An Efficient Private Algorithm for Community Detection

2026-06-12

AI Summary

This work addresses the challenge of achieving differentially private exact community recovery in the stochastic block model (SBM). The authors propose a novel adaptive disjoint-star algorithmic framework that explores graph structure by querying node degrees over edge-disjoint subgraphs, with differential privacy guarantees built into the design. For the first time, this approach enables differentially private exact recovery with nearly linear time and space complexity across a broad parameter regime. Under a constant privacy budget, the method scales to graphs two orders of magnitude larger than those handled by existing techniques, substantially advancing both scalability and practical applicability in private community detection.

Abstract

In this paper, we study the community detection problem in the stochastic block model (SBM) under privacy constraints. We introduce private and highly efficient algorithms for exact community detection within the SBM framework. Our algorithms represent the first differentially private methods capable of achieving exact recovery in a wide range of model parameters with near-linear time and space complexity. This is a significant improvement over previous SBM recovery algorithms, which either required pseudo-polynomial time or a quadratic scaling of resources for a constant privacy budget. Central to our approach is the introduction of a new concept, adaptive disjoint-star algorithms. These algorithms efficiently explore the graph's structure by querying node degrees on edge-disjoint subgraphs. We demonstrate that this general class of algorithms inherently offers strong privacy guarantees, a result that potentially holds value beyond the scope of SBM community detection. Finally, in we perform an empirical analysis of our algorithms showing that they can scale exact recovery on graphs with two orders of magnitude more nodes than prior work.

Problem

• community detection
• stochastic block model
• differential privacy
• exact recovery
• privacy constraints

Innovation

• differentially private
• stochastic block model
• exact recovery
• adaptive disjoint-star algorithms
• near-linear complexity