On embedding a cycle in a plane graph
GD'05 Proceedings of the 13th international conference on Graph Drawing
A mixed-integer program for drawing high-quality metro maps
GD'05 Proceedings of the 13th international conference on Graph Drawing
An ILP for the metro-line crossing problem
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Line crossing minimization on metro maps
GD'07 Proceedings of the 15th international conference on Graph drawing
An improved algorithm for the metro-line crossing minimization problem
GD'09 Proceedings of the 17th international conference on Graph Drawing
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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(n2) time, where n is the number of terminating paths.