Is there a name for the following problem?
Given a bipartite graph $G = (U,V,E)$:
What is a minimum subset $U'$ of $U$ that covers all of $V$?
(i.e. every vertex of $V$ is connected to at least on vertex of $U'$)
For example, in the graph above, the set $[u_2, u_3]$ (the vertices 2 and 3 of $U$) is a solution.