A robust information source estimator with sparse observations

In this paper, we consider the problem of locating the information source with sparse observations. We assume that a piece of information spreads in a network following a heterogeneous susceptible-infected-recovered (SIR) model, where a node is said to be
infected
when it receives the information and
recovered
when it removes or hides the information. We further assume that a small subset of infected nodes are reported, from which we need to find the source of the information. We adopt the sample path based estimator developed in [1], and prove that on infinite trees, the sample path based estimator is a Jordan infection center with respect to the set of observed infected nodes. In other words, the sample path based estimator minimizes the maximum distance to observed infected nodes. We further prove that the distance between the estimator and the actual source is upper bounded by a constant independent of the number of infected nodes with a high probability on infinite trees. Our simulations on tree networks and real world networks show that the sample path based estimator is closer to the actual source than several other algorithms.