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Optimal Pure Differentially Private Sparse Histograms in Near-Linear Deterministic Time

Published: July 22, 2025 | arXiv ID: 2507.17017v1

By: Florian Kerschbaum, Steven Lee, Hao Wu

Potential Business Impact:

Keeps data private while showing trends.

We introduce an algorithm that releases a pure differentially private sparse histogram over $n$ participants drawn from a domain of size $d \gg n$. Our method attains the optimal $\ell_\infty$-estimation error and runs in strictly $O(n \ln \ln d)$ time in the word-RAM model, thereby improving upon the previous best known deterministic-time bound of $\tilde{O}(n^2)$ and resolving the open problem of breaking this quadratic barrier (Balcer and Vadhan, 2019). Central to our algorithm is a novel private item blanket technique with target-length padding, which transforms the approximate differentially private stability-based histogram algorithm into a pure differentially private one.

Country of Origin
🇨🇦 Canada

Page Count
41 pages

Category
Computer Science:
Data Structures and Algorithms