Known algorithms on graphs of bounded treewidth are probably optimal

We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2 - ∈)nmO(1) time, we show that for any ∈ > 0;