Catch Me If You Can: Finding the Source of Infections in Temporal Networks

TL;DR

This paper introduces a formal model for source detection in temporal networks, accounting for time-varying connections, and provides algorithms and bounds for identifying infection sources under this realistic setting.

Contribution

It is the first to formalize source detection on temporal graphs, extending previous models to more accurately reflect dynamic real-world networks.

Findings

Developed lower bounds for source detection in temporal graphs.

Proposed algorithms for source identification with various source behaviors.

Analyzed source detection on general graphs and trees.

Abstract

Source detection (SD) is the task of finding the origin of a spreading process in a network. Algorithms for SD help us combat diseases, misinformation, pollution, and more, and have been studied by physicians, physicists, sociologists, and computer scientists. The field has received considerable attention and been analyzed in many settings (e.g., under different models of spreading processes), yet all previous work shares the same assumption that the network the spreading process takes place in has the same structure at every point in time. For example, if we consider how a disease spreads through a population, it is unrealistic to assume that two people can either never or at every time infect each other, rather such an infection is possible precisely when they meet. Therefore, we propose an extended model of SD based on temporal graphs, where each link between two nodes is only present at some time step. Temporal graphs have become a standard model of time-varying graphs, and, recently, researchers have begun to study infection problems (such as influence maximization) on temporal graphs (arXiv:2303.11703, [Gayraud et al., 2015]). We give the first formalization of SD on temporal graphs. For this, we employ the standard SIR model of spreading processes ([Hethcote, 1989]). We give both lower bounds and algorithms for the SD problem in a number of different settings, such as with consistent or dynamic source behavior and on general graphs as well as on trees.