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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16507 |
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| _version_ | 1866915526787203072 |
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| author | Lohrey, Markus Rische, Leon Benkner, Louisa Seelbach Xochitemol, Julio |
| author_facet | Lohrey, Markus Rische, Leon Benkner, Louisa Seelbach Xochitemol, Julio |
| contents | We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-ε$. It is shown that every randomized streaming algorithm for this problem needs space $Ω(\log n + \log b - \log ε) - \mathcal{O}(1)$, where $n$ is length of the input stream and $b$ is the bit length of the input numbers. This matches an upper bound from Alur et al.~up to a constant multiplicative factor. Moreover, we consider the threshold problem, where it is asked whether the product of the input probabilities is below a given threshold. It is shown that every randomized streaming algorithm for this problem needs space $Ω(n \cdot b)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Streaming algorithms for products of probabilities Lohrey, Markus Rische, Leon Benkner, Louisa Seelbach Xochitemol, Julio Data Structures and Algorithms We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-ε$. It is shown that every randomized streaming algorithm for this problem needs space $Ω(\log n + \log b - \log ε) - \mathcal{O}(1)$, where $n$ is length of the input stream and $b$ is the bit length of the input numbers. This matches an upper bound from Alur et al.~up to a constant multiplicative factor. Moreover, we consider the threshold problem, where it is asked whether the product of the input probabilities is below a given threshold. It is shown that every randomized streaming algorithm for this problem needs space $Ω(n \cdot b)$. |
| title | Streaming algorithms for products of probabilities |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2504.16507 |