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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.06090 |
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| _version_ | 1866915279431270400 |
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| author | Dullerud, Jonathan E. Har-Peled, Sariel |
| author_facet | Dullerud, Jonathan E. Har-Peled, Sariel |
| contents | We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a building block, we construct a data-structure of expected linear size, that can answer predecessor/rank queries, in constant time, for random numbers sampled uniformly from $[0,1]$.
While the basic idea we use is known [Dev89], we believe our results are still interesting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthogonal Emptiness Queries for Random Points Dullerud, Jonathan E. Har-Peled, Sariel Computational Geometry We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a building block, we construct a data-structure of expected linear size, that can answer predecessor/rank queries, in constant time, for random numbers sampled uniformly from $[0,1]$. While the basic idea we use is known [Dev89], we believe our results are still interesting. |
| title | Orthogonal Emptiness Queries for Random Points |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2505.06090 |