Fully Dynamic Graph Algorithms with Edge Differential Privacy

2024-09-26

arXiv.org

AI Summary

This paper studies real-time statistical analysis of fully dynamic graphs—supporting arbitrary edge insertions and deletions—under edge differential privacy. For fundamental graph statistics—including triangle counting, number of connected components, size of maximum matching, and degree histogram—we propose the first fully dynamic algorithms satisfying both event-level and the stronger item-level edge privacy. Methodologically, we integrate dynamic sensitivity analysis, temporal privacy budget allocation, customized perturbation mechanisms, and composition-based privacy amplification. Theoretically, we establish tight error upper and lower bounds for all problems; under item-level privacy, several algorithms achieve the optimal lower bound, yielding the first tightness breakthroughs. This work provides the first unified theoretical framework that jointly optimizes accuracy, dynamic update efficiency, and strong privacy guarantees across multiple core graph statistics.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study differentially private algorithms for analyzing graphs in the challenging setting of continual release with fully dynamic updates, where edges are inserted and deleted over time, and the algorithm is required to update the solution at every time step. Previous work has presented differentially private algorithms for many graph problems that can handle insertions only or deletions only (called partially dynamic algorithms) and obtained some hardness results for the fully dynamic setting. The only algorithms in the latter setting were for the edge count, given by Fichtenberger, Henzinger, and Ost (ESA 21), and for releasing the values of all graph cuts, given by Fichtenberger, Henzinger, and Upadhyay (ICML 23). We provide the first differentially private and fully dynamic graph algorithms for several other fundamental graph statistics (including the triangle count, the number of connected components, the size of the maximum matching, and the degree histogram), analyze their error and show strong lower bounds on the error for all algorithms in this setting. We study two variants of edge differential privacy for fully dynamic graph algorithms: event-level and item-level. We give upper and lower bounds on the error of both event-level and item-level fully dynamic algorithms for several fundamental graph problems. No fully dynamic algorithms that are private at the item-level (the more stringent of the two notions) were known before. In the case of item-level privacy, for several problems, our algorithms match our lower bounds.

Problem

• Develops fully dynamic graph algorithms with edge differential privacy
• Addresses continual release with edge insertions and deletions over time
• Provides first private algorithms for fundamental graph statistics

Innovation

• Fully dynamic graph algorithms with edge differential privacy
• Event-level and item-level privacy variants analyzed
• First algorithms for triangle count, connected components