Advertisement

A Fast and Efficient Method for #2SAT via Graph Transformations

  • Marco A. López
  • J. Raymundo Marcial-RomeroEmail author
  • Guillermo De Ita
  • Rosa M. Valdovinos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10632)

Abstract

In this paper we present an implementation (markSAT) for computing #2SAT via graph transformations. For that, we transform the input formula into a graph and test whether it is which we call a cactus graph. If it is not the case, the formula is decomposed until cactus sub-formulas are obtained. We compare the efficiency of markSAT against sharpSAT which is the leading sequential algorithm in the literature for computing #SAT obtaining better results with our proposal.

References

  1. 1.
    Ita Luna, G.: Polynomial classes of boolean formulas for computing the degree of belief. In: Lemaître, C., Reyes, C.A., González, J.A. (eds.) IBERAMIA 2004. LNCS (LNAI), vol. 3315, pp. 430–440. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30498-2_43CrossRefGoogle Scholar
  2. 2.
    Brightwell, G., Winkler, P.: Counting linear extensions. Order 8(3), 225–242 (1991)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Paulusma, D., Slivovsky, F., Szeider, S.: Model counting for cnf formulas of bounded modular treewidth. Algorithmica 76(1), 168–194 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wahlström, M.: A tighter bound for counting max-weight solutions to 2SAT instances. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 202–213. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-79723-4_19CrossRefGoogle Scholar
  5. 5.
    Schmitt, M., Wanka, R.: Exploiting independent subformulas: a faster approximation scheme for #k-sat. Inf. Process. Lett. 113(9), 337–344 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bayardo Jr., R.J., Schrag, R.C.: Using CSP look-back techniques to solve real-world sat instances. In: Proceedings of the Fourteenth National Conference on Artificial Intelligence and Ninth Conference on Innovative Applications of Artificial Intelligence, AAAI 1997/IAAI 1997, pp. 203–208. AAAI Press (1997)Google Scholar
  7. 7.
    Thurley, M.: sharpSAT – counting models with advanced component caching and implicit BCP. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 424–429. Springer, Heidelberg (2006).  https://doi.org/10.1007/11814948_38CrossRefGoogle Scholar
  8. 8.
    Burchard, J., Schubert, T., Becker, B.: Laissez-faire caching for parallel #SAT solving. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 46–61. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-24318-4_5CrossRefzbMATHGoogle Scholar
  9. 9.
    Szeider, S.: On fixed-parameter tractable parameterizations of SAT. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 188–202. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24605-3_15CrossRefzbMATHGoogle Scholar
  10. 10.
    De Ita, G., Bello López, P., González, M.C.: New polynomial classes for #2SAT established via graph-topological structure. Eng. Lett. 15, 250–258 (2007)Google Scholar
  11. 11.
    Marcial-Romero, J.R., De Ita Luna, G., Hernández, J.A., Valdovinos, R.M.: A parametric polynomial deterministic algorithm for #2SAT. In: Sidorov, G., Galicia-Haro, S.N. (eds.) MICAI 2015. LNCS (LNAI), vol. 9413, pp. 202–213. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-27060-9_16CrossRefGoogle Scholar
  12. 12.
    Bondy, J.A., Murty, U.S.R.: Graph Theory, 3rd printing edn. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Marco A. López
    • 3
  • J. Raymundo Marcial-Romero
    • 1
    Email author
  • Guillermo De Ita
    • 2
  • Rosa M. Valdovinos
    • 1
  1. 1.Facultad de IngenieríaUAEMWashington, D.C.USA
  2. 2.Facultad de Ciencias de la ComputaciónBUAPPueblaMexico
  3. 3.Facultad de IngenieríaUAEMTolucaMexico

Personalised recommendations