A Mixed-Integer Program for Drawing High-Quality Metro Maps

  • Martin Nöllenburg
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


In this paper we investigate the problem of drawing metro maps which is defined as follows. Given a planar graph G of maximum degree 8 with its embedding and vertex locations (e.g. the physical location of the tracks and stations of a metro system) and a set \({\mathcal L}\) of paths or cycles in G (e.g. metro lines), draw G and \({\mathcal L}\) nicely. We first specify the niceness of a drawing by listing a number of hard and soft constraints. Then we present a mixed-integer program (MIP) which always finds a drawing that fulfills all hard constraints (if such a drawing exists) and optimizes a weighted sum of costs corresponding to the soft constraints. We also describe some heuristics that speed up the MIP. We have implemented both the MIP and the heuristics. We compare their output to that of previous algorithms for drawing metro maps and to official metro maps drawn by graphic designers.


Planar Graph Edge Direction Soft Constraint Hard Constraint Graph Drawing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Nöllenburg
    • 1
  • Alexander Wolff
    • 1
  1. 1.Fakultät für InformatikUniversität KarlsruheKarlsruhe

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