Consider a weighted graph $G=(V,E,w)$. We are given a family of $k$ disjoint subsets of vertices $V_1, \cdots, V_k$.
A Steiner Forest is a forest that for each subset of vertices $V_i$ connects all of the vertices in this subset with a tree.
Example: only one subset of vertices $V_1 = V$. In this case a Steiner forest is a spanning tree of the whole graph.
Finding such a forest with minimal weight is difficult (NP-complete). Do you know any quicker approximate algorithm to find such a forest with non-optimal weight?