Deleting edges to restrict the size of an epidemic in temporal networks

TL;DR

This paper investigates how deleting edges in temporal networks can limit the spread of epidemics or information, analyzing the complexity and approximability of such interventions.

Contribution

It introduces a new edge-deletion problem for temporal graphs and explores its computational complexity and approximation limits.

Findings

The problem is computationally hard in general.

Certain cases admit approximation algorithms.

Edge deletion can effectively restrict epidemic spread.

Abstract

Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these processes spread are dynamic in nature, and can be modeled with temporal graphs. Here, we study the problem of deleting edges from a given temporal graph in order to reduce the number of vertices (temporally) reachable from a given starting point. This could be used to control the spread of a disease, rumour, etc. in a temporal graph. In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices using a temporally-feasible path. We introduce a natural edge-deletion problem for temporal graphs and provide positive and negative results on its computational complexity and approximability.