Best possible approximation algorithm for MAX SAT with cardinality constraint
In this work we consider the MAX SAT problem with the additional constraint that at most p variables have a true value. We obtain (1 — e −1)-approximation algorithm for this problem. Feige  proves that for the MAX SAT with cardinality constraint with clauses without negations this is the best possible performance guarantee unless P=NP.
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- 1.Alon, N., Spencer, J.H.: Probabilistic Method. Wiley, 1992.Google Scholar
- 2.Asano, T.: Approximation algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson. In Proceedings of the 5nd Israel Symposium on Theory and Computing Systems (1997) 182–189Google Scholar
- 5.Feige, U.: A threshold of Inn for approximating set cover. Journal of ACM (to appear)Google Scholar
- 6.Feige, U., Goemans, M.: Approximating the value of two-prover proof systems, with applications to MAX 2-SAT and MAX-DICUT. In Proceedings of the 3nd Israel Symposium on Theory and Computing Systems (1995) 182–189Google Scholar
- 7.Feller, W.: An Introduction to Probability Theory and Its Applications. John Wiley & Sons New York (1968)Google Scholar
- 8.Hastad, J.: Some optimal inapproximability results. In Proceedings of the 28 Annual ACM Symp. on Theory of Computing (1996) 1–10Google Scholar
- 9.Karloff, H., Zwick, U.: A 7/8-approximation algorithm for MAX 3SAT? In Proceedings of the 38th FOCS (1997) 406–415Google Scholar
- 10.Khanna, S., Motwani, R.: Towards syntactic characterization of PTAS. In Proceedings of the 28 Annual ACM Symp. on Theory of Computing (1996) 329–337Google Scholar