  This paper revisits the 2-approximation algorithm for $k$-MST presented by
Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the
goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul
et al. extend Garg's primal-dual subroutine to improve the approximation ratios
for the budgeted prize-collecting traveling salesman and minimum spanning tree
problems. We follow their algorithm and analysis to provide a cleaner version
of Garg's result. Additionally, we introduce the novel concept of a kernel
which allows an easier visualization of the stages of the algorithm and a
clearer understanding of the pruning phase. Other notable updates include
presenting a linear programming formulation of the $k$-MST problem, including
pseudocode, replacing the coloring scheme used by Garg with the simpler concept
of neutral sets, and providing an explicit potential function.
