License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.12
URN: urn:nbn:de:0030-drops-178628
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17862/
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Bandyapadhyay, Sayan ; Lochet, William ; Saurabh, Saket

FPT Constant-Approximations for Capacitated Clustering to Minimize the Sum of Cluster Radii

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LIPIcs-SoCG-2023-12.pdf (0.7 MB)

Abstract

Clustering with capacity constraints is a fundamental problem that attracted significant attention throughout the years. In this paper, we give the first FPT constant-factor approximation algorithm for the problem of clustering points in a general metric into k clusters to minimize the sum of cluster radii, subject to non-uniform hard capacity constraints (Capacitated Sum of Radii ). In particular, we give a (15+ε)-approximation algorithm that runs in 2^?(k²log k) ⋅ n³ time.
When capacities are uniform, we obtain the following improved approximation bounds.
- A (4 + ε)-approximation with running time 2^?(klog(k/ε)) n³, which significantly improves over the FPT 28-approximation of Inamdar and Varadarajan [ESA 2020].
- A (2 + ε)-approximation with running time 2^?(k/ε² ⋅log(k/ε)) dn³ and a (1+ε)-approxim- ation with running time 2^?(kdlog ((k/ε))) n³ in the Euclidean space. Here d is the dimension.
- A (1 + ε)-approximation in the Euclidean space with running time 2^?(k/ε² ⋅log(k/ε)) dn³ if we are allowed to violate the capacities by (1 + ε)-factor. We complement this result by showing that there is no (1 + ε)-approximation algorithm running in time f(k)⋅ n^?(1), if any capacity violation is not allowed.

BibTeX - Entry

@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.12,
  author =	{Bandyapadhyay, Sayan and Lochet, William and Saurabh, Saket},
  title =	{{FPT Constant-Approximations for Capacitated Clustering to Minimize the Sum of Cluster Radii}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17862},
  URN =		{urn:nbn:de:0030-drops-178628},
  doi =		{10.4230/LIPIcs.SoCG.2023.12},
  annote =	{Keywords: Clustering, FPT-approximation}
}

Keywords: Clustering, FPT-approximation
Collection: 39th International Symposium on Computational Geometry (SoCG 2023)
Issue Date: 2023
Date of publication: 09.06.2023

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