A Stochastic Approach to Finding Densest Temporal Subgraphs in Dynamic Graphs

Xuanming Liu, Tingjian Ge, Yinghui Wu

Abstract: One important problem that is insufficiently studied is finding densest <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lasting</i> -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.