Finding Densest Lasting Subgraphs in Dynamic Graphs: A Stochastic Approach

Abstract

One important problem that is insufficiently studied is finding densest lasting-subgraphs in large dynamic graphs, which considers the time duration of the subgraph pattern. We propose a framework called Expectation-Maximization with Utility functions (EMU), a novel stochastic approach that nontrivially extends the conventional EM approach. EMU has the flexibility of optimizing any user-defined utility functions. We validate our EMU approach by showing that it converges to the optimum—by proving that it is a specification of the general Minorization-Maximization (MM) framework with convergence guarantees. We then devise EMU algorithms for the densest lasting subgraph problem. Using real-world graph data, we experimentally verify the effectiveness and efficiency of our techniques, and compare with two prior approaches on dense subgraph detection.