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Incremental Planar Nearest Neighbor Queries with Optimal Query Time

par Iacono, John ;Nekrich, Yakov
Référence arXiv.org, arXiv:2504.07366
Publication Publié, 2025-04-09

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Résumé :

In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal time while supporting insertions in time. No previous data structure was known that supports -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.