Upper bounds for MaxSat : Further improved

Given a boolean CNF formula 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. These bounds improve the recent bounds of respectively O(1.3972^m |F|), O(k^2 1.3995^k + |F|) and O(1.12791^|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)