### Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

Robert Ganian, Petr HlinenÃ½ & Jan ObdrzÃ¡Lek
We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known --e.g. [Fischer, Makowsky, and Ravve]-- with a single-exponential dependency on the clique-width of a formula. Our algorithm thus presents an exponential runtime improvement (since clique-width reaches up to exponentially higher values than rank-width), and can be of practical interest for small values of rank-width....