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

Authors Max Dupré la Tour , David Saulpic

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LIPIcs.ICALP.2026.84.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • Clustering
  • k-means
  • approximation algorithm

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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: our algorithm matches the state-of-the-art running time for computing a constant-factor approximation in Euclidean space and graph metrics, and, in addition, is the first near-linear-time to compute a polylogarithmic approximation in Euclidean space.

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Max Dupré la Tour and David Saulpic. Faster and Simpler Greedy Algorithm for k-Median and k-Means. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.84

Author Details

Max Dupré la Tour
  • McGill University, Montreal, Canada
David Saulpic
  • CNRS & Université Paris Cité, IRIF, F-75013, Paris, France

References

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