Dynamic Influence Analysis in Evolving Networks.

We propose the first real-time fully-dynamic index data structure designed for influence analysis on evolving networks. With this aim, we carefully redesign the data structure of the state-of-the-art sketching method introduced by Borgs et al., and construct corresponding update algorithms. Using this index, we present algorithms for two kinds of queries, influence estimation and influence maximization, which are strongly motivated by practical applications, such as viral marketing. We provide a thorough theoretical analysis, which guarantees the non-degeneracy of the solution accuracy after an arbitrary number of updates. Furthermore, we introduce a reachability-tree-based technique and a skipping method, which greatly reduce the time consumption required for edge/vertex deletions and vertex additions, respectively, and counter-based random number generators, which improve the space efficiency. Experimental evaluations using real dynamic networks with tens of millions of edges demonstrate the efficiency, scalability, and accuracy of our proposed indexing scheme. Specifically, it can reflect a graph modification within a time of several orders of magnitude smaller than that required to reconstruct an index from scratch, estimate the influence spread of a vertex set accurately within a millisecond, and select highly influential vertices at least ten times faster than state-of-the-art static algorithms.