Spreading processes on networks (graphs) have become ubiquitous in modern society with prominent examples such as infections, rumors, excitations, contaminations, or disturbances. Finding the source of such processes based on observations is important and difficult. We abstract the problem mathematically as an optimization problem on graphs. For the deterministic setting we make connections to the metric dimension of a graph and introduce the concept of spread resolving sets. For the stochastic setting we propose a new algorithm combining parameter estimation and experimental design. We discuss well-posedness of the algorithm and show encouraging numerical results on a benchmark library.

网络（图表）上的传播过程在现代社会中已变得无处不在，突出的例子包括感染、谣言、兴奋、污染或骚乱。根据观察找到此类过程的来源既重要又困难。我们在数学上将问题抽象为图上的优化问题。对于确定性设置，我们连接到图的度量维度并引入扩展解析集的概念。对于随机设置，我们提出了一种结合参数估计和实验设计的新算法。我们讨论了算法的适定性，并在基准库上展示了令人鼓舞的数值结果。