Garg (FOCS '96) gives two approximation algorithms for the
minimum-cost tree spanning $k$ vertices in an undirected graph.
Recently Jain and Vazirani (JACM '01) discovered primal-dual
approximation algorithms for the metric uncapacitated facility
location and $k$-median problems. In this paper we show how
Garg's algorithms can be explained simply with ideas introduced
by Jain and Vazirani, in particular via a Lagrangean relaxation
technique together with the primal-dual method for approximation
algorithms. We also derive a constant factor approximation
algorithm for the $k$-Steiner tree problem using these ideas,
and point out the common features of these problems that allow
them to be solved with similar techniques.