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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引用次数: 1

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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图中k-MST问题的Garg 2-逼近算法重述
本文根据Paul等人最近的一篇论文,重新审视了Garg提出的$k$-MST的2逼近算法。在$k$-MST问题中,目标是返回一棵树,它生成$k$个顶点,并且总边代价最小。Paul等人扩展了Garg的原始对偶子程序,以改进预算奖励旅行推销员和最小生成树问题的近似比率。我们遵循他们的算法和分析,提供一个更清晰的Garg结果。此外,我们引入了核的新概念,它可以更容易地可视化算法的各个阶段,并更清楚地理解修剪阶段。其他值得注意的更新包括提出k -MST问题的线性规划公式,包括伪代码,用更简单的中性集概念取代Garg使用的着色方案,并提供显式的势函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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