Abstract
In this paper, we consider the (n,3)-MAXSAT problem. The problem is a special case of the Maximum Satisfiability problem with an additional requirement that in input formula each variable appears at most three times. Here, we improve previous upper bounds for (n,3)-MAXSAT in terms of n (number of variables) and in terms of k (number of clauses that we are required to satisfy). Moreover, we prove that satisfying more clauses than the simple all true assignment is an NP-hard problem.
Research is supported by Russian Science Foundation (project 18-71-10042).
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Acknowledgments
We would like to thank Sergey Kopeliovich for discussions in early stage of the project and Danil Sagunov as well as the anonymous reviewers for valuable comments that improved the presentation of this paper.
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Belova, T., Bliznets, I. (2018). Upper and Lower Bounds for Different Parameterizations of (n,3)-MAXSAT. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_20
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