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Dynamic L-Budget Clustering of Curves

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

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Author Details

Kevin Buchin
  • Faculty of Computer Science, TU Dortmund University, Germany
Maike Buchin
  • Faculty of Computer Science, Ruhr University Bochum, Germany
Joachim Gudmundsson
  • Faculty of Engineering, The University of Sydney, Australia
Lukas Plätz
  • Faculty of Computer Science, Ruhr University Bochum, Germany
Lea Thiel
  • Faculty of Computer Science, Ruhr University Bochum, Germany
Sampson Wong
  • Department of Computer Science, University of Copenhagen, Denmark

Funding

  • Plätz, Lukas: The work was supported by the PhD School "SecHuman - Security for Humans in Cyberspace" by the federal state of NRW.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.SWAT.2024.18

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}.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • clustering
  • streaming algorithm
  • polygonal curves
  • Fréchet distance
  • storage efficiency
  • simplification
  • approximation algorithms

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Supplementary Materials

References

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