Can an algorithm run in "O(n/a)" time?
For approximation algorithms, the algorithm must return an answer within a factor of $1\pm\epsilon$ of the true value. As such, smaller values of&nbsp;$\epsilon$ correspond to better approximations. As such, a running time that's polynomial in $n$ and&nbsp;$1/\epsilon$ is what you'd intuitively look for: it's saying that a better approximation (smaller&nbsp;$\epsilon$, so larger $1/\epsilon$) will take more time, but not by an unerasonable amount.

Also, note that we typically have an upper bound on&nbsp;$\epsilon$. For example, suppose we want to approximately compute the distance between two distinct vertices in a connected graph. We know the distance must be between $1$ and&nbsp;$n$ the number of vertices) so if we just want an approximation within $1\pm\epsilon$ and $\epsilon\ge\sqrt{n}$, we can just return $\sqrt{n}$.