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arXiv · 2610.10075

BetweenCut: Private Heavy-Node Classification with Doubly Logarithmic Error in Tree Height

Ergute Bao·Graham Cormode·Xiaokui Xiao·Ting Yu
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Abstract

Finding heavy nodes in a tree---those whose counts exceed a given threshold---is a building block for analysis and learning over structured data. Achieving record-level differential privacy (DP) without sacrificing accuracy is challenging because each record contributes to counts along an entire root-to-leaf path, allowing privacy costs to accumulate across levels. Existing methods account for the multiple threshold comparisons for each record incur additive error margins of $Ω_{\varepsilon,δ}(\log h)$ or $Ω_{\varepsilon,δ}(\sqrt{\log h})$ for tree height $h$. We introduce \textsc{BetweenCut}, an $(\varepsilon,δ)$-DP algorithm with an additive error margin of $O_{\varepsilon,δ}(\log\log h)$, improving the existing bounds for deep trees. This error holds simultaneously for all nodes and is independent of the input database size.

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Ergute Bao, Graham Cormode, Xiaokui Xiao, Ting Yu. 2026-10-07. BetweenCut: Private Heavy-Node Classification with Doubly Logarithmic Error in Tree Height. https://arxiv.org/abs/2610.10075

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