Software that is used to compute or adjust train schedules is based on so-called event graphs. The vertices of such a graph correspond to events; each event is associated with a point in time, a location, and a train. A train line corresponds to a sequence of events (ordered by time) that are associated with the same train. The event graph has a directed edge from an earlier to a later event if they are consecutive along a train line. Events that occur at the same location do not occur at the same time. In this paper, we present a way to visualize such graphs, namely time-space diagrams. A time-space diagram is a straight-line drawing of the event graph with the additional constraint that all vertices that belong to the same location lie on the same horizontal line and that the x-coordinate of each vertex is given by its point in time. Hence, it remains to determine the y-coordinates of the locations. A good drawing of a time-space diagram supports users (or software developers) when creating (software for computing) train schedules. To enhance readability, we aim to minimize the number of turns in time-space diagrams. To this end, we establish a connection between this problem and Maximum Betweenness. Then we develop exact reduction rules to reduce the instance size. We also propose a parameterized algorithm and devise a heuristic that we evaluate experimentally on a real-world dataset.

翻译：用于计算或调整列车时刻表的软件基于所谓的事件图。此类图的顶点对应事件；每个事件与一个时间点、一个位置和一列列车相关联。一条列车线路对应一系列（按时间排序的）与同一列车相关联的事件。如果两个事件在列车线路上连续发生，则事件图中存在从较早事件指向较晚事件的有向边。发生在同一位置的事件不会同时发生。本文提出了一种可视化此类图的方法，即时空图。时空图是事件图的一种直线绘制方式，其附加约束是：所有属于同一位置的顶点位于同一水平线上，且每个顶点的x坐标由其时间点给出。因此，剩余问题在于确定各位置的y坐标。良好的时空图绘制能够帮助用户（或软件开发人员）创建（用于计算）列车时刻表的软件。为提高可读性，我们致力于最小化时空图中的转折点数量。为此，我们建立了该问题与最大中介度之间的联系。随后，我们开发了精确的归约规则以减少实例规模。我们还提出了一种参数化算法，并设计了一种启发式方法，在真实世界数据集上进行了实验评估。