Approaches to the size constrained weighted set cover problem I am trying to solve a weighted set cover problem where the number of selected subsets is limited by a constant $k$.
Assuming this is a pretty straight-forward variation of weighted set cover I ended up quite confused with only one, also rather recent paper by Golab et al. [1].

Am I missing something here?

[1] Golab, Korn, Li, Saha and Srivastava, Size-constrained weighted set cover. In _Proceedings of 31st International Conference on Data Engineering (ICDE), pp.&nbsp;879&ndash;890. IEEE, 2015. IEEE Digital Library; author PDF.
The problem is in P and can be solved in $O(m^k)$ time, where $m$ is the number of sets to select from.  For this reason, it is fundamentally different from standard set cover (which is NP-hard) and might not have been studied as much in the complexity theory literature.