Evaluation of Labeling Strategies for Rotating Maps

  • Andreas Gemsa
  • Martin Nöllenburg
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)


We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with one corner to its respective point. We require that each label remains horizontally aligned during the map rotation and our goal is to find a set of mutually non-overlapping active labels for every rotation angle α ∈ [0,2π) so that the number of active labels over a full map rotation of 2π is maximized.

We discuss and experimentally evaluate several labeling models that define additional consistency constraints on label activities in order to reduce flickering effects during monotone map rotation. We introduce three heuristic algorithms and compare them experimentally to an existing approximation algorithm and exact solutions obtained from an integer linear program. Our results show that on the one hand low flickering can be achieved at the expense of only a small reduction in the objective value, and that on the other hand the proposed heuristics achieve a high labeling quality significantly faster than the other methods.


Greedy Algorithm Total Activity Integer Linear Program Active Range Consistency Model 
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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  1. 1.
    Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Comput. Geom. Theory Appl. 11(3-4), 209–218 (1998)CrossRefzbMATHGoogle Scholar
  2. 2.
    Been, K., Daiches, E., Yap, C.: Dynamic map labeling. IEEE Trans. Vis. Comput. Graph. 12(5), 773–780 (2006)CrossRefGoogle Scholar
  3. 3.
    Been, K., Nöllenburg, M., Poon, S.-H., Wolff, A.: Optimizing active ranges for consistent dynamic map labeling. Comput. Geom. Theory Appl. 43(3), 312–328 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    de Berg, M., Gerrits, D.H.P.: Approximation algorithms for free-label maximization. Comput. Geom. Theory Appl. 45(4), 153–168 (2011)CrossRefGoogle Scholar
  5. 5.
    de Berg, M., Gerrits, D.H.P.: Labeling moving points with a trade-off between label speed and label overlap. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 373–384. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th Ann. ACM Symp. Comput. Geom., pp. 281–288. ACM, New York (1991)Google Scholar
  7. 7.
    Gemsa, A., Niedermann, B., Nöllenburg, M.: Trajectory-based dynamic map labeling. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) ISAAC 2013. LNCS, vol. 8283, pp. 413–423. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Gemsa, A., Nöllenburg, M., Rutter, I.: Consistent labeling of rotating maps. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 451–462. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Gemsa, A., Nöllenburg, M., Rutter, I.: Evaluation of Labeling Strategies for Rotating Maps. CoRR, abs/1404.1849 (2014)Google Scholar
  10. 10.
    Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32(1), 130–136 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Nöllenburg, M., Polishchuk, V., Sysikaski, M.: Dynamic one-sided boundary labeling. In: Proc. 18th ACM SIGSPATIAL GIS, pp. 310–319. ACM, New York (2010)Google Scholar
  12. 12.
    Ooms, K., Kellens, W., Fack, V.: Dynamic map labeling for users. In: Proc. 24th Internat. Cartographic Conf., pp. 1–12. Military Geographic Institute, Santiago (2009)Google Scholar
  13. 13.
    van Kreveld, M., Strijk, T., Wolff, A.: Point labeling with sliding labels. Comput. Geom. Theory Appl. 13(1), 21–47 (1999)CrossRefzbMATHGoogle Scholar
  14. 14.
    Vaaraniemi, M., Treib, M., Westermann, R.: Temporally coherent real-time labeling of dynamic scenes. In: Proc. 3rd Internat. Conf. Computing for Geospatial Research and Applications, pp. 17:1–17:10. ACM, New York (2012)Google Scholar
  15. 15.
    Yokosuka, Y., Imai, K.: Polynomial time algorithms for label size maximization on rotating maps. In: Proc. 25th Canadian Conf. Comput. Geom., University of Waterloo, Waterloo, pp. 187–192 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Andreas Gemsa
    • 1
  • Martin Nöllenburg
    • 1
  • Ignaz Rutter
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany

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