Acyclic Graph Pattern Counting under Local Differential Privacy

2026-03-20

AI Summary

This work addresses the limited generality of existing local differential privacy (LDP) approaches, which support counting only specific acyclic graph patterns such as triangles or stars. The paper proposes the first general LDP framework for counting arbitrary acyclic subgraph patterns. By leveraging a multi-round recursive construction of subpatterns, randomized labeling, and a tailored communication protocol, the method effectively handles pattern generalization and node duplication in distributed graph data while providing rigorous theoretical error bounds. Empirical evaluations on real-world datasets demonstrate utility improvements of 46–2600× over baseline methods and a 300–650× reduction in communication overhead. For an acyclic pattern with $k$ edges, the framework achieves an additive error of $\tilde{O}(\sqrt{N} \cdot d(G)^k)$, where $d(G)$ denotes the maximum degree of the graph.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• acyclic graph pattern counting
• local differential privacy
• graph analysis
• privacy-preserving

Innovation

• Local Differential Privacy
• Acyclic Graph Pattern Counting
• Recursive Subpattern Counting
• Random Marking
• Distributed Graph Analysis