On the Minimum Differentially Resolving Set Problem for Diffusion Source Inference in Networks

In this paper we theoretically study the minimum Differentially Resolving Set (DRS) problem derived from the classical sensor placement optimization problem in network source locating. A DRS of a graph G = (V, E) is defined as a subset S C V where any two elements in V can be distinguished by their different differential characteristic sets defined on S. The minimum DRS problem aims to find a DRS S in the graph G with minimum total weight ∑v∈S w(v). In this paper we establish a group of Integer Linear Programming (ILP) models as the solution. By the weighted set cover theory, we propose an approximation algorithm with the Θ(ln n) approximability for the minimum DRS problem on general graphs, where n is the graph size.

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

[2]  Jure Leskovec,et al.  Inferring networks of diffusion and influence , 2010, KDD.

[3]  Lei Ying,et al.  Information source detection in the SIR model: A sample path based approach , 2013, ITA.

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

[5]  Erik Jan van Leeuwen,et al.  On the Complexity of Metric Dimension , 2011, ESA.

[6]  Junqing Yu,et al.  Source Tracing and Pursuing of Network Virus , 2008, 2008 IEEE 8th International Conference on Computer and Information Technology Workshops.

[7]  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.

[8]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

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

[10]  Marek Cygan,et al.  Exponential-time approximation of weighted set cover , 2009, Inf. Process. Lett..

[11]  Li Guo,et al.  Locating multiple sources in social networks under the SIR model: A divide-and-conquer approach , 2015, J. Comput. Sci..

[12]  Xiaozhou Li,et al.  Efficient querying and maintenance of network provenance at internet-scale , 2010, SIGMOD Conference.

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

[14]  Lei Ying,et al.  A robust information source estimator with sparse observations , 2014 .

[15]  Martin Vetterli,et al.  Locating the Source of Diffusion in Large-Scale Networks , 2012, Physical review letters.

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

[17]  Bruno Sinopoli,et al.  Network observability and localization of the source of diffusion based on a subset of nodes , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[19]  David R. Wood,et al.  On the Metric Dimension of Cartesian Products of Graphs , 2005, SIAM J. Discret. Math..

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

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