Fast and Optimal Differentially Private Frequent-Substring Mining

• URL: http://arxiv.org/abs/2603.09166v1
• Date: Tue, 10 Mar 2026 04:04:52 GMT
• Title: Fast and Optimal Differentially Private Frequent-Substring Mining
• Abstract summary: Given a dataset of $n$ user-contributed strings, each of length at most $ell$, a key problem is how to identify all frequent invocations.<n>We present a new $varepsilon$-differentially private algorithm that retains the same near-optimal error guarantees while reducing space complexity.
• Score: 2.451701057085567
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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