Clustering problems such as $k$-means and $k$-median are staples of unsupervised learning, and many algorithmic techniques have been developed to tackle their numerous aspects. In this paper, we focus on the class of greedy approximation algorithm, that attracted less attention than local-search or primal-dual counterparts. In particular, we study the recursive greedy algorithm developed by Mettu and Plaxton [SIAM J. Comp 2003]. We provide a simplification of the algorithm, allowing for faster implementation, in graph metrics or in Euclidean space, where our algorithm matches or improves the state-of-the-art.

翻译：$k$-均值与$k$-中位数等聚类问题是无监督学习的基础课题，已有多种算法技术被开发用于处理其诸多方面。本文聚焦于贪心近似算法类别，该类算法相较于局部搜索或原始对偶方法受到的关注较少。具体而言，我们研究了Mettu与Plaxton[SIAM J. Comp 2003]提出的递归贪心算法。我们提供了该算法的简化版本，在图度量或欧几里得空间中实现了更快的计算效率，且我们的算法达到或超越了当前最优性能水平。