Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling
This work addresses privacy-preserving graph analysis for applications like social networks, though it is incremental as it builds on prior DP and streaming methods.
The paper tackles the problem of releasing densest subgraphs continually under edge-differential privacy in a streaming setting, achieving an additive error of O(log n) and space complexity of O(n log n), matching the best static DP algorithms and non-private streaming algorithms.
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.