Fast and Optimal Differentially Private Frequent-Substring Mining

TL;DR

This paper introduces a scalable differentially private algorithm for frequent substring mining that significantly reduces computational complexity while maintaining near-optimal error guarantees.

Contribution

It presents a novel $$-differentially private algorithm with reduced space and time complexity, improving scalability over prior methods.

Findings

Achieves near-optimal error with lower computational costs.

Reduces space complexity to $O(n \u00ell + |\u03a3|)$.

Reduces time complexity to $O(n \u00ell \u2217 \u03a3 + |\u03a3|)$.

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 $O(n \ell+ |\Sigma| )$ and time complexity to $O(n \ell\log |\Sigma| + |\Sigma| )$, for input alphabet $\Sigma$. 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.