Limiting the Neighborhood: De-Small-World Network for Outbreak Prevention

Abstract

In this work, we study a basic and practically important strategy to help prevent and/or delay an outbreak in the context of network: limiting the contact between individuals. In this paper, we introduce the average neighborhood size as a new measure for the degree of being small-world and utilize it to formally define the desmall-world network problem. We also prove the NP-hardness of the general reachable pair cut problem and propose a greedy edge betweenness based approach as the benchmark in selecting the candidate edges for solving our problem. Furthermore, we transform the de-small-world network problem as an OR-AND Boolean function maximization problem, which is also an NP-hardness problem. In addition, we develop a numerical relaxation approach to solve the Boolean function maximization and the de-small-world problem. Also, we introduce the short-betweenness, which measures the edge importance in terms of all short paths with distance no greater than a certain threshold, and utilize it to speed up our numerical relaxation approach. The experimental evaluation demonstrates the effectiveness and efficiency of our approaches. underlying (social) network less small-world, or simply "de-smallworld", i.e., the distances between individuals increase to delay the spreading process. In many situations, such a strategy is often easily and even voluntarily adopted. For instance, during the SARS epidemic in Beijing, 2004, there are much less people appearing in the public places. In addition, this approach can also be deployed in complement to the quarantine approach.