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.

翻译：源点检测（SD）是指在网络中定位传播过程起源的任务。SD算法帮助我们对抗疾病、虚假信息、污染等问题，并已受到医学、物理学、社会学和计算机科学领域研究者的广泛关注。该领域已获得大量研究，并在多种情境下得到分析（例如基于不同的传播过程模型），但所有先前工作都基于同一假设：传播过程发生的网络结构在任意时间点均保持不变。例如，若考虑疾病在人群中的传播过程，假设两个人要么永远无法相互感染、要么始终可以相互感染是不符合现实的——感染恰恰在他们相遇时才可能发生。因此，我们提出一种基于时序图的扩展SD模型，其中节点间的连边仅在特定时间步存在。时序图已成为时变图的标准模型，且近期研究者已开始在时序图上研究感染问题（如影响力最大化）（arXiv:2303.11703, [Gayraud et al., 2015]）。我们首次对时序图上的SD问题进行了形式化定义。为此，我们采用标准的SIR传播模型（[Hethcote, 1989]）。针对多种不同场景（如源点行为一致或动态变化的情形，以及在通用图和树结构上的情形），我们给出了SD问题的下界证明与算法设计。