Information source localization with protector diffusion in networks

Recently, the problem of detecting the information source in a network has been much studied, where it has been shown that the detection probability cannot be beyond 31% even for regular trees if the number of infected nodes is sufficiently large. In this paper, we study the impact of an anti-information spreading on the original information source detection. We first show a negative result: the anti-information diffusion does not increase the detection probability under Maximum-Likelihood-Estimator (MLE) when the number of infected nodes are sufficiently large by passive diffusion that the anti-information starts to be spread by a special node, called the protector, after is reached by the original information. We next consider the case when the distance between the information source and the protector follows a certain type of distribution, but its parameter is hidden. Then, we propose the following learning algorithm: a) learn the distance distribution parameters under MLE, and b) detect the information source under Maximum-A-Posterior-Estimator (MAPE) based on the learnt parameters. We provide an analytic characterization of the source detection probability for regular trees under the proposed algorithm, where MAPE outperforms MLE by up to 50% for 3-regular trees and by up to 63% when the degree of the regular tree becomes large. We demonstrate our theoretical findings through numerical results, and further present the simulation results for general topologies (e.g., Facebook and US power grid networks) 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.