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L-Budget Clustering (SWAT 24)

Authors: Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Lukas Plätz, Lea Thiel, and Sampson Wong

Abstract

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Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Lukas Plätz, Lea Thiel, Sampson Wong. L-Budget Clustering (SWAT 24) (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22471,
   title = {{L-Budget Clustering (SWAT 24)}}, 
   author = {Buchin, Kevin and Buchin, Maike and Gudmundsson, Joachim and Pl\"{a}tz, Lukas and Thiel, Lea and Wong, Sampson},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:c28806ab33cb4a564e1d492efd322b1dc32f7245;origin=https://github.com/NathenMat/SWAT24;visit=swh:1:snp:a052784ff6c68e081ad8aefeaedc032aef15e906;anchor=swh:1:rev:1d5a24b78bbc02b2b3c1e30bce4378db47c66101}{\texttt{swh:1:dir:c28806ab33cb4a564e1d492efd322b1dc32f7245}} (visited on 2024-11-28)},
   url = {https://github.com/NathenMat/SWAT24},
   doi = {10.4230/artifacts.22471},
}

Document

DOI: 10.4230/LIPIcs.SWAT.2024.18

Dynamic L-Budget Clustering of Curves

Authors: Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Lukas Plätz, Lea Thiel, and Sampson Wong

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract

A key goal of clustering is data reduction. In center-based clustering of complex objects therefore not only the number of clusters but also the complexity of the centers plays a crucial role. We propose L-Budget Clustering as unifying perspective on this task, optimizing the clustering under the constraint that the summed complexity of all centers is at most L. We present algorithms for clustering planar curves under the Fréchet distance, but note that our algorithms more generally apply to objects in metric spaces if a notion of simplification of objects is applicable. A scenario in which data reduction is of particular importance is when the space is limited. Our main result is an efficient (8 + ε)-approximation algorithm with a (1 + ε)-resource augmentation that maintains an L-budget clustering under insertion of curves using only O(Lε^{-1}) space and O^*(L³log(L) + L²log(r^*/r₀)) time where O^* hides factors of ε^{-1}.

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Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Lukas Plätz, Lea Thiel, and Sampson Wong. Dynamic L-Budget Clustering of Curves. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{buchin_et_al:LIPIcs.SWAT.2024.18,
  author =	{Buchin, Kevin and Buchin, Maike and Gudmundsson, Joachim and Pl\"{a}tz, Lukas and Thiel, Lea and Wong, Sampson},
  title =	{{Dynamic L-Budget Clustering of Curves}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.18},
  URN =		{urn:nbn:de:0030-drops-200588},
  doi =		{10.4230/LIPIcs.SWAT.2024.18},
  annote =	{Keywords: clustering, streaming algorithm, polygonal curves, Fr\'{e}chet distance, storage efficiency, simplification, approximation algorithms}
}

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Documents authored by Thiel, Lea

L-Budget Clustering (SWAT 24)

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Dynamic L-Budget Clustering of Curves

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