Information Source Detection with Limited Time Knowledge

We study the source detection problem using limited timestamps on a given network. Due to the NP-completeness of the maximum likelihood estimator (MLE), we propose an approximation solution called infection-path-based estimator (INF), the essence of which is to identify the most likely infection path that is consistent with observed timestamps. The source node associated with that infection path is viewed as the estimated source û. For the tree network, we transform the INF into integer linear programming and find a reduced search region using BFS, within which the estimated source is provably always on a path termed as candidate path. This notion enables us to analyze the accuracy of the INF in terms of error distance on arbitrary tree. Specifically, on the infinite g-regular tree with uniform sampled timestamps, we get a refined performance guarantee in the sense of a constant bounded d(u*, û). By virtue of time labeled BFS tree, the estimator still performs fairly well when extended to more general graphs. Simulations on both trees and general networks further demonstrate the superior performance of the INF.