Minimal Covering Set: System of Distinct Representatives

[WWGD]

Hi All,
Let $s: \{s_1,s_2,...,s_j \}$ be a collection of elements contained in the sets $S:=\{S_1,S_2,...S_k \}$ , no relation between $j,k$; a given $s_i$ may be contained in one or more $S_n$. I want to find a minimal "cover" for $s$, i.e., the smallest subcollection of sets in $S$ that contains every element in $s$. I think this is called an SDR : System of Distinct Representatives.
Is there a general formula dealing with this? Obviously, $k$ is an upper bound.

 

[mfb]

This is called set cover problem, and it is NP-complete.