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 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 [4] . 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.
This work has been funded by the project PENED-2003. PENED-2003 is co - funded by the European Social Fund (75%) and Greek National Resources (25%).
Chapter PDF
Similar content being viewed by others
References
Asquith, M., Gudmundsson, J., Merrick, D.: An ILP for the line ordering problem. Technical Report PA006288, National ICT Australia (2007)
Battista, G.D., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Line crossing minimization on metro maps. Technical Report WSI-2007-03, University of Tübingen (2007)
Benkert, M., Nöllenburg, M., Uno, T., Wolff, A.: Minimizing intra-edge crossings in wiring diagrams and public transport maps. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 270–281. Springer, Heidelberg (2007)
Hong, S.-H., Merrick, D., Nascimento, H.A.D.d.: The metro map layout problem. In: Churcher, N., Churcher, C. (eds.) invis.au 2004. Australasian Symposium on Information Visualisation, CRPIT, ACS, vol. 35, pp. 91–100 (2004)
Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)
Masuda, S., Nakajima, K., Kashiwabara, T., Fujisawa, T.: Crossing minimization in linear embeddings of graphs. IEEE Trans. Comput. 39(1), 124–127 (1990)
Nöllenburg, M., Wolff, A.: A mixed-integer program for drawing high-quality metro maps. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 321–333. Springer, Heidelberg (2006)
Stott, J.M., Rodgers, P.: Metro map layout using multicriteria optimization. In: Proc. 8th International Conference on Information Visualisation, pp. 355–362. IEEE Computer Society, Los Alamitos (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A. (2008). Line Crossing Minimization on Metro Maps. In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-77537-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77536-2
Online ISBN: 978-3-540-77537-9
eBook Packages: Computer ScienceComputer Science (R0)