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arXiv · 2306.01867

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

Emmett Breen·Renee Mirka·Zichen Wang·David P. Williamson
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Abstract

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.

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Emmett Breen, Renee Mirka, Zichen Wang, David P. Williamson. 2023-06-02. Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs. https://doi.org/10.1137/1.9781611977585.ch6

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