Abstract
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.
Research partially supported by the French Agency for Research under the DEFIS program “Time vs. Optimality in Discrete Optimization”, ANR-09-EMER-010.
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References
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)
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)
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)
Björklund, A.: Determinant sums for undirected Hamiltonicity. In: Proc. FOCS 2010, pp. 173–182. IEEE Computer Society (2010)
Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)
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)
Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient approximation of min coloring by moderately exponential algorithms. Inform. Process. Lett. 109(16), 950–954 (2009)
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)
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)
Chen, J., Kanj, I.A.: Improved exact algorithms for max sat. Discrete Appl. Math. 142, 17–27 (2004)
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)
Cygan, M., Kowalik, L., Wykurz, M.: Exponential-time approximation of weighted set cover. Inform. Process. Lett. 109(16), 957–961 (2009)
Cygan, M., Pilipczuk, M.: Exact and approximate bandwidth. Theoret. Comput. Sci. 411(40-42), 3701–3713 (2010)
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)
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)
Escoffier, B., Paschos, V.T.: A survey on the structure of approximation classes. Computer Science Review 4(1), 19–40 (2010)
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)
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)
Håstad, J.: Some optimal inapproximability results. In: Proc. 29th Ann. ACM Symp. on Theory of Comp., pp. 1–10. ACM (1997)
Hirsch, E.A.: Worst-case study of local search for Max-k-SAT. Discrete Applied Mathematics 130, 173–184 (2003)
Impagliazzo, R., Paturi, R.: On the Complexity of k-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)
Moshkovitz, D., Raz, R.: Two-query PCP with subconstant error. J. ACM 57(5) (2010)
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Escoffier, B., Paschos, V.T., Tourniaire, E. (2012). Approximating MAX SAT by Moderately Exponential and Parameterized Algorithms. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_23
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