Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling
Felix Zhou
TL;DR
This work addresses private graph analysis under continual release by focusing on the densest subgraph problem in insertion-only streams. It introduces a simple yet powerful strategy that couples subsampling with graph densification to achieve privacy amplification and sparsification simultaneously, thereby matching the additive error of static DP DSG algorithms while retaining the space efficiency of non-private streaming methods. The key technical advance is a black-box reduction to static DP DSG, together with a densification-based subsampling scheme that eliminates extra log factors in both error and space. The results push forward the practicality of DP graph algorithms in dynamic, large-scale networks and open the door to applying graph densification ideas to other private graph problems.
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 $O(n\log n)$ 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.