Faster and Simpler Greedy Algorithm for $k$-Median and $k$-Means

TL;DR

This paper simplifies and accelerates a greedy approximation algorithm for $k$-median and $k$-means clustering, achieving comparable or better results than existing methods in various metric spaces.

Contribution

The authors provide a simplified version of the recursive greedy algorithm, enabling faster implementation and improved performance in graph and Euclidean metrics.

Findings

Algorithm matches or improves state-of-the-art results.

Simplification leads to faster implementation.

Effective in both graph metrics and Euclidean space.

Abstract

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.