Skip to main content

Trajectory-Based Dynamic Map Labeling

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

Abstract

In this paper we introduce trajectory-based labeling, a new variant of dynamic map labeling where a movement trajectory for the map viewport is given. We define a general labeling model and study the active range maximization problem in this model. The problem is \(\cal NP\)-complete and \(\mathcal W[1]\)-hard. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms. For the general case we present a practical ILP formulation with an experimental evaluation as well as approximation algorithms.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Article  MATH  Google Scholar 

  2. Been, K., Daiches, E., Yap, C.: Dynamic map labeling. IEEE Trans. Visualization and Computer Graphics 12(5), 773–780 (2006)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  4. Carlisle, M.C., Lloyd, E.L.: On the k-coloring of intervals. Discr. Appl. Math. 59(3), 225–235 (1995)

    MathSciNet  MATH  Google Scholar 

  5. Chalermsook, P., Chuzhoy, J.: Maximum independent set of rectangles. In: ACM-SIAM Symp. Discr. Algorithms (SODA 2009), pp. 892–901 (2009)

    Google Scholar 

  6. Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are NP-complete. Inform. Process. Lett. 12(3), 133–137 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gemsa, A., Niedermann, B., Nöllenburg, M.: Trajectory-based dynamic map labeling. CoRR, arXiv:1309.3963 (2013)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  9. Hsiao, J.Y., Tang, C.Y., Chang, R.S.: An efficient algorithm for finding a maximum weight 2-independent set on interval graphs. Inform. Process. Lett. 43(5), 229–235 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Marx, D.: Efficient approximation schemes for geometric problems? In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 448–459. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Niedermann, B.: Consistent labeling of dynamic maps using smooth trajectories. Master’s thesis, Karlsruhe Institute of Technology (June 2012)

    Google Scholar 

  12. Sester, M., Brenner, C.: Continuous generalization for visualization on small mobile devices. In: Fisher, P.F. (ed.) Spatial Data Handling (SDH 2004), pp. 355–368. Springer (2004)

    Google Scholar 

  13. Wagner, F., Wolff, A.: A practical map labeling algorithm. Comput. Geom. Theory Appl. 7, 387–404 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wagner, F., Wolff, A., Kapoor, V., Strijk, T.: Three rules suffice for good label placement. Algorithmica 30, 334–349 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gemsa, A., Niedermann, B., Nöllenburg, M. (2013). Trajectory-Based Dynamic Map Labeling. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45030-3_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics