# Is there a name for approximation algorithms with $f(OPT)$ approximation factor?

I have read that there are approximation algorithms with two different kinds of approximation factors:

• $$c$$ . A constant approximation factor.
• $$f(n)$$ . An approximation factor that is function of the input size.

However, right know I'm dealing with an approximation factor of the following nature:

• $$f(OPT)$$ . Namely, an approximation factor that is a function of the optimal solution size.

Is there an special name for this kind of approximation algorithms?

• This type of ratio has been described in a number of recent papers, see for example Marx'08 and CCKLMNT'17. The latter, more recent paper refers to this as a Fixed Parameter Approximation Algorithm, or FPT-Approximation. Mar 17 at 1:08
• This is common for geometric set cover problems. There is no special name for it, because ultimately opt might be $\Theta(n)$, so people are not convinced by the importance of such cases. Mar 17 at 1:51