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

TL;DR

This paper introduces a new measure called average neighborhood size to define and solve the de-small-world network problem, aiming to prevent outbreaks by limiting contacts, with proven NP-hardness and a developed relaxation approach.

Contribution

It defines the de-small-world network problem using average neighborhood size, proves its NP-hardness, and proposes a numerical relaxation method with short-betweenness to efficiently solve it.

Findings

The proposed methods effectively prevent outbreaks in network models.

The relaxation approach outperforms baseline heuristics in speed and accuracy.

Short-betweenness accelerates the solution process significantly.

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.