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.
This is a preview of subscription content, log in via an institution to check access.
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)