Picking elements from a set covering

Question

I came recently to the following optimization problem:

"Let {${S_{1},S_{2},...,S_{n}}$} be a covering of the set $U$. The task is to pick the maximum number of elements from the set $U$ in such a way that from each subset $S_{k}$ at most one element is extracted."

Does anybody know how this problem is called in discrete optimization? Do you know some book or paper where it is treated? Thanks a lot. Janos

Answer 1

In fact the problem above seems to be a variant of the exact hitting set problem. In my case the hitting constraint is relaxed to "at most one" and the requirement is a maximization of the hitting set. Thank you for the useful answer!