Source Localization in Networks: Trees and Beyond

Information diffusion in networks can be usedto model many real-world phenomena, including rumorspreading on online social networks, epidemics in humanbeings, and malware on the Internet. Informally speaking,the source localization problem is to identify a node in thenetwork that provides the best explanation of the observeddiffusion. Despite significant efforts and successes overlast few years, theoretical guarantees of source localizationalgorithms were established only for tree networks dueto the complexity of the problem. This paper presents anew source localization algorithm, called the Short-Fat Tree(SFT) algorithm. Loosely speaking, the algorithm selects thenode such that the breadth-first search (BFS) tree from thenode has the minimum depth but the maximum numberof leaf nodes. Performance guarantees of SFT under theindependent cascade (IC) model are established for both treenetworks and the Erdos-Renyi (ER) random graph. On treenetworks, SFT is the maximum a posterior (MAP) estimator.On the ER random graph, the following fundamental limitshave been obtained: (i) when the infection duration <23 tu,SFT identifies the source with probability one asymptotically,wheretu =⌈log nlog μ⌉+ 2 and μ is the average node degree,(ii) when the infection duration >tu, the probability ofidentifying the source approaches zero asymptotically underany algorithm; and (iii) when infection duration <tu, theBFS tree starting from the source is a fat tree. Numericalexperiments on tree networks, the ER random graphs andreal world networks with different evaluation metrics showthat the SFT algorithm outperforms existing algorithms.