Acyclic Graph Pattern Counting under Local Differential Privacy

TL;DR

This paper introduces the first general method for counting arbitrary acyclic graph patterns under local differential privacy, addressing key challenges with a recursive framework and random node marking.

Contribution

It presents a novel recursive subpattern counting framework and a random marking technique for acyclic pattern counting under LDP, filling a significant research gap.

Findings

Achieves an additive error of  O( tilde; \, sqrt{N}d(G)^k) for patterns with k edges.

Demonstrates up to 2600old improvement in utility over baseline methods.

Reduces communication cost by 300old compared to existing approaches.

Abstract

Graph pattern counting serves as a cornerstone of network analysis with extensive real-world applications. Its integration with local differential privacy (LDP) has gained growing attention for protecting sensitive graph information in decentralized settings. However, existing LDP frameworks are largely ad hoc, offering solutions only for specific patterns such as triangles and stars. A general mechanism for counting arbitrary graph patterns, even for the subclass of acyclic patterns, has remained an open problem. To fill this gap, we present the first general solution for counting arbitrary acyclic patterns under LDP. We identify and tackle two fundamental challenges: generalizing pattern construction from distributed data and eliminating node duplication during the construction. To address the first challenge, we propose an LDP-tailored recursive subpattern counting framework that incrementally builds patterns across multiple communication rounds. For the second challenge, we apply a random marking technique that restricts each node to a unique position in the pattern during computation. Our mechanism achieves strong utility guarantees: for any acyclic graph pattern with $k$ edges, we achieve an additive error of $\tilde{O}(\sqrt{N}d(G)^k)$, where $N$ is the number of nodes and $d(G)$ is the maximum degree of the input graph $G$. Experiments on real-world graph datasets across multiple types of acyclic patterns demonstrate that our mechanisms achieve up to $46$-$2600\times$ improvement in utility and $300$-$650\times$ reduction in communication cost compared to the baseline methods.