Label Number Maximization in the Slider Model

  • Dietmar Ebner
  • Gunnar W. Klau
  • René Weiskircher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


We consider the NP-hard label number maximization problem lnm: Given a set of rectangular labels, each of which belongs to a point feature in the plane, the task is to find a labeling for a largest subset of the labels. A labeling is a placement such that none of the labels overlap and each is placed so that its boundary touches the corresponding point feature. The purpose of this paper is twofold: We present a new force-based simulated annealing algorithm to heuristically solve the problem and we provide the results of a very thorough experimental comparison of the best known labeling methods on widely used benchmark sets. The design of our new method has been guided by the goal to produce labelings that are similar to the results of an experienced human performing the same task. So we are not only looking for a labeling where the number of labels placed is high but also where the distribution of the placed labels is good.

Our experimental results show that the new algorithm outperforms the other methods in terms of quality while still being reasonably fast and confirm that the simulated annealing method is well-suited for map labeling problems.


  1. 1.
    Christensen, J., Marks, J., Shieber, S.: An empirical study of algorithms for point-feature label placement. ACM Trans. Graph. 14(3), 203–232 (1995)CrossRefGoogle Scholar
  2. 2.
    Davidson, R., Harel, D.: Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics 15(4), 301–331 (1996)CrossRefGoogle Scholar
  3. 3.
    Eades, P.: A heuristic for graph drawing. Congressus Numerantium 42, 149–160 (1984)MathSciNetGoogle Scholar
  4. 4.
    Herodotus: The History of Herodotus. 440 B.CGoogle Scholar
  5. 5.
    Hirsch, S.A.: An algorithm for automatic name placement around point data. The American Cartographer 9, 5–17 (1982)CrossRefGoogle Scholar
  6. 6.
    Imhof, E.: Die Anordnung der Namen in der Karte. International Yearbook of Cartography 2, 93–129 (1962)Google Scholar
  7. 7.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Klau, G.W., Lesh, N., Marks, J., Mitzenmacher, M., Schafer, G.T.: The HuGS platform: A toolkit for interactive optimization. In: Proc. of AVI 2002 International Working Conference on Advanced Visual Interfaces (2002)Google Scholar
  9. 9.
    Klau, G.W., Mutzel, P.: Optimal labelling of point features in rectangular labelling models. Mathematical Programming 94(2-3), 435–458 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kruskal, J., Seery, J.: Designing network diagrams. In: First General Conf. on Social Graphics, pp. 22–50 (1980)Google Scholar
  11. 11.
    Marks, J., Shieber, S.: The computational complexity of cartographic label placement. Technical Report TR-05-91, Harvard University, Cambridge, MA, U.S.A (1991)Google Scholar
  12. 12.
    Strijk, T., van Kreveld, M.: Practical extensions of point labeling in the slider model. In: Proc. 7th ACM Symp. Adv. Geogr. Inform. Syst., pp. 47–52 (1999)Google Scholar
  13. 13.
    van Kreveld, M., Strijk, T., Wolff, A.: Point labeling with sliding labels. Computational Geometry: Theory and Applications 13, 21–47 (1999)MATHMathSciNetGoogle Scholar
  14. 14.
    Yoeli, P.: The logic of automated map lettering. The Cartographic Journal 9, 99–108 (1972)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dietmar Ebner
    • 1
  • Gunnar W. Klau
    • 1
  • René Weiskircher
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of Technology 

Personalised recommendations