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

2024-12-14

arXiv.org

AI Summary

This paper addresses source localization in temporal networks, moving beyond conventional static-network assumptions to formalize the source detection task on temporal graphs for the first time, incorporating dynamic edge existence constraints to model realistic time-varying contacts (e.g., human encounters). Method: Building upon the SIR epidemic model, we integrate temporal graph theory, graph algorithms, and computational complexity analysis to design exact algorithms for general graphs and efficient approximation algorithms for trees. Contribution/Results: Theoretically, we establish the first tight lower-bound framework for temporal source detection. Algorithmically, we propose several provably optimal polynomial-time algorithms supporting both uniform-source and dynamic-source behavioral models. Extensive experiments on real-world temporal contact datasets demonstrate the effectiveness and robustness of our approach under varying infection dynamics and observation conditions.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Source detection in temporal networks with time-varying links
• Finding infection origins using SIR model on dynamic graphs
• Algorithms for source detection with consistent or dynamic behavior

Innovation

• Temporal graph model for source detection
• SIR spreading process on dynamic networks
• Algorithms with lower bounds analysis