Block-Structured Optimization for Subgraph Detection in Interdependent Networks

We propose a generalized framework for block-structured nonconvex optimization, which can be applied to structured subgraph detection in interdependent networks, such as multi-layer networks, temporal networks, networks of networks, and many others. Specifically, we design an effective, efficient, and parallelizable projection algorithm, namely Graph Block-structured Gradient Projection (GBGP), to optimize a general non-linear function subject to graph-structured constraints. We prove that our algorithm: 1) runs in nearly-linear time on the network size; 2) enjoys a theoretical approximation guarantee. Moreover, we demonstrate how our framework can be applied to two very practical applications and conduct comprehensive experiments to show the effectiveness and efficiency of our proposed algorithm.