Weighting for SAT. In: AAAI 2004, pp. 191–196 (July 2004)Google Scholar
  9. 9.
    Prestwich, S.D.: Random Walk with Continuously Smoothed Variable Weights. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 203–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Li, C.-M., Huang, W.Q.: Diversification and Determinism in Local Search for Satisfiability. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 158–172. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Balint, A., Fröhlich, A.: Improving Stochastic Local Search for SAT with a New Probability Distribution. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 10–15. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Shylo, O.V., Middelkoop, T., Pardalos, P.M.: Restart Strategies in Optimization: Parallel and Serial Cases. Parallel Computing 37(1), 60–68 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Pham, D.N., Gretton, C.: gNovelty+. In: Solver Description, SAT Competition 2007 (2007)Google Scholar
  14. 14.
    Roli, A.: Criticality and Parallelism in Structured SAT Instances. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 714–719. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Kroc, L., Sabharwal, A., Gomes, C.P., Selman, B.: Integrating Systematic and Local Search Paradigms: A New Strategy for MaxSAT. In: IJCAI 2009, pp. 544–551 (July 2009)Google Scholar
  16. 16.
    Arbeleaz, A., Codognet, P.: Massivelly Parallel Local Search for SAT. In: ICTAI 2012, Athens, Greece, pp. 57–64. IEEE Computer Society (November 2012)Google Scholar
  17. 17.
    Martins, R., Manquinho, V., Lynce, I.: An Overview of Parallel SAT Solving. Constraints 17, 304–347 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Tompkins, D.A.D., Hoos, H.H.: UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT and MAX-SAT. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Achlioptas, D., Gomes, C.P., Kautz, H.A., Selman, B.: Generating satisfiable problem instances. In: AAAI 2000, pp. 256–261 (July 2000)Google Scholar
  20. 20.
    Clarke, E., Kroening, D., Lerda, F.: A Tool for Checking ANSI-C Programs. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 168–176. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Tompkins, D.A.D., Balint, A., Hoos, H.H.: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 302–316. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Gent, I.P., Walsh, T.: The SAT Phase Transition. In: ECAI 1994, pp. 105–109 (August 1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alejandro Arbelaez
    • 1
  • Philippe Codognet
    • 2
    • 3
  1. 1.JFLIUniversity of TokyoJapan
  2. 2.JFLI - CNRS / UPMCUniversity of TokyoJapan
  3. 3.Dept. of Computer ScienceUniversity of TokyoBunkyo-kuJapan

Personalised recommendations