Line Crossing Minimization on Metro Maps
Bekos, Michael A. and Kaufmann, Michael and Potika, Katerina and Symvonis, Antonios (2008) Line Crossing Minimization on Metro Maps. In: Graph Drawing 15th International Symposium, GD 2007, September 24-26, 2007, Sydney, Australia , pp. 231-242 (Official URL: http://dx.doi.org/10.1007/978-3-540-77537-9_24).
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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.
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