Abstract
The rigorous theoretical analyses of algorithms for exact 3-satisfiability (X3SAT) have been proposed in the literature. As we know, previous algorithms for solving X3SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving X3SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving X3SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.15855m), where m is the number of clauses.
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
Schaefer, T.J.: The Complexity of Satisfiability Problems. In: 10th Annual ACM Symposium on Theory of Computing, pp. 216–226 (1978)
Drori, L., Peleg, D.: Faster Exact Solutions for Some NP-hard Problems. Theoretical Computer Science 287(2), 473–499 (2002)
Porschen, S., Randerath, B., Speckenmeyer, E.: X3SAT is Decidable in time O(2n/5). In: Fifth International Symposium on the Theory and Applications of Satisfiability Testing, pp. 231–235. Springer, Heidelberg (2002)
Porschen, S., Randerath, B., Speckenmeyer, E.: Exact 3-Satisfiability is Decidable in time O(20.16254n) (June 2002) (manuscript); Annals of Mathematics and Artificial Intelligence 43(1) 173-193 (2005)
Kulikov, A.S.: An Upper Bound O(20.16254n) for Exact 3-Satisfiability: a Simpler Proof. Zapiski Nauchnyh Seminarov POMI 293, 118–128 (2002)
Dahllof, V., Jonsson, P., Beigel, R.: Algorithms for Four Variants of the Exact Satisfiability Problem. Theoretical Computer Science 320(2-3), 373–394 (2004)
Byskov, J.M., Madsen, B.A., Skjernaa, B.: New Algorithms for Exact Satisfiability. Theoretical Computer Science 332(1-3), 515–541 (2005)
Skjernaa, B.: Exact Algorithms for Variants of Satisfiability and Colouring Problems. PhD thesis, Department of Computer Science, Aarhus University (2004)
Bolette, A.M.: An Algorithm for Exact Satisfiability Analysed with the Number of Clauses as Parameter. Information Processing Letters 97(1), 28–30 (2006)
Hirsch, E.A.: New Worst-Case Upper Bounds for SAT. J. Auto. Reasoning 24(4), 397–420 (2000)
Monien, B., Speckenmeyer, E., Vornberger, O.: Upper Bounds for Covering Problems. Methods Oper. Res. 43, 419–431 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhou, J., Yin, M. (2012). The Worst-Case Upper Bound for Exact 3-Satisfiability with the Number of Clauses as the Parameter. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-29700-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29699-4
Online ISBN: 978-3-642-29700-7
eBook Packages: Computer ScienceComputer Science (R0)