Activity preserving graph simplification

We study the problem of simplifying a given directed graph by keeping a small subset of its arcs. Our goal is to maintain the connectivity required to explain a set of observed traces of information propagation across the graph. Unlike previous work, we do not make any assumption about an underlying model of information propagation. Instead, we approach the task as a combinatorial problem. We prove that the resulting optimization problem is 𝐍𝐏 -hard. We show that a standard greedy algorithm performs very well in practice, even though it does not have theoretical guarantees. Additionally, if the activity traces have a tree structure, we show that the objective function is supermodular, and experimentally verify that the approach for size-constrained submodular minimization recently proposed by Nagano et al. (28th International Conference on Machine Learning, 2011 ) produces very good results. Moreover, when applied to the task of reconstructing an unobserved graph, our methods perform comparably to a state-of-the-art algorithm devised specifically for this task.