Multiple Infection Sources Identification with Provable Guarantees
  Given an aftermath of a cascade in the network, i.e. a set $V_I$ of "infected" nodes after an epidemic outbreak or a propagation of rumors/worms/viruses, how can we infer the sources of the cascade? Answering this challenging question is critical for computer forensic, vulnerability analysis, and risk management. Despite recent interest towards this problem, most of existing works focus only on single source detection or simple network topologies, e.g. trees or grids.   In this paper, we propose a new approach to identify infection sources by searching for a seed set $S$ that minimizes the \emph{symmetric difference} between the cascade from $S$ and $V_I$, the given set of infected nodes. Our major result is an approximation algorithm, called SISI, to identify infection sources \emph{without the prior knowledge on the number of source nodes}. SISI, to our best knowledge, is the first algorithm with \emph{provable guarantee} for the problem in general graphs. It returns a $\frac{2}{(1-\epsilon)^2}\Delta$-approximate solution with high probability, where $\Delta$ denotes the maximum number of nodes in $V_I$ that may infect a single node in the network. Our experiments on real-world networks show the superiority of our approach and SISI in detecting true source(s), boosting the F1-measure from few percents, for the state-of-the-art NETSLEUTH, to approximately 50\%. 
Hung T. Nguyen, Preetam Ghosh, Michael L. Mayo, Thang N. Dinh
cs.SI