A Tighter Bound for Counting Max-Weight Solutions to 2SAT Instances

We give an algorithm for counting the number of max-weight solutions to a 2SAT formula, and improve the bound on its running timeto O(1.2377n). The main source of the improvement is a refinement ofthe method of analysis, where we extend the concept of compound (piecewiselinear) measures to multivariate measures, also allowing the optimalparameters for the measure to be found automatically. This method extensionshould be of independent interest.

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