Entropy-Driven Sensor Deployment and Source Detection in Hypergraphs

Abstract: Identifying the diffusion source in complex networks is critical for understanding and controlling epidemic spread. In realistic settings, full observation of node states is rarely available, making sensor-based source detection a practical alternative. However, existing sensor-based methods are often confined to simple networks, failing to capture the higher-order group dynamics of real-world spreading process. By deploying a limited number of sensors to monitor the diffusion process, one can infer the origin from partial observations. Yet, determining optimal sensor placement is challenging, i.e., poor deployment leads to redundant or noisy data, while optimal placement must balance coverage diversity and information value under limited resources. To address these challenges, we propose a dedicated framework termed Sensor-based Source Detection in Hypergraphs (SSDH). Specifically, we introduce a novel entropy-driven sensor deployment strategy that effectively captures critical early-stage diffusion signals by maximizing information gain under limited resources. Furthermore, we develop a source localization algorithm that quantifies propagation uncertainty through a newly defined path uncertainty-based score. By integrating this score with topological distance, SSDH enables accurate and robust source identification. Extensive experiments on both synthetic and empirical hypergraphs demonstrate that SSDH consistently outperforms competing algorithms by 5%--30% across different sensor ratios, final spreading ratios, and infection probabilities. These results validate the effectiveness of SSDH and highlight its superior capability to tackle source localization in complex systems characterized by higher-order interactions.