Summary: The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order \(O(c^n)\), but with the constant \(c\) as small as possible. In this work we extend this line of research and we investigate whether the constant \(c\) can be made even smaller when one allows constant factor approximation.In fact, we describe a kind of approximation schemes-trade-offs between approximation factor and the time complexity. We use general transformations from exponential-time exact algorithms to approximations that are faster but still exponential-time. For example, we show that for any reduction rate \(r\), one can transform any \(O^{*}(c^n)\)-time\(^{1}\) algorithm for Set Cover into a (1+\(\ln r\))-approximation algorithm running in time \(O^{*}(c^n/r)\). We believe that results of that kind extend the applicability of exact algorithms for NP-hard problems.