Line Crossing Minimization on Metro Maps
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 line which connects them, whereas the paths illustrate the lines connecting terminal stations. We call this the metro-line crossing minimization problem (MLCM).
In contrast to the problem of drawing the underlying graph nicely, MLCM has received fewer attention. It was recently introduced by Benkert et. al in  . In this paper, as a first step towards solving MLCM in arbitrary graphs, we study path and tree networks. We examine several variations of the problem for which we develop algorithms for obtaining optimal solutions.
KeywordsMetro Maps Crossing Minimization Lines Paths Trees
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