Identifying the patient-zero of an epidemic outbreak, locating the person who started a rumor in a social network, finding the computer that initiated the spreading of a computer virus in a network-these are all applications of localizing the source of diffusion in a network. Since most of the networks of interest are very large, we are usually able to observe only a part of the network. In this paper, we first present a model for the dynamics of network diffusion similar to state update of a linear time-varying system. Based on this model, we provide a sufficient condition for observability of the network, i.e., we establish when is the partial information available to us sufficient to uniquely localize the source. Also, we connect the problem of finding the smallest subset of observed nodes to the problem of metric basis of the graph. We then present different methods to perform source localization depending on network observability.
Identifying the source of network diffusion is an important task in applications such as epidemics management and understanding the trend propagation over social networks. As observing each node carries a cost, we study the problem of sequential selection of observed nodes from two aspects: which nodes to observe such that the source is localized with the lowest cost, and for a pre-specified number of time-steps, which nodes to observe such that the resulting number of possible source candidates is the lowest. We show that both problems can be framed, under a simple propagation scenario, as dynamic programing with imperfect state knowledge. The proposed approach is optimal, but computationally intensive, hence we propose two simple greedy strategies. Using adaptive submodularity, we provide performance guarantees for one greedy algorithm. We evaluate the proposed approaches through simulation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.