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Assume I need to solve an NP-complete problem, for which problem-specific methods (e.g. efficient heuristics or exponential algorithms faster than naive one) are not well developed. If the size of input is n, then, in theory, I could reduce the problem to SAT of size P(n), where P is some polynomial, and use SAT solvers. Or I could reduce it to other NP-complete problem with well-developed algorithms available.

Of course, I would like to use reduction with P(n) being polynomial with as low degree as possible.

1) Is there a (reasonably recent) book/survey/webpage in which I can learn what are the most efficient known reductions from some (as many as possible) NP-complete problems to (say) SAT?

2) I am sure many such reductions has already been implemented, some of them open source. Is there a webpage collecting links to such implementations?

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For the reduction of the Asymmetric Traveling Salesman Problem to the Symmetric Traveling Salesman Problem two methods exist: one reduces ATSP instances to STSP instances using three nodes and a later one requires only two nodes per node of the ATSP instance; a description can be found in On Asymmetric TSP: Transformation to Symmetric TSP and Performance Bound. The reduction using two nodes is likely the most efficient possible reduction from ATSP to STSP.

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