Sorry if my question is banal. Consider an approximation scheme such as FPTAS that guarantees to find a soln>(1-eps)OPT for maximization. Now consider if OPT=exp(|input|) so It easily can be seen that soln is exp(|input|) So its run-time will be exponential too(just a print of result is exponential). So can we say the condition OPT<P(|input|) is a necessary condition for any problem that we want to find an approximation scheme algorithm for that?
Is there an implicit condition OPT
approximation