Abstract
We characterize the optimal solution to the LP relaxation of the standard formulation for the minimum satisfiability problem. Based on the characterization, we give a \(O(nm^2)\) combinatorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n(m) is the number of variables (clauses). As a by-product, we obtain a \(2(1-1/2^k)\) approximation algorithm for the minimum satisfiability problem where k is the maximum number of literals in any clause. We also give a simple linear time 2 approximation algorithm.
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Acknowledgments
Robert Benkoczi, Daya Gaur, Ramesh Krishnamurti would like to acknowledge the support from NSERC in the form of individual discovery grants. The authors would like thank the reviewers for the comments.
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Arif, U., Benkoczi, R., Gaur, D.R., Krishnamurti, R. (2020). On the Minimum Satisfiability Problem. In: Changat, M., Das, S. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2020. Lecture Notes in Computer Science(), vol 12016. Springer, Cham. https://doi.org/10.1007/978-3-030-39219-2_23
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DOI: https://doi.org/10.1007/978-3-030-39219-2_23
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