Approximating MAX SAT by Moderately Exponential and Parameterized Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)


We study approximation of the max sat problem by moderately exponential algorithms. The general goal of the issue of moderately exponential approximation is to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-case running times importantly smaller than those needed for exact computation, approximation ratios unachievable in polynomial time. We develop several approximation techniques that can be applied to max sat in order to get approximation ratios arbitrarily close to 1.


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  1. 1.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and approximation. In: Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin (1999)Google Scholar
  2. 2.
    Avidor, A., Berkovitch, I., Zwick, U.: Improved Approximation Algorithms for MAX NAE-SAT and MAX SAT. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 27–40. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Battiti, R., Protasi, M.: Algorithms and heuristics for max-sat. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 1, pp. 77–148. Kluwer Academic Publishers (1998)Google Scholar
  4. 4.
    Björklund, A.: Determinant sums for undirected Hamiltonicity. In: Proc. FOCS 2010, pp. 173–182. IEEE Computer Society (2010)Google Scholar
  5. 5.
    Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bourgeois, N., Escoffier, B., Paschos, V.T.: Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms. Discrete Appl. Math. 159(17), 1954–1970 (2011)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient approximation of min coloring by moderately exponential algorithms. Inform. Process. Lett. 109(16), 950–954 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient approximation of min set cover by moderately exponential algorithms. Theoret. Comput. Sci. 410(21-23), 2184–2195 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Cai, L., Huang, X.: Fixed-Parameter Approximation: Conceptual Framework and Approximability Results. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 96–108. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Chen, J., Kanj, I.A.: Improved exact algorithms for max sat. Discrete Appl. Math. 142, 17–27 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Crescenzi, P., Silvestri, R., Trevisan, L.: To weight or not to weight: where is the question? In: Proc. Israeli Symposium on Theory of Computing and Systems, ISTCS 1996, pp. 68–77. IEEE (1996)Google Scholar
  12. 12.
    Cygan, M., Kowalik, L., Wykurz, M.: Exponential-time approximation of weighted set cover. Inform. Process. Lett. 109(16), 957–961 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Cygan, M., Pilipczuk, M.: Exact and approximate bandwidth. Theoret. Comput. Sci. 411(40-42), 3701–3713 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Dantsin, E., Gavrilovich, M., Hirsch, E.A., Konev, B.: max sat approximation beyond the limits of polynomial-time approximation. Ann. Pure and Appl. Logic 113, 81–94 (2001)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Downey, R.G., Fellows, M.R., McCartin, C.: Parameterized Approximation Problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 121–129. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Escoffier, B., Paschos, V.T.: A survey on the structure of approximation classes. Computer Science Review 4(1), 19–40 (2010)CrossRefGoogle Scholar
  17. 17.
    Feige, U., Goemans, M.X.: Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT. In: Proc. 3rd Israel Symp. on Theory of Computing and Systems, pp. 182–189. IEEE Computer Society (1995)Google Scholar
  18. 18.
    Fürer, M., Gaspers, S., Kasiviswanathan, S.P.: An Exponential Time 2-Approximation Algorithm for Bandwidth. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 173–184. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Håstad, J.: Some optimal inapproximability results. In: Proc. 29th Ann. ACM Symp. on Theory of Comp., pp. 1–10. ACM (1997)Google Scholar
  20. 20.
    Hirsch, E.A.: Worst-case study of local search for Max-k-SAT. Discrete Applied Mathematics 130, 173–184 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Impagliazzo, R., Paturi, R.: On the Complexity of k-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Moshkovitz, D., Raz, R.: Two-query PCP with subconstant error. J. ACM 57(5) (2010)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Paris Sciences et LettresUniversité Paris-Dauphine, LAMSADE, CNRS UMR 7243France
  2. 2.Institut Universitaire de FranceFrance

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