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arXiv · 2504.16507

Streaming algorithms for products of probabilities

Markus Lohrey·Leon Rische·Louisa Seelbach Benkner·Julio Xochitemol
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Abstract

We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-\epsilon$. It is shown that every randomized streaming algorithm for this problem needs space $\Omega(\log n + \log b - \log \epsilon) - \mathcal{O}(1)$, 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 $\Omega(n \cdot b)$.

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Markus Lohrey, Leon Rische, Louisa Seelbach Benkner, Julio Xochitemol. 2025-04-23. Streaming algorithms for products of probabilities. https://arxiv.org/abs/2504.16507

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