  Network analysis has played a key role in knowledge discovery and data
mining. In many real-world applications in recent years, we are interested in
mining multilayer networks, where we have a number of edge sets called layers,
which encode different types of connections and/or time-dependent connections
over the same set of vertices. Among many network analysis techniques, dense
subgraph discovery, aiming to find a dense component in a network, is an
essential primitive with a variety of applications in diverse domains. In this
paper, we introduce a novel optimization model for dense subgraph discovery in
multilayer networks. Our model aims to find a stochastic solution, i.e., a
probability distribution over the family of vertex subsets, rather than a
single vertex subset, whereas it can also be used for obtaining a single vertex
subset. For our model, we design an LP-based polynomial-time exact algorithm.
Moreover, to handle large-scale networks, we also devise a simple, scalable
preprocessing algorithm, which often reduces the size of the input networks
significantly and results in a substantial speed-up. Computational experiments
demonstrate the validity of our model and the effectiveness of our algorithms.
