There are well-known families of approximation algorithms.
PTAS (Polynomial-Time Approximation Scheme)
A $\operatorname{PTAS}$ is a family of algorithms that achieves a $(1 + \epsilon)$-approximation for minimization problems and a $(1 - \epsilon)$-approximation for maximization problems. The running time may depend on $\epsilon$, but must be polynomial in the input size (without any polynomial restriction on $\epsilon$).
FPTAS (Fully Polynomial-Time Approximation Scheme)
An $\operatorname{FPTAS}$ is a $\operatorname{PTAS}$ whose running time is also bounded by a polynomial in $\frac{1}{\epsilon}$.