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