Approximation Algorithms on Consistent Dynamic Map Labeling

  • Chung-Shou Liao
  • Chih-Wei Liang
  • Sheung-Hung Poon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8497)


We consider the dynamic map labeling problem: given a set of rectangular labels on the map, the goal is to appropriately select visible ranges for all the labels such that no two consistent labels overlap at every scale and the sum of total visible ranges is maximized. We propose approximation algorithms for several variants of this problem. For the simple ARO problem, we provide a 3c logn-approximation algorithm for the unit-width rectangular labels if there is a c-approximation algorithm for unit-width label placement problem in the plane; and a randomized polynomial-time O(logn loglogn)-approximation algorithm for arbitrary rectangular labels. For the general ARO problem, we prove that it is NP-complete even for congruent square labels with equal selectable scale range. Moreover, we contribute 12-approximation algorithms for both arbitrary square labels and unit-width rectangular labels, and a 6-approximation algorithm for congruent square labels.


Approximation Algorithm Active Range Consistent Dynamic Consistent Label Prism Pair 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangIes. Computational Geometry: Theory and Application 11, 209–218 (1998)CrossRefzbMATHGoogle Scholar
  2. 2.
    Been, K., Daiches, E., Yap, C.: Dynamic map labeling. IEEE Transactions on Visualization and Computer Graphics 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. Computational Geometry: Theory and Application 43(3), 312–328 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Berlin (2008)CrossRefGoogle Scholar
  5. 5.
    Berman, P., DasGupta, B., Muthukrishnan, S., Ramaswami, S.: Efficient approximation algorithms for tiling and packing problems with rectangles. Journal of Algorithms 41, 443–470 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Chalermsook, P., Chuzhoy, J.: Maximum independent set of rectangles. In: Proc. 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), pp. 892–901 (2009)Google Scholar
  7. 7.
    Chan, T.M.: Polynomial-time approximation schemes for packing and piercing fat objects. Journal of Algorithms 46, 178–189 (2003)CrossRefzbMATHGoogle Scholar
  8. 8.
    Chan, T.M.: A note on maximum independent sets in rectangle intersection graphs. Information Processing Letters 89(1), 19–23 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Chazelle, B., et al.: The computational geometry impact task force report. In: Advances in Discrete and Computational Geometry, vol. 223, pp.407–463. American Mathematical Society, Providence (1999)Google Scholar
  10. 10.
    Doddi, S., Marathe, M.V., Mirzaian, A., Moret, B.M.E., Zhu, B.: Map labeling and generalizations. In: Proc.8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1997), pp. 148–157 (1997)Google Scholar
  11. 11.
    Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th Annual Symposium on Computational Geometry (SoCG 1991), pp. 281–288 (1991)Google Scholar
  12. 12.
    Gemsa, A., Nöllenburg, M., Rutter, I.: Sliding labels for dynamic point labeling. In: Proc. 23th Canadian Conference on Computational Geometry (CCCG 2011), pp. 205–210 (2011)Google Scholar
  13. 13.
    Hochbaum, D.S., Maas, W.: Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM (JACM) 32(1), 130–136 (1985)CrossRefzbMATHGoogle Scholar
  14. 14.
    Knuth, D.E., Raghunathan, A.: The problem of compatible representatives. SIAM J. Discrete Math. 5(3), 422–427 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Poon, S.-H., Shin, C.-S.: Adaptive zooming in point set labeling. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 233–244. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Wolff, A., Strijk, T.: The map-labeling bibliography (2009),
  17. 17.
    Yap, C.K.: Open problem in dynamic map labeling. In: Proc. International Workshop on Combinatoral Algorithms, IWOCA 2009 (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Chung-Shou Liao
    • 1
  • Chih-Wei Liang
    • 1
  • Sheung-Hung Poon
    • 2
  1. 1.Department of Industrial Engineering and Engineering ManagementNational Tsing Hua UniversityHsinchuTaiwan, R.O.C.
  2. 2.Department of Computer Science & Institute of Information Systems and ApplicationsNational Tsing Hua UniversityHsinchuTaiwan, R.O.C.

Personalised recommendations