Abstract
The optimization problem Max-2SAT-CC is Max-2SAT with the additional cardinality constraint that the value one may be assigned to at most K variables. We present an approximation algorithm with polynomial running time for Max-2SAT-CC. This algorithm achieves, for any ε > 0, approximation ratio \( \frac{{6 + 3 \cdot e}} {{16 + 2 \cdot e}} - \varepsilon \approx 0 \cdot 6603 \). Furthermore, we present a greedy algorithm with running time O(N log N) and approximation ratio 1/2. The latter algorithm even works for clauses of arbitrary length.
Birth name: Bodo Siebert. Supported by DFG research grant Re 672/3.
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References
A. A. Ageev and M. I. Sviridenko. Approximation algorithms for maximum coverage and max cut with given sizes of parts. In Proc. of the 7th Int. Conf. on Integer Programming and Combinatorial Optimization (IPCO), volume 1620 of Lecture Notes in Comput. Sci., pages 17–30. Springer, 1999.
N. A1on, J. H. Spencer, and P. Erdös. The Probabilistic Method. John Wiley and Sons, 1992.
T. Asano and D. P. Williamson. Improved approximation algorithms for MAX SAT. J. Algorithms, 42(1):173–202, 2002.
G. P. Cornuéjols, M. L. Fisher, and G. L. Nemhauser. Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Science, 23:789–810, 1977.
R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer, 1999.
U. Feige. A threshold of ln n for approximating set cover. J. ACM, 45(4):634–652, 1998.
U. Feige and M. X. Goemans. Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT. In Proc. of the 3rd Israel Symp. on the Theory of Comput. and Systems (ISTCS), pages 182–189, 1995.
M. X. Goemans and D. P. Williamson. New 34-approximation algorithms for the maximum satisfiability problem. SIAM J. Discrete Math., 7(4):656–666, 1994.
J. H∮astad. Some optimal inapproximability results. J. ACM, 48(4):798–859, 2001.
M. I. Sviridenko. Best possible approximation algorithm for MAX SAT with cardinality constraint. Algorithmica, 30(3):398–405, 2001.
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Bläser, M., Manthey, B. (2002). Improved Approximation Algorithms for Max-2SAT with Cardinality Constraint. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_17
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DOI: https://doi.org/10.1007/3-540-36136-7_17
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