Elastic Labels Around the Perimeter of a Map

  • Claudia Iturriaga
  • Anna Lubiw
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)


In this paper we study the map labeling problem of attaching rectangular labels to points, but with the novelty that our labels are elastic, in the sense that the height and width of each rectangle may vary though we require a fixed area. Our main result is a polynomial time algorithm for the rectangle perimeter labeling problem, where the points to be labeled lie on the boundary of a rectangular map. This problem is likely to be relevant in Geographical Information Systems (GIS) as maps are displayed dynamically on a computer screen using clipping, panning, and zooming.


Geographical Information System Geographical Information System Polynomial Time Algorithm Label Problem Horizontal Line Segment 
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.
    B. Chazelle et al. Application challenges to computational geometry: CG impact task force report. Technical Report TR-521-96, Princeton Univ., April 1996.Google Scholar
  2. 2.
    J. Christensen, J. Marks, and S. Shieber. An empirical study of algorithms for point feature label placement. ACM Transactions on Graphics. 14(3) (1995), 203–232.CrossRefGoogle Scholar
  3. 3.
    J. Christensen, S. Friedman, J. Marks, and S. Shieber. Empirical testing of algorithms for variable-sized label placement. Proc. 13th ACM Symp. on Comp. Geom. (1997), 415–417.Google Scholar
  4. 4.
    M. Formann and F. Wagner. A packing problem with applications in lettering of maps. In Proc. 7th ACM Symp. on Comp. Geom. (1991) 281–288.Google Scholar
  5. 5.
    C. Iturriaga and A. Lubiw. NP-hardness of some map labeling problems. Technical Report CS 97-18. University of Waterloo, 1997.Google Scholar
  6. 6.
    C. Iturriaga and A. Lubiw. Elastic labels: the two-axis case. In G. Di Battista editor, Graph Drawing (Proc. GD’97). vol. 1353 of LNCS. Springer-Verlag. (1998), 181–192.Google Scholar
  7. 7.
    C. Iturriaga. Map Labeling Problems, Ph.D. Thesis, University of Waterloo, 1999.Google Scholar
  8. 8.
    T. Kato and H. Imai. The NP-completeness of the character placement problem of 2 or 3 degrees of freedom. Record of Joint Conference of Electrical and Electronic engineers in Kyushu. (1988) 11–18. In Japanese.Google Scholar
  9. 9.
    D. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM Disc. Math. 5(3) (1992), 422–427.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    L. Kučera, K. Mehlhorn, B. Preis, and E. Schwarzenecker. Exact algorithms for a geometric packing problem. In Proc. 10th Symp. Theoret. Aspects Comput. Sci., 665 of LNCS, 317–322. Springer-Verlag, 1993.Google Scholar
  11. 11.
    J. Marks and S. Shieber. The computational complexity of cartographic label placement. Technical Report CRCT-05-91. Harvard University, 1991.Google Scholar
  12. 12.
    F. Wagner and A. Wolff. A practical map labeling algorithm. Computational Geometry: Theory and Applications. (1997) 387–404.Google Scholar
  13. 13.
    A. Wolff and T. Strijk. A map labeling bibliography, 1996.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Claudia Iturriaga
    • 1
  • Anna Lubiw
    • 2
  1. 1.University of New BrunswickCanada
  2. 2.University of WaterlooCanada

Personalised recommendations