Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling

2025-10-13

AI Summary

This paper studies the densest subgraph (DSG) problem under edge differential privacy in the insertion-only data stream model with continual release. To address the limitations of existing static differentially private (DP) algorithms—namely, large additive error—and non-private streaming algorithms—namely, high space overhead—we propose a unified framework integrating subsampling-based privacy amplification and sparsification, formally characterizing the privacy amplification gain from subsampling in graph DP for the first time. We further introduce a graph densification mechanism to eliminate redundant logarithmic factors. Leveraging black-box reductions, our approach seamlessly integrates streaming computation with static DP mechanisms, supporting both pure and approximate DP. Theoretically, our algorithm achieves optimal $O(log n)$ additive error—matching the known lower bound for static DP—and $O(n log n)$ space complexity—matching the space efficiency of non-private streaming algorithms—thus attaining state-of-the-art accuracy and space efficiency simultaneously.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Data Stream Mining
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We study the sublinear space continual release model for edge-differentially private (DP) graph algorithms, with a focus on the densest subgraph problem (DSG) in the insertion-only setting. Our main result is the first continual release DSG algorithm that matches the additive error of the best static DP algorithms and the space complexity of the best non-private streaming algorithms, up to constants. The key idea is a refined use of subsampling that simultaneously achieves privacy amplification and sparsification, a connection not previously formalized in graph DP. Via a simple black-box reduction to the static setting, we obtain both pure and approximate-DP algorithms with $O(log n)$ additive error and $O(nlog n)$ space, improving both accuracy and space complexity over the previous state of the art. Along the way, we introduce graph densification in the graph DP setting, adding edges to trigger earlier subsampling, which removes the extra logarithmic factors in error and space incurred by prior work [ELMZ25]. We believe this simple idea may be of independent interest.

Problem

• Achieving edge-differential privacy in continual release densest subgraph algorithms
• Matching additive error of static DP algorithms with sublinear space
• Using subsampling for simultaneous privacy amplification and sparsification

Innovation

• Subsampling achieves privacy amplification and sparsification
• Graph densification removes logarithmic error factors
• Black-box reduction enables sublinear space complexity