Abstract
We study adaptive priority algorithms for MAX SAT and show that no such deterministic algorithm can reach approximation ratio \(\frac{3}{4}\), assuming an appropriate model of data items. As a consequence we obtain that the Slack–Algorithm of [13] cannot be derandomized. Moreover, we present a significantly simpler version of the Slack–Algorithm and also simplify its analysis. Additionally, we show that the algorithm achieves a ratio of \(\frac{3}{4}\) even if we compare its score with the optimal fractional score.
Partially supported by DFG SCHN 503/5-1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alekhnovich, M., Borodin, A., Buresh-Oppenheim, J., Impagliazzo, R., Magen, A.: Toward a model for backtracking and dynamic programming. Electronic Colloquium on Computational Complexity (ECCC) 16, 38 (2009)
Angelopoulos, S., Borodin, A.: Randomized priority algorithms. Theor. Comput. Sci. 411(26-28), 2542–2558 (2010)
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)
Azar, Y., Gamzu, I., Roth, R.: Submodular Max-SAT. In: ESA (2011)
Borodin, A., Boyar, J., Larsen, K.S., Mirmohammadi, N.: Priority algorithms for graph optimization problems. Theor. Comput. Sci. 411(1), 239–258 (2010)
Borodin, A., Nielsen, M.N., Rackoff, C.: (Incremental) priority algorithms. Algorithmica 37(4), 295–326 (2003)
Chen, J., Friesen, D.K., Zheng, H.: Tight bound on Johnson’s algorithm for maximum satisfiability. J. Comput. Syst. Sci. 58(3), 622–640 (1999)
Costello, K.P., Shapira, A., Tetali, P.: Randomized greedy: new variants of some classic approximation algorithms. In: SODA, pp. 647–655 (2011)
Davis, S., Impagliazzo, R.: Models of greedy algorithms for graph problems. Algorithmica 54(3), 269–317 (2009)
Goemans, M.X., Williamson, D.P.: New 3/4-approximation algorithms for the maximum satisfiability problem. SIAM J. Discrete Math. 7(4), 656–666 (1994)
Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256–278 (1974)
Poloczek, M.: Bounds on greedy algorithms for MAX SAT, http://www.thi.cs.uni-frankfurt.de/poloczek/maxsatesa11.pdf
Poloczek, M., Schnitger, G.: Randomized variants of Johnson’s algorithm for MAX SAT. In: SODA, pp. 656–663 (2011)
van Zuylen, A.: Simpler 3/4 approximation algorithms for MAX SAT (submitted)
Yao, A.C.-C.: Lower bounds by probabilistic arguments. In: FOCS, pp. 420–428. IEEE, Los Alamitos (1983)
Yung, C.K.: Inapproximation result for exact Max-2-SAT (unpublished manuscript)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Poloczek, M. (2011). Bounds on Greedy Algorithms for MAX SAT. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-23719-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23718-8
Online ISBN: 978-3-642-23719-5
eBook Packages: Computer ScienceComputer Science (R0)