A Stochastic Approach to Finding Densest Temporal Subgraphs in Dynamic Graphs

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 devise EMU algorithms for the densest lasting subgraph problem, as well as several variants by varying the utility function. Using real-world data, we evaluate the effectiveness and efficiency of our techniques, and compare them with two prior approaches on dense subgraph detection.