Full components and approximation algorithms for the Steiner problem

based on a result stating that the Steiner tree of minimum length can be
approximated arbitrarily well by Steiner trees that only have full
components of bounded size. This relates the Steiner problem to the
problem of finding minimum spanning subgraphs in hypergraphs. We present a
general result on the latter problem and, building on that, an algorithm
for the Steiner problem which achieves a 1.217-approximation for uniformly
quasi-bipartite instances.