Detecting Multiple Information Sources in Networks under the SIR Model

In this paper, we study the problem of detecting multiple information sources in networks under the Susceptible-Infected-Recovered (SIR) model. First, assuming the number of information sources is known, we develop a sample-path-based algorithm, named clustering and localization, for trees. For $g$ -regular trees, the estimators produced by the proposed algorithm are within a constant distance from the real sources with a high probability. We further present a heuristic algorithm for general networks and an algorithm for estimating the number of sources when the number of real sources is unknown.

[1]  Chee Wei Tan,et al.  Rooting out the rumor culprit from suspects , 2013, 2013 IEEE International Symposium on Information Theory.

[2]  Wuqiong Luo,et al.  Identifying Infection Sources and Regions in Large Networks , 2012, IEEE Transactions on Signal Processing.

[3]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[4]  Devavrat Shah,et al.  Detecting sources of computer viruses in networks: theory and experiment , 2010, SIGMETRICS '10.

[5]  Wuqiong Luo,et al.  Finding an infection source under the SIS model , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[6]  Christos Faloutsos,et al.  Spotting Culprits in Epidemics: How Many and Which Ones? , 2012, 2012 IEEE 12th International Conference on Data Mining.

[7]  Jon M. Kleinberg,et al.  The small-world phenomenon: an algorithmic perspective , 2000, STOC '00.

[8]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[9]  Yue M. Lu,et al.  A fast Monte Carlo algorithm for source localization on graphs , 2013, Optics & Photonics - Optical Engineering + Applications.

[10]  Devavrat Shah,et al.  Rumor centrality: a universal source detector , 2012, SIGMETRICS '12.

[11]  Chris Arney,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World (Easley, D. and Kleinberg, J.; 2010) [Book Review] , 2013, IEEE Technology and Society Magazine.

[12]  Wuqiong Luo,et al.  Estimating infection sources in a network with incomplete observations , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[13]  Massimo Franceschetti,et al.  Rumor source detection under probabilistic sampling , 2013, 2013 IEEE International Symposium on Information Theory.

[14]  Lenka Zdeborová,et al.  Inferring the origin of an epidemy with dynamic message-passing algorithm , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Wuqiong Luo,et al.  Identifying multiple infection sources in a network , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[16]  Lei Ying,et al.  Information source detection in the SIR model: A sample path based approach , 2012, 2013 Information Theory and Applications Workshop (ITA).

[17]  Eunsoo Seo,et al.  Identifying rumors and their sources in social networks , 2012, Defense + Commercial Sensing.

[18]  Devavrat Shah,et al.  Rumors in a Network: Who's the Culprit? , 2009, IEEE Transactions on Information Theory.