The effect of transmission variance on observer placement for source-localization

Detecting where an epidemic started, i.e., which node in a network was the source, is of crucial importance in many contexts. However, finding the source of an epidemic can be challenging, especially because the information available is often sparse and noisy. We consider a setting in which we want to localize the source based exclusively on the information provided by a small number of observers - i.e., nodes that can reveal if and when they are infected - and we study where such observers should be placed. We show that the optimal observer placement depends not only on the topology of the network, but also on the variance of the node-to-node transmission delays. We consider both low-variance and high-variance regimes for the transmission delays and propose algorithms for observer placement in both cases. In the low-variance regime, it suffices to only consider the network-topology and to choose observers that, based on their distances to all other nodes in the network, can distinguish among possible sources. However, the high-variance regime requires a new approach in order to guarantee that the observed infection times are sufficiently informative about the location of the source and do not get masked by the noise in the transmission delays; this is accomplished by additionally ensuring that the observers are not placed too far apart. We validate our approaches with simulations on three real-world networks. Compared to state-of-the-art strategies for observer placement, our methods have a better performance in terms of source-localization accuracy for both the low- and the high-variance regimes.