The Binary Tree Mechanism is Optimal for Differentially Private Continual Counting
Private continual counting is a fundamental problem in differential privacy: given a binary stream of length $n$, where each $1$ corresponds to the contribution of one individual, the goal is to release all running counts while protecting the privacy of each individual. For fixed privacy parameters, the standard binary tree mechanism achieves expected $\ell_\infty$ error $O(\log^{3/2} n)$ under approximate differential privacy and $O(\log^2 n)$ under pure differential privacy. Whether these dependences on the stream length are necessary has remained a central open problem. For fixed $\varepsilon\in(0,1)$, we prove a lower bound of $Ω(\log^{3/2} n)$ under approximate DP with sufficiently s...
| Authors | Konstantina Bairaktari, Markus Engelund Dahl, Kasper Green Larsen |
|---|---|
| Primary category | cs.DS |
| Published | 1 July 2026 |
| Last updated at source | 18 September 2026 |
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