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Streaming Diameter of High-Dimensional Points

Authors Magnús M. Halldórsson , Nicolaos Matsakis , Pavel Veselý

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  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • streaming algorithm
  • farthest pair
  • diameter
  • minimum enclosing ball
  • coreset

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Abstract

We improve the space bound for streaming approximation of Diameter but also of Farthest Neighbor queries, Minimum Enclosing Ball and its Coreset, in high-dimensional Euclidean spaces. In particular, our deterministic streaming algorithms store 𝒪(ε^{-2}log(1/(ε))) points. This improves by a factor of ε^{-1} the previous space bound of Agarwal and Sharathkumar (SODA 2010), while retaining the state-of-the-art approximation guarantees, such as √2+ε for Diameter or Farthest Neighbor queries, and also offering a simpler and more complete argument. Moreover, we show that storing Ω(ε^{-1}) points is necessary for a streaming (√2+ε)-approximation of Farthest Pair and Farthest Neighbor queries.

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Magnús M. Halldórsson, Nicolaos Matsakis, and Pavel Veselý. Streaming Diameter of High-Dimensional Points. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 58:1-58:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.58

Author Details

Magnús M. Halldórsson
  • Department of Computer Science, Reykjavik University, Iceland
Nicolaos Matsakis
  • Department of Computer Science, Reykjavik University, Iceland
Pavel Veselý
  • Computer Science Institute of Charles University, Prague, Czech Republic

Funding

  • Halldórsson, Magnús M.: Partially supported by Icelandic Research Fund grant 2511609.
  • Matsakis, Nicolaos: Partially supported by Icelandic Research Fund grant 2511609 and by Czech Science Foundation project 22-22997S.
  • Veselý, Pavel: Partially supported by Czech Science Foundation project 22-22997S, by ERC-CZ project LL2406 of the Ministry of Education of Czech Republic, and by Center for Foundations of Modern Computer Science (Charles Univ. project UNCE 24/SCI/008).

Acknowledgements

We would like to thank Martin Tancer for helpful discussions on high-dimensional geometry.

References

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