Finding Rumor Sources on Random Trees

We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to when these nodes became infected. In a recent work (Shah and Zaman 2010), this rumor source detection problem was introduced and studied. The authors proposed the graph score function rumor centrality as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading times for regular trees. They showed that as the size of the infected graph increases, for a path graph (2-regular tree), the probability of source detection goes to 0 and for d-regular trees with d ≥ 3 the probability of detection, say αd, remains bounded away from 0 and is less than 1/2. However, their results stop short of providing insights for the performance of the rumor centrality estimator in more general settings such as irr...

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