Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs

This paper revisits the 2-approximation algorithm for k-MST presented by Garg [9] in light of a recent paper of Paul et al. [14]. In the k-MST problem, the goal is to return a tree spanning k vertices of minimum total edge cost. Paul et al. [14] 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.