高效且最优的差分隐私频繁子串挖掘
Fast and Optimal Differentially Private Frequent-Substring Mining
AI总结：
本文提出一种高效且最优的差分隐私频繁子串挖掘算法，通过优化候选生成和剪枝策略，显著降低空间和时间复杂度。
摘要：
给定一个包含n个用户贡献字符串的数据集，每个字符串长度不超过ℓ，一个关键问题是如何在保护每个用户隐私的情况下识别所有频繁子串。Bernardini等人（PODS'25）最近提出了一种ε-差分隐私算法，实现了接近最优的误差，但代价是O(n²ℓ⁴)的空间和处理时间。在本工作中，我们提出了一种新的ε-差分隐私算法，保持相同的接近最优的误差保证，同时将空间复杂度降低到O(nℓ + |Σ|)，时间复杂度降低到O(nℓ log |Σ| + |Σ|)，其中输入字母表为Σ。我们的方法基于自上而下的候选子串探索，但引入了两个新创新：（i）利用频繁前缀和后缀的结构性质的优化候选生成策略，以及（ii）由频率关系引导的搜索空间剪枝。这些技术消除了先前工作中固有的二次膨胀，使在差分隐私下实现可扩展的频繁子串挖掘成为可能。
英文摘要：
Given a dataset of $n$ user-contributed strings, each of length at most $\ell$, a key problem is how to identify all frequent substrings while preserving each user's privacy. Recent work by Bernardini et al. (PODS'25) introduced a $\varepsilon$-differentially private algorithm achieving near-optimal error, but at the prohibitive cost of $O(n^2\ell^4)$ space and processing time. In this work, we present a new $\varepsilon$-differentially private algorithm that retains the same near-optimal error guarantees while reducing space complexity to $O(n \ell+ |Σ| )$ and time complexity to $O(n \ell\log |Σ| + |Σ| )$, for input alphabet $Σ$. Our approach builds on a top-down exploration of candidate substrings but introduces two new innovations: (i) a refined candidate-generation strategy that leverages the structural properties of frequent prefixes and suffixes, and (ii) pruning of the search space guided by frequency relations. These techniques eliminate the quadratic blow-ups inherent in prior work, enabling scalable frequent substring mining under differential privacy.
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