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Incremental Consistent k-Center Clustering

Authors Mara Grilnberger , Antonis Skarlatos

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Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • Consistent Clustering
  • k-Center
  • Dynamic Algorithms

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Abstract

In the incremental consistent k-center clustering problem, we are given a sequence of adversarial point insertions and aim to maintain a k-center solution with small approximation ratio and small recourse. In this work, we explore the following question: what is the best approximation ratio of a polynomial-time algorithm with a worst-case recourse of 1? Our result improves upon the 6-approximation algorithm of Forster and Skarlatos [SODA '25], which itself improved over the 8-approximation algorithm of Charikar, Chekuri, Feder, and Motwani [STOC '97]. Moreover, we show that any incremental k-center algorithm that achieves an approximation ratio strictly less than √ 2 requires a worst-case recourse of k.

Cite As Get BibTex

Mara Grilnberger and Antonis Skarlatos. Incremental Consistent k-Center Clustering. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.29

Author Details

Mara Grilnberger
  • Department of Computer Science, University of Salzburg, Austria
Antonis Skarlatos
  • Department of Computer Science, University of Warwick, Coventry, UK

Funding

  • Grilnberger, Mara: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 947702). This publication has been supported by the EXDIGIT (Excellence in Digital Sciences and Interdisciplinary Technologies) project, funded by Land Salzburg under grant number 20204-WISS/263/6-6022.
  • Skarlatos, Antonis: Antonis Skarlatos is funded by the European Union (ERC grant, DYNALP, 101170133). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

References

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