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Incremental Planar Nearest Neighbor Queries with Optimal Query Time

par Iacono, John ;Nekrich, Yakov
Référence Leibniz international proceedings in informatics, 332, 59
Publication Publié, 2025-06-01

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Résumé :

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.