Abstract
We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V;E) so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway track connecting them, whereas the paths illustrate the metro lines connecting terminal stations. We call this the metro-line crossing minimization problem (MLCM). We examine several variations of the problem for which we develop algorithms that yield optimal solutions.
Highlights
Metro maps or public transportation networks are quite common in our daily life and familiar to most people
A metro map can be modeled as a tuple (G, L), which consists of a connected graph G = (V, E), referred to as the underlying network, and a set L of simple paths on G
The nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway track connecting them, whereas the paths illustrate the metro lines connecting terminal stations
Summary
Metro maps or public transportation networks are quite common in our daily life and familiar to most people The visualization of such maps takes inspiration from the fact that the passengers riding the trains are not too concerned about the geographical accuracy of the train stations, but they are more interested in how to get from one station to another and where to change trains. Since crossings within a visualization are often considered as the main source of confusion, the main goal is to draw the lines so that they cross each other as few times as possible. This problem is referred to as the metro-line crossing minimization problem (MLCM) and it is the topic of this paper
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