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arXiv · 2211.11718

Private Counting of Distinct and k-Occurring Items in Time Windows

Badih Ghazi·Ravi Kumar·Pasin Manurangsi·Jelani Nelson
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Abstract

In this work, we study the task of estimating the numbers of distinct and $k$-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times $t_1$ and $t_2$), or are restricted to being cumulative (between times $1$ and $t_2$), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last $W$ updates with error polylogarithmic in $W$; this answers an open question of Bolot et al. (ICDT 2013).

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Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Jelani Nelson. 2022-11-21. Private Counting of Distinct and k-Occurring Items in Time Windows. https://arxiv.org/abs/2211.11718

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