# Upper Bounds for MaxSat: Further Improved

Conference paper

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## Abstract

Given a boolean CNF formula These bounds improve the recent bounds of respectively

*F*of length |*F*| (sum of the number of variables in each clause) with*m*clauses on*n*variables, we prove the following results.-
The MAXSAT problem, which asks for an assignment satisfying the maximum number of clauses of

*F*, can be solved in*O*(1:341294^{m}|*F*|) time. -
The parameterized version of the problem, that is determining whether there exists an assignment satisfying at least

*k*clauses of the formula (for some integer*k*), can be solved in*O*(*k*^{2}1:380278^{k}+ |*F*|) time. -
MAXSAT can be solved in

*O*(1:105729^{|F|}|*F*|) time.

*O*(1:3972^{m}|*F*|),*O*(*k*^{2}1:3995^{k}+ |*F*|) and*O*(1:1279^{|F|}|*F*|) due to Niedermeier and Rossmanith [11] for these problems. Our last bound comes quite close to the*O*(1:07578^{|F|}|*F*|) bound of Hirsch[6] for the Satisfiability problem (not MAXSAT).## Keywords

Vertex Cover Conjunctive Normal Form Reduction Rule Parameterized Case Unit Clause
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

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