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