Recently, the problem of detecting the rumor source in a social network has been much studied,
where it has been shown that the detection probability cannot be beyond 31% even for regular
trees [1,2]. In this paper, we study the impact of an anti-rumor on the rumor source detection. We
rst show a negative result: the anti-rumor's diffusion does not increase the detection probability
under Maximum-Likelihood-Estimator (MLE) under passive diffusion that the anti-rumor starts
to be spread by a special node, called the protector, after is reached by the rumor. We next
consider the case when the distance between the rumor source and the protector follows certain
type of distributions such as Zipf, Geometric and Poisson distribution (but their parameters are
hidden) where the higher probabilities are assigned to nearer rumor sources from the protector
source under them. This is reasonable in practice since it is natural to place a protector near
prior rumor sources by historical information of the location of rumor sources. Then, we propose
the following learning algorithm: a) learn the distance distribution parameters under MLE, and
b) detect the rumor source under Maximum-A-Posterior-Estimator (MAPE) based on the learnt
parameters. We provide an analytic characterization of the rumor source detection probability for
regular trees under the proposed algorithm, where MAPE outperforms MLE by up to 50% for 3-
regular tree and by up to 63% when the degree of the regular tree becomes large. We demonstrate
our theoretical ndings through numerical results, and further present the simulation results for
general topologies by using a heuristic algorithm based on Breadth-First Search (MAP-BFS) even
without knowledge of the distance distribution, showing that under a simple protector placement
algorithm, MAPE produces the detection probability much larger than that by MLE