📝 SummarXiv

Abstract

Train timetables can be represented as event graphs, where correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and (the development of) dispatching software. A common way to represent event graphs are time-space diagrams. In such a diagram, key locations are visualized on the y-axis and time on the x-axis of a coordinate system. A train's movement is then represented as a connected sequence of line segments in this coordinate system. This visualization allows for an easy detection of infrastructure conflicts and safety distance violations. However, time-space diagrams are usually used only to depict event graphs that are restricted to corridors, where an obvious ordering of the locations exists. In this paper, we consider the visualization of general event graphs in time-space diagrams, where the challenge is to find an ordering of the locations that produces readable drawings. We argue that this means to minimize the number of turns, i.e., the total number of changes in y-direction. To this end, we establish a connection between this problem and Maximum Betweenness. Then we develop a preprocessing strategy to reduce the instance size. We also propose a parameterized algorithm and integer linear programming formulations. We experimentally evaluate the preprocessing strategy and the integer programming formulations on a real-world dataset. Our best algorithm solves every instance in the dataset in less than a second. This suggests that turn-optimal time-space diagrams can be computed in real time.