Abstract
In this paper we consider a new problem that occurs when drawing wiring diagrams or public transportation networks. Given an embedded graph G = (V,E) (e.g., the streets served by a bus network) and a set L of paths in G (e.g., the bus lines), we want to draw the paths along the edges of G such that they cross each other as few times as possible. For esthetic reasons we insist that the relative order of the paths that traverse a node does not change within the area occupied by that node.
Our main contribution is an algorithm that minimizes the number of crossings on a single edge {u,v} ∈ E if we are given the order of the incoming and outgoing paths. The difficulty is deciding the order of the paths that terminate in u or v with respect to the fixed order of the paths that do not end there. Our algorithm uses dynamic programming and takes O(n 2) time, where n is the number of terminating paths.
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Cortese, P.F., Battista, G.D., Patrignani, M., Pizzonia, M.: On embedding a cycle in a plane graph. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 49–60. Springer, Heidelberg (2006)
Durbin, R., Eddy, S., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Cambridge University Press, Cambridge (1998)
Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM J. Alg. Disc. Meth. 4, 312–316 (1983)
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)
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Benkert, M., Nöllenburg, M., Uno, T., Wolff, A. (2007). Minimizing Intra-edge Crossings in Wiring Diagrams and Public Transportation Maps. In: Kaufmann, M., Wagner, D. (eds) Graph Drawing. GD 2006. Lecture Notes in Computer Science, vol 4372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70904-6_27
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DOI: https://doi.org/10.1007/978-3-540-70904-6_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70903-9
Online ISBN: 978-3-540-70904-6
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