Incremental Planar Nearest Neighbor Queries with Optimal Query Time

Authors

John Iacono, Université Libre de Bruxelles
Yakov Nekrich, Michigan Technological UniversityFollow

Document Type

Conference Proceeding

Publication Date

6-20-2025

Department

Department of Computer Science

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(log1+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.

Publisher's Statement

© 2025. John Iacono and Yakov Nekrich. Publisher’s version of record: https://doi.org/10.4230/LIPIcs.SoCG.2025.59

Publication Title

Leibniz International Proceedings in Informatics Lipics

ISBN

9783959773706

Recommended Citation

Iacono, J., & Nekrich, Y. (2025). Incremental Planar Nearest Neighbor Queries with Optimal Query Time. Leibniz International Proceedings in Informatics Lipics, 332. http://doi.org/10.4230/LIPIcs.SoCG.2025.59
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1875

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Version

Publisher's PDF