  We assume that the state of a number of nodes in a network could be
investigated if necessary, and study what configuration of those nodes could
facilitate a better solution for the diffusion-source-localization (DSL)
problem. In particular, we formulate a candidate set which contains the
diffusion source for sure, and propose the method, Percolation-based
Evolutionary Framework (PrEF), to minimize such set. Hence one could further
conduct more intensive investigation on only a few nodes to target the source.
To achieve that, we first demonstrate that there are some similarities between
the DSL problem and the network immunization problem. We find that the
minimization of the candidate set is equivalent to the minimization of the
order parameter if we view the observer set as the removal node set. Hence,
PrEF is developed based on the network percolation and evolutionary algorithm.
The effectiveness of the proposed method is validated on both model and
empirical networks in regard to varied circumstances. Our results show that the
developed approach could achieve a much smaller candidate set compared to the
state of the art in almost all cases. Meanwhile, our approach is also more
stable, i.e., it has similar performance irrespective of varied infection
probabilities, diffusion models, and outbreak ranges. More importantly, our
approach might provide a new framework to tackle the DSL problem in extreme
large networks.
