Identify information sources with different start times in complex networks based on sparse observers

Abstract The dissemination of information across various locations is an ubiquitous occurrence, however, prevalent methodologies for multi-source identification frequently overlook the fact that sources may initiate dissemination at distinct initial moments. Although there are many research results of multi-source identification, the challenge of locating sources with varying initiation times using a limited subset of observational nodes remains unresolved. In this study, we provide the backward spread tree theorem and source centrality theorem, and develop a backward spread centrality algorithm to identify all the information sources that trigger the spread at different start times. The proposed algorithm does not require prior knowledge of the number of sources, however, it can estimate both the initial spread moment and the spread duration. The core concept of this algorithm involves inferring suspected sources through source centrality theorem and locating the source from the suspected sources with linear programming. Extensive experiments from synthetic and real network simulation corroborate the superiority of our method in terms of both efficacy and efficiency. Furthermore, we find that our method maintains robustness irrespective of the number of sources and the average degree of network. Compared with classical and state-of-the art source identification methods, our method generally improves the AUROC value by 0.1 to 0.2.