Exact algorithms for NP-complete problems are sometimes feasible, if the input is small enough.
I’ve also came across some algorithms which are not practical even for very small inputs, and their importance is questionable.
I’m wondering what's the "hardest" (time complexity-wise) problems people have worked on its exact solution:
- The problem is in NP.
- A non-trivial exact algorithm is known for the problem (preferably from the last few years).
- No better algorithm is known.
For example, the minimum dominating set of queens has an algorithm which runs in $O(39.51^n\cdot poly(n))$ time.