Efficient approaches for attaining epidemic-free networks with minimum edge removal set

Spreads can be contained through tuning the underlying contact networks, such as the social distance policy reducing the average degree of social contacts and the suspension of flights increasing the average length of travel distances. This paper studies how to find the optimal removal edge set of minimum size, such that the resulted network can survive from varied outbreaks. Specifically, we investigate the containment strategies from network epidemiology and immunization, and propose three novel methods that can well balance the transmission characteristics and topology of the remaining network and can thus effectively suppress varied spreads. In particular, the developed methods use the epidemic threshold to characterize the transmission characteristics and the largest connected component to measure the topology, and obtain the edge set by simultaneously optimizing them. We further introduce a bound strategy to scale up our methods, providing a time complexity of O(mlog_ω(n/ℓ)). We also conduct extensive experiments to evaluate the proposed methods. Results show that the developed approaches outperform the state-of-the-art by a large margin. Meanwhile, our methods are also much faster than those compared strategies. We are convinced that the proposed containment approaches promise to be effective tools to suppress spread on large-scale networks.