Abstract. We consider the problem of reconstructing an epidemic over time, or, more general, reconstructing the propagation of an activity in a network. Our input consists of a temporal network, which contains information about when two nodes interacted, and a small sample of nodes that have been reported as infected. The goal is to recover the flow of the spread, including discovering the starting nodes, and identifying other likely-infected nodes that were not reported. This has multiple applications, from public health to social media and viral marketing purposes.

Previous work explicitly factor-in many unrealistic assumptions: (a) the underlying network does not change or that we see all interactions; (b) that we have access to perfect noise-free data; or (c) that we know the exact propagation model. In contrast, we avoid these simplifications, and take into account the temporal network, require only a small sample of reported infections, and do not make any restrictive assumptions on the propagation model.

We develop CulT, a scalable and effective algorithm to reconstruct epidemics that is also suited for an online setting. It works by formulating the problem as that of a temporal Steiner-tree computation, for which we design a fast algorithm leveraging the specific structure of our problem. We demonstrate the efficacy of CulT through extensive experiments on diverse datasets.