Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g. the spread of disease or dissemination of information. Motivated by real-world applications, modification of static graphs to control this spread has proven a rich topic for previous research. Here, we introduce a new type of modification for temporal graphs: the number of active times for each edge is fixed, but we can change the relative order in which (sets of) edges are active. We investigate the problem of determining an ordering of edges that minimises the maximum number of vertices reachable from any single starting vertex; epidemiologically, this corresponds to the worst-case number of vertices infected in a single disease outbreak. We study two versions of this problem, both of which we show to be $\mathsf{NP}$-hard, and identify cases in which the problem can be solved or approximated efficiently.

时间图（其中边在特定时间处于活动状态）与图上的传播过程（例如疾病的传播或信息的传播）特别相关。受到现实世界应用程序的启发，对静态图进行修改以控制这种传播已被证明是以前研究的一个热门话题。在这里，我们为时间图引入了一种新型的修改方式：每个边的活动时间是固定的，但是我们可以更改边（组）被活动的相对顺序。我们研究确定边的排序的问题，该边的排序使从任何单个起始顶点可到达的最大顶点数量最小化；在流行病学上，这对应于一次疾病暴发中感染的最坏情况的顶点数量。我们研究了这个问题的两个版本，我们都证明这两个版本是$\mathsf{NP}$-困难，并确定可以有效解决或近似解决问题的情况。