An Algorithmic Framework for Labeling Network Maps

  • Jan-Henrik Haunert
  • Benjamin NiedermannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9198)


Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of metro maps. We present a flexible and versatile labeling model. Despite its simplicity, we prove that it is NP-complete to label a single line of the network. For a restricted variant of that model, we introduce an efficient algorithm that optimally labels a single line. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.


Full Version Simple Polygon Incoming Edge Algorithmic Framework Transitivity Property 
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  1. 1.
    Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Comp. Geom.-Theor. Appl. 11, 209–218 (1998)zbMATHCrossRefGoogle Scholar
  2. 2.
    Christensen, J., Marks, J., Shieber, S.: An empirical study of algorithms for point-feature label placement. Acm. T. Graphic. 14(3), 203–232 (1995)CrossRefGoogle Scholar
  3. 3.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)Google Scholar
  4. 4.
    Fink, M., Haverkort, H., Nöllenburg, M., Roberts, M., Schuhmann, J., Wolff, A.: Drawing metro maps using Bézier curves. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 463–474. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  5. 5.
    Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: ACM Sympos. on Comput. Geom., pp. 281–288 (1991)Google Scholar
  6. 6.
    Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are np-complete. Inf. Process. Lett. 12(3), 133–137 (1981)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Haunert, J.-H., Niedermann, B.: An algorithmic framework for labeling network maps (2015). CoRR, abs/1505.00164Google Scholar
  8. 8.
    Imhof, E.: Positioning names on maps. Am. Cartographer, 128–144 (1975)Google Scholar
  9. 9.
    Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329–343 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Nöllenburg, M., Wolff, A.: Drawing and labeling high-quality metro maps by mixed-integer programming. IEEE T. Vis. Comput. Gr. 17(5), 626–641 (2011)CrossRefGoogle Scholar
  11. 11.
    Stott, J., Rodgers, P., Martinez-Ovando, J., Walker, S.: Automatic metro map layout using multicriteria optimization. IEEE T. Vis. Comput. Gr. 17(1), 101–114 (2011)CrossRefGoogle Scholar
  12. 12.
    van Goethem, A., Meulemans, W., Reimer, A., Haverkort, H., Speckmann, B.: Topologically safe curved schematisation. Cartogr. J. 50(3), 276–285 (2013)CrossRefGoogle Scholar
  13. 13.
    Wang, Y.-S., Chi, M.-T.: Focus+context metro maps. IEEE T. Vis. Comput. Gr. 17(12), 2528–2535 (2011)CrossRefGoogle Scholar
  14. 14.
    Wolff, A.: Graph drawing and cartography. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization, chapter 23, pp. 697–736. CRC Press (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of OsnabrückOsnabrückGermany
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany

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