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Estimating the number of infection sources in a tree

Most algorithms for identifying multiple rumor or infection sources require prior knowledge of the number of sources, or at least an upper bound on the number of sources. In this paper, we consider a deterministic Susceptible-Infected (SI) spreading model in which infection at different source nodes may start at different times. We introduce the concept of a minimal and linear cover of the infection graph, and propose the use of graph signals on the infection graph to estimate the number of sources. Under certain mild conditions, we demonstrate that our method gives a good estimate of the number of infection sources for tree graphs.