Subexponential Weighted Counting and Exact Optimisation
The deterministic algorithm of \oai{} that counts the satisfying assignments of a $k$-CNF in time $2^{o(n)}$ is reproduced in full and extended from counting to sums of local weights with values in any commutative $\Q$-algebra. The extension gives deterministic $2^{o(n)}$ algorithms for exact Max-Cut and Max-$k$-SAT on sparse instances, for the independence polynomial, the maximum independent set and the knapsack problem with a conflict graph on every graph, for $0$-$1$ integer programs whose rows involve boundedly many variables, for Vertex Cover in time $2^{o(k)}+\poly(n)$, for the density…
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