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Incremental Planar Nearest Neighbor Queries with Optimal Query Time

Authors John Iacono , Yakov Nekrich

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Data structures design and analysis
Keywords
  • Data Structures
  • Dynamic Data Structures
  • Nearest Neighbor Queries

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Abstract

In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal O(log n) time while supporting insertions in O(log^{1+ε} n) time. No previous data structure was known that supports O(log n)-time queries and polylog-time insertions. In order to achieve logarithmic queries our data structure uses a new technique related to fractional cascading that leverages the inherent geometry of this problem. Our method can be also used in other semi-dynamic scenarios.

Cite As Get BibTex

John Iacono and Yakov Nekrich. Incremental Planar Nearest Neighbor Queries with Optimal Query Time. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 59:1-59:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.59

Author Details

John Iacono
  • Université libre de Bruxelles, Belgium
Yakov Nekrich
  • Michigan Technological University, Houghton, MI, USA

Funding

  • Iacono, John: Research supported by the Fonds de la Recherche Scientifique - FNRS.
  • Nekrich, Yakov: Supported by the National Science Foundation under NSF grant 2203278.

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