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Computationally 'hard' polynomialtime reduction to other NPcomplete problems / Hierarchy of NPcomplete problems
As we all know there exist plenty of polynomialtime reductions from one NPcomplete problem to another. Are there any NPcomplete problems that have a rather large polynomial bound for reductions to other NPcomplete problems, like a polytime subhierarchy of NPcomplete problems...?
E.g. lets assume I have NPcomplete problem A and B. They are reducible to each other in lets say at most $n^3$. Does there exist a NPcomplete problem such that the best known reduction to both A and B (and all other) is, lets say, $n^{100}$.
Question: Are there NPcomplete problems with a large best known (deterministic?) polynomialtime reduction?
Question: Is there a upper (deterministic?) polynomial bound for polynomialtime reductions between NPcomplete problems
(There is a question here asking for a hierarchy of NPcomplete problems but with a different baseproblem, so solution does not really answer my question:
Understanding reductions: Would a polynomial time algorithm for

The graph of known reductions between NPcomplete problems looks a lot more like a tree than a complete graph. So for most pairs of NPcomplete problems the best known reduction follows a rather long path through that tree. Due to the blowup at each step I doubt that you'd want to implement the resulting reductions.
I doubt that there is an upper bound on the reduction size. You surely can come up with artificial problems that are very difficult to reduce to, say, SAT. I'm not aware of any family of problems with known (increasing) lower bounds for reductions though.
20171017 08:43:58