Abstract
Locating source of information diffusion in networks has very important applications such as locating the sources of epidemics, news/rumors in social networks or online computer virus. In this paper, we consider detecting multiple rumor sources from a deterministic point of view by modeling it as the set resolving set (SRS) problem. Let G be a network on n nodes. A node subset K is an SRS of G if all detectable node sets are distinguishable by K. The problem of multiple rumor source detection (MRSD) in the network can be modeled as finding an SRS K with the smallest cardinality. In this paper, we propose a polynomial-time greedy algorithm for finding a minimum SRS in a general network, achieving performance ratio \(O(\ln n)\). This is the first work establishing a relation between the MRSD problem and a deterministic concept of SRS, and a first work to give the minimum SRS problem a polynomial-time performance-guaranteed approximation algorithm. Our framework suggests a robust and efficient approach for estimating multiple rumor sources independent of diffusion models in networks.
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References
Agaskar A, Lu YM (2013) A fast monte carlo algorithm for source localization on graphs. In: SPIE optical engineering and applications
Berman P, DasGupta B, Kao M (2005) Tight approximability results for test set problems in bioinformatics. J Comput Syst Sci 71:145–162
Chen X, Wang C (2014) Approximability of the minimum weighted doubly resolving set problem. In: COCOON 2014, LNCS 8591, pp 357368
Dong W, Zhang W, Tan CW (2013) Rooting out the rumor culprit from suspects. In: Proceedings of the IEEE international symposium on information theory (ISIT), Istanbul, pp 2671–2675
Du D-Z, Ko K-I, Hu X (2012) Design and analysis of approximation algorithms. Springer, New York
Ganesh A, Massouli L, Towsley D (2005) The effect of network topology on the spread of epidemics. In: IEEE INFOCOM
Gerschenfeld A, Montanari A (2007) Reconstruction for models on random graphs. In: Proceedings of the 48th IEEE symposium on foundations of computer science, pp 194–204
Karamchandani N, Franceschetti M (2013) Rumor source detection under probabilistic sampling. In: Proceedings of the IEEE international symposium on information theory (ISIT), Istanbul
Leskovec J, Adamic LA, Huberman BA (2007) The dynamics of viral marketing. ACM Trans Web 1(1):5
Lokhov AY, Mezard M, Ohta H, Zdeborova L (2013) Inferring the origin of an epidemic with dynamic message-passing algorithm. arXiv:1303.5315
Luo W, Tay WP (2012) Identifying multiple infection sources in a network. In: Proceedings of the asilomar conference on signals, systems and computers
Luo W, Tay WP (2013) Finding an infection source under the SIS model. In: Proceedings of the IEEE international conference on acoustics, speech and signal (ICASSP), Vancouver
Luo W, Tay WP (2013) Estimating infection sources in a network with incomplete observations. In: Proceedings of the IEEE global conference on signal and information processing (GlobalSIP), Austin, pp 301–304
Luo W, Tay WP, Leng M (2013) Identifying infection sources and regions in large networks. IEEE Trans Signal Process 61:2850–2865
Moore C, Newman MEJ (2000) Epidemics and percolation in smallworld networks. Phys Rev E 61:5678–5682
Pinto PC, Thiran P, Vetterli M (2012) Locating the source of diffusion in large-scale networks. Phys Rev Lett 109:068–702
Prakash BA, Vreeken J, Faloutsos C (2012) Spotting culprits in epidemics: how many and which ones? In: IEEE international conference data mining (ICDM), Brussels, pp 11–20
Seo E, Mohapatra P, Abdelzaher T (2012) Identifying rumors and their sources in social networks. In: SPIE defense, security, and sensing
Shah D, Zaman T (2010) Finding sources of computer viruses in networks: theory and experiment. Proc ACM Sigmetrics 15:5249–5262
Shah D, Zaman T (2011) Rumors in a network: whos the culprit? IEEE Trans Inf Theory 57:5163–5181
Shah D, Zaman T (2012) Rumor centrality: a universal source detector. In: Proceedings of the ACM SIGMETRICS conference, London, pp 199–210
Zhu K, Ying L (2013) Information source detection in the SIR model: a sample path based approach. In: Proceedings of the information theory and applications workshop (ITA)
Zhu K, Ying L (2014) A robust information source estimator with sparse observations. In: Proceedings of the IEEE international conference on computer communications (INFOCOM), Toronto. arXiv:1309.4846v1
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This research is supported by NSFC (61222201,61472272), SRFDP (20126501110001), Xingjiang Talent Youth Project (2013711011).
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Zhang, Z., Xu, W., Wu, W. et al. A novel approach for detecting multiple rumor sources in networks with partial observations. J Comb Optim 33, 132–146 (2017). https://doi.org/10.1007/s10878-015-9939-x
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DOI: https://doi.org/10.1007/s10878-015-9939-x