Is there an algorithm for finding minimal covers of a set of sets in which each element of the universe appears in exactly 2 sets? I realize that LP relaxation approximates this to within a factor of 2.



Minimum cover for sets in which each element appears in exactly 2 sets?
This is the well-known problem of [Minimum Vertex Cover](https://en.wikipedia.org/wiki/Vertex_cover). It is conjectured to be NP-hard to approximate within $2-\epsilon$ for any $\epsilon > 0$. Many $2$-approximation algorithms exist.


