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Exact Ratio Preservation via Outliers for Fair k-Center Clustering

Authors Anna Arutyunova, Irina Fast, Annika Hennes , Carsten Krollmann, Daniel R. Schmidt , Melanie Schmidt

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Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Fairness
  • k-center
  • approximation algorithms

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Abstract

We study the k-center clustering problem under demographic fairness constraints, where the point set is partitioned into groups, and the aim is to compute clusters that exhibit a given group proportion. Previous work in this direction assumes that the entire point set already respects the desired proportions or uses relaxed notions of fairness.
In this work, we propose a model that facilitates the creation of clusters that exactly match given target ratios, even when the input point set does not. We combine the well-known fair clustering model initiated by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [Flavio Chierichetti et al., 2017] with the notion of outliers to obtain a practical combinatorial framework that provides constant-factor approximate solutions for all proportion settings from 1:1 for two groups to t₁:t₂:…:t_m for m ≥ 2 groups, where t₁,…,t_m are integers.
We implement and evaluate our algorithms, compare different variants, and provide evidence of the practicability of this approach.

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Anna Arutyunova, Irina Fast, Annika Hennes, Carsten Krollmann, Daniel R. Schmidt, and Melanie Schmidt. Exact Ratio Preservation via Outliers for Fair k-Center Clustering. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.23

Author Details

Anna Arutyunova
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany
Irina Fast
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany
Annika Hennes
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany
Carsten Krollmann
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany
Daniel R. Schmidt
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany
Melanie Schmidt
  • Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Germany

Funding

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project 456558332 through the Emmy Noether Programme.

Supplementary Materials

References

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