Differentially Private Triangle and 4-Cycle Counting in the Shuffle Model

TL;DR

This paper introduces one-round shuffle model algorithms for differentially private counting of triangles and 4-cycles in graphs, significantly improving accuracy over local differential privacy methods while maintaining strong privacy guarantees.

Contribution

The paper presents novel one-round shuffle model algorithms for subgraph counting, reducing estimation errors and eliminating multi-round interaction requirements.

Findings

Algorithms achieve small estimation errors under reasonable privacy budgets.

Shuffle model algorithms outperform local differential privacy methods in accuracy.

Upper bounds on estimation errors are established for each algorithm.

Abstract

Subgraph counting is fundamental for analyzing connection patterns or clustering tendencies in graph data. Recent studies have applied LDP (Local Differential Privacy) to subgraph counting to protect user privacy even against a data collector in social networks. However, existing local algorithms suffer from extremely large estimation errors or assume multi-round interaction between users and the data collector, which requires a lot of user effort and synchronization. In this paper, we focus on a one-round of interaction and propose accurate subgraph counting algorithms by introducing a recently studied shuffle model. We first propose a basic technique called wedge shuffling to send wedge information, the main component of several subgraphs, with small noise. Then we apply our wedge shuffling to counting triangles and 4-cycles -- basic subgraphs for analyzing clustering tendencies -- with several additional techniques. We also show upper bounds on the estimation error for each algorithm. We show through comprehensive experiments that our one-round shuffle algorithms significantly outperform the one-round local algorithms in terms of accuracy and achieve small estimation errors with a reasonable privacy budget, e.g., smaller than 1 in edge DP.