Abstract
An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-Cnf formula. The worst case running time of O( 1.246n) for formulas with n variables improves on the previous bound of O( 1.256n) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246n) time algorithm for counting maximum weighted independent sets in a graph.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Angelsmark, O.: Constructing algorithms for constraint satisfaction and related problems: Methods and applications. PhD. thesis, Linköping University (2005)
Beigel, R., Eppstein, D.: 3-coloring in time O(1.3289n). Journal of Algorithms 54(2), 168–204 (2005)
Björklund, A., Husfeldt, T.: Inclusion–exclusion algorithms for counting set partitions. In: Foundations of Computer Science, pp. 575–582. IEEE Computer Society Press, Los Alamitos (2006)
Dahllöf, V., Jonsson, P.: An algorithm for counting maximum weighted independent sets and its applications. In: Symposium on Discrete Algorithms, pp. 292–298. SIAM, Philadelphia (2002)
Dahllöf, V., Jonsson, P., Wahlström, M.: Counting satisfying assignments in 2-SAT and 3-SAT. In: H. Ibarra, O., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 535–543. Springer, Heidelberg (2002)
Dahllöf, V., Jonsson, P., Wahlström, M.: Counting models for 2SAT and 3SAT formulae. Theoretical Computer Science 332(1-3), 265–291 (2005)
Dantsin, E., Gavrilovich, M., Hirsch, E., Konev, B.: MAX SAT approximation beyond the limits of polynomial-time approximation. Annals of Pure and Applied Logic 113, 81–94 (2002)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5(7), 394–397 (1962)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of Association Computer Machinery 7, 201–215 (1960)
Dubois, O.: Counting the number of solutions for instances of satisfiability. Theoretical Computer Science 81(1), 49–64 (1991)
Fürer, M., Kasiviswanathan, S.P.: Algorithms for counting 2-SAT solutions and colorings with applications. TR05-033, Electronic Colloquium on Computational Complexity (2005)
Koivisto, M.: An O *(2n ) algorithm for graph coloring and other partitioning problems via inclusion–exclusion. In: Foundations of Computer Science, pp. 583–590. IEEE Computer Society Press, Los Alamitos (2006)
Kozen, D.C.: The Design and Analysis of Algorithms. Springer, Berlin (1992)
Kullmann, O.: New methods for 3-SAT decision and worst-case analysis. Theoretical Computer Science 223, 1–72 (1999)
Littman, M.L., Pitassi, T., Impagliazzo, R.: On the complexity of counting satisfying assignments. In: The Working notes of LICS 2001 Workshop on Satisfiability (2001)
Roth, D.: On the hardness of approximate reasoning. Artificial Intelligence 82(2), 273–302 (1996)
Vadhan, S.P.: The complexity of counting in sparse, regular, and planar graphs. SIAM Journal on Computing 31(2), 398–427 (2002)
Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8(2), 189–201 (1979)
Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM Journal of Computing 8(3), 410–421 (1979)
Zhang, W.: Number of models and satisfiability of sets of clauses. Theoretical Computer Science 155(1), 277–288 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Fürer, M., Kasiviswanathan, S.P. (2007). Algorithms for Counting 2-Sat Solutions and Colorings with Applications. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-72870-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72868-9
Online ISBN: 978-3-540-72870-2
eBook Packages: Computer ScienceComputer Science (R0)