Incremental Planar Nearest Neighbor Queries with Optimal Query Time
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909573650055168 |
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| author | Iacono, John Nekrich, Yakov |
| author_facet | Iacono, John Nekrich, Yakov |
| contents | In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal $O(\log n)$ time while supporting insertions in $O(\log^{1+\varepsilon}n)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incremental Planar Nearest Neighbor Queries with Optimal Query Time Iacono, John Nekrich, Yakov Data Structures and Algorithms Computational Geometry In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal $O(\log n)$ time while supporting insertions in $O(\log^{1+\varepsilon}n)$ 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. |
| title | Incremental Planar Nearest Neighbor Queries with Optimal Query Time |
| topic | Data Structures and Algorithms Computational Geometry |
| url | https://arxiv.org/abs/2504.07366 |