I am trying to understand the difference between $\epsilon$-additive and $\epsilon$-multiplicative algorithms. The way I understand this definition is as follows. An $\epsilon$-additive algorithm is one that, for a true solution OPT, returns $OPT' \in [OPT - \epsilon, OPT + \epsilon]$. For an $\epsilon$-multiplicative algorithm, we have $OPT'' \in [OPT(1 - \epsilon), OPT(1+\epsilon)]$. While I can see the differences between these (for instance, if true OPT = 10 and $\epsilon = 0.1$, then in one case, the error is $\pm 0.1$, while in the other, it is $\pm 1$), I would like to know the answers to the following questions:
1) Why is it sometimes easier to achieve $\epsilon$-additive accuracy than $\epsilon$-multiplicative (example, as stated in https://arxiv.org/pdf/0801.1987.pdf)?
2) When is one type of accuracy more important or relevant than the other?
3) How can one one translate between the two? For instance, if you tell me an algorithm solves a problem to $\epsilon$-additive accuracy in time $T$, is it possible to say how fast it will be for $\epsilon$-multiplicative accuracy? (and vice versa)?