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FPT Approximations for Capacitated Sum of Radii and Diameters

Authors Arnold Filtser , Ameet Gadekar

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LIPIcs.SoCG.2026.48.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Facility location and clustering
Keywords
  • clustering
  • sum of radii
  • sum of diameter
  • capacitated clustering
  • fpt

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Abstract

The Capacitated Sum of Radii problem involves partitioning a set of points P, where each point p ∈ P has capacity U_p, into k clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered at point p is at most U_p. We begin by showing that the problem is APX-hard, and that under gap-ETH there is no parameterized approximation scheme (FPT-AS). We then construct a ≈5.83-approximation algorithm in FPT time (improving a previous ≈7.61 approximation in FPT time). Our results also hold when the objective is a general monotone symmetric norm of radii. We also improve the approximation factors for the uniform capacity case, and for the closely related problem of Capacitated Sum of Diameters.

Cite As Get BibTex

Arnold Filtser and Ameet Gadekar. FPT Approximations for Capacitated Sum of Radii and Diameters. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.48

Author Details

Arnold Filtser
  • Bar-Ilan University, Ramat Gan, Israel
Ameet Gadekar
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

Funding

  • Filtser, Arnold: This research was supported by the Israel Science Foundation (Grant No. 1042/22).
  • Gadekar, Ameet: This work was partially supported by the Israel Science Foundation (Grant No. 1042/22) while the author was affiliated with Bar-Ilan University.

Acknowledgements

The authors thank the anonymous reviewer for suggesting the construction used in Theorem 2, which improves upon the one presented in an earlier version of the paper.

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