Abstract
#SAT problem is NP-complete, so the small improvement of #SAT problems at the worst case (such as from O(ck) to O((c-ε)k)) will make the efficiency of the algorithm improved in the level of exponent. In this paper, we present a new #2-SAT algorithm based on DPLL regarding the number of clauses as parameter. In order to improve the upper bound, we propose two new transformation rules and make a more elaborate analysis of the constraint graph for choosing better variables to branch. By analyzing, we obtain the new worst case upper bound O(1.1740m), which is the best result up to now within our knowledge.
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Acknowledgments
The authors acknowledge the support of the National Natural Science Foundation of China (61070084, 60803102, 60873146) and the Research Fund for the Doctoral Program of Higher (20050183065).
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Wang, H., Gu, W. (2013). The Worst Case Minimized Upper Bound in #2-SAT. In: Lu, W., Cai, G., Liu, W., Xing, W. (eds) Proceedings of the 2012 International Conference on Information Technology and Software Engineering. Lecture Notes in Electrical Engineering, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34522-7_72
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DOI: https://doi.org/10.1007/978-3-642-34522-7_72
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