Moderate complexity between polynomial and exponential There are ,,plenty'' of functions growing faster then any polynomial and at the same time growing slower than any exponential function (with base $>1$) e.g. $f(x)=e^{g(x)}$ where $g(x)=\log^{c} x$ where $c>1$ or $g(x)=x^c$ where $c \in (0,1)$. I would like to know some examples of problems for which there are (most efficient) algorithms which run in the time $f(n)$ for any such $f$. This question is motivated by the visible dichotomy between polynomial time algoritms and exponential time algoritms which one encounters in almost all classical problems. 

The Graph isomorphism problem is an example of a problem unknown to be in $\text{P}$, that was conjectured to not be $\text{NP-Hard}$, and relatively recently (2015) Laszlo Babai published a paper proving it can be done in $\exp(\log(n)^{O(1)})$ which is quasi-polynomial time.
Remark: Someone found a mistake in the paper, that was later fixed.
