Real-Time Targeted-Influence Queries over Large Graphs.

Social networks are important communication and information media. Individuals in a social network share information and influence each other through their social connections. Understanding social influence and information diffusion is a fundamental research endeavor and it has important applications in online social advertising and viral marketing. In this work, we introduce the Targeted-Influence problem (TIP): Given a network G = (V, ε) and a model of influence, we want to be able to estimate in real-time (e.g. a few seconds per query) the influence of a subset of users S over another subset of users T, for any possible query (S; T), S, T ⊆ V. To do so, we allow an efficient preprocessing. We provide the first scalable real-time algorithm for TIP. Our algorithm requires Õ(|V| + |ε|) space and preprocessing time, and it provides a provable approximation of the influence of S over T, for every subsets of nodes S, T ⊆ V in the query with large enough influence. The running time for answering each query (a.k.a query stage) is theoretically guaranteed to be Õ(|S| + |T|) in general undirected and for directed graphs under certain assumptions, supported by experiments. We also introduce the Snapshot model as our model of influence, which extends and includes as special case both the Independent Cascade and the Linear Threshold models. The analysis and the theoretical guarantees of our algorithms hold under the more general Snapshot model. Finally, we perform an extensive experimental analysis, demonstrating the accuracy, efficiency, and scalability of our methods.