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Fully Dynamic k-Means Coreset in Near-Optimal Update Time

Authors Max Dupré la Tour , Monika Henzinger , David Saulpic

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Author Details

Max Dupré la Tour
  • McGill University, Montreal, Canada
Monika Henzinger
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria
David Saulpic
  • CNRS & IRIF, Université Paris Cité, France

Funding

  • Henzinger, Monika: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct Grant agreement No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024.
  • Saulpic, David: Work partially done while at ISTA. Received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).

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Max Dupré la Tour, Monika Henzinger, and David Saulpic. Fully Dynamic k-Means Coreset in Near-Optimal Update Time. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 100:1-100:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.100

Abstract

We study in this paper the problem of maintaining a solution to k-median and k-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that allows easy computation of a clustering solution at query time. Our coreset algorithm has near-optimal update time of Õ(k) in general metric spaces, which reduces to Õ(d) in the Euclidean space ℝ^d. The query time is O(k²) in general metrics, and O(kd) in ℝ^d. 
To maintain a constant-factor approximation for k-median and k-means clustering in Euclidean space, this directly leads to an algorithm with update time Õ(d), and query time Õ(kd + k²). To maintain a O(polylog k)-approximation, the query time is reduced to Õ(kd).

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • clustering
  • fully-dynamic
  • coreset
  • k-means

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