Linear Hashing Is Optimal
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918025868869632 |
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| author | Jaber, Michael Kumar, Vinayak M. Zuckerman, David |
| author_facet | Jaber, Michael Kumar, Vinayak M. Zuckerman, David |
| contents | We prove that hashing $n$ balls into $n$ bins via a random matrix over $\mathbf{F}_2$ yields expected maximum load $O(\log n / \log \log n)$. This matches the expected maximum load of a fully random function and resolves an open question posed by Alon, Dietzfelbinger, Miltersen, Petrank, and Tardos (STOC '97, JACM '99). More generally, we show that the maximum load exceeds $r\cdot\log n/\log\log n$ with probability at most $O(1/r^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Hashing Is Optimal Jaber, Michael Kumar, Vinayak M. Zuckerman, David Data Structures and Algorithms Computational Complexity We prove that hashing $n$ balls into $n$ bins via a random matrix over $\mathbf{F}_2$ yields expected maximum load $O(\log n / \log \log n)$. This matches the expected maximum load of a fully random function and resolves an open question posed by Alon, Dietzfelbinger, Miltersen, Petrank, and Tardos (STOC '97, JACM '99). More generally, we show that the maximum load exceeds $r\cdot\log n/\log\log n$ with probability at most $O(1/r^2)$. |
| title | Linear Hashing Is Optimal |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2505.14061 |