Scalable K-clique Estimation with Differential Privacy

2026-06-15

AI Summary

This work addresses the high computational complexity and poor scalability of existing methods for differentially private k-clique counting. We propose an efficient and scalable estimation algorithm that refines the step function to construct a smooth upper bound on local sensitivity and injects noise proportional to this bound within an approximate sensitivity framework. Our approach achieves, for the first time, accurate and efficient differentially private k-clique estimation on graphs with millions of edges and relatively large values of k, substantially reducing computational overhead while maintaining high accuracy. Compared to current step-function-based methods, our algorithm offers speedups of several orders of magnitude and successfully handles large-scale graph data previously intractable under differential privacy constraints.

Abstract

Counts of $k$-cliques are commonly used metrics in subgraph mining. Since graphs often have sensitive data, there also has been a lot of work on $k$-clique counts with differential privacy. However, these metrics have very high global sensitivity, and so more sophisticated techniques have been developed for counting $k$-cliques with privacy. Smooth sensitivity and ladder functions were developed for reducing the noise magnitude for private estimates of these metrics. However, these are computationally very inefficient to estimate. No polynomial time algorithms are known for smooth sensitivity of $k$-cliques for $k>3$, while the time complexity of ladder functions is lower bounded by the time for exact counts, which does not scale very well. In this paper, we develop a new highly scalable algorithm for estimating $k$-clique counts with differential privacy. Our algorithm adapts the ladder function to serve as a smooth upper bound on its local sensitivity, and utilizes the approximation sensitivity framework to calibrate noise with magnitude proportional to an approximation of the bound. This gives us a significant improvement in the running time. Experiments show that our method is several orders of magnitude faster than the ladder function based estimates of $k$-clique counts, while the accuracy is similar. Our algorithm is the first to scale to graphs with millions of edges, and for larger $k$, for which the ladder function algorithm doesn't complete.

Problem

• k-clique counting
• differential privacy
• scalability
• subgraph mining
• global sensitivity

Innovation

• differential privacy
• k-clique counting
• scalable algorithm
• approximation sensitivity
• local sensitivity