Network observability and localization of sources of diffusion in tree networks with missing edges

In order to quickly curb infections or prevent spreading of rumors, first the source of diffusion needs to be localized. We analyze the problem of source localization, based on infection times of a subset of nodes in incompletely observed tree networks, under a simple propagation model. Our scenario reflects the assumption that having access to all the nodes and full network topology is often not feasible. We evaluate the number of possible topologies that are consistent with the observed incomplete tree. We provide a sufficient condition for the selection of observed nodes, such that correct localization is possible, i.e. the network is observable. Finally, we formulate the source localization problem under these assumptions as a binary linear integer program. We then provide a small simulation example to illustrate the effect of the number of observed nodes on the problem complexity and on the number of possible solutions for the source.