Moreover, it was already known that some NP-complete problems admit sub-exponential algorithms. For example, planar graph 3-colorability can be solved in 2^O(sqrt(n)) time. This is not only sub-exponential, but vastly better than the running time of the new 3-SAT algorithm.

Still, the result is very interesting, since many problems can be solved asymptotically faster once subproblems that can be represented as 3-SAT can be solved faster. For example, we now have now have a deterministic interger factoring algorithm with run time N^o(1), where N is the integer being factored. Heuristic algorithms already achieved this bound, but the new claim is a deterministic worst-case guarantee. The result is a fairly straightforward application of the new 3-SAT solver.