Elastic Labels on the Perimeter of a Rectangle

  • Claudia Iturriaga
  • Anna Lubiw
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


An important and challenging task in cartography is the labeling of maps-attaching text to geographic features. Usually, the features to be labeled are regions, lines, and points on a map. One of the traditional formulations of the problem of labeling points is the point-feature-label placement problem, where we are given a set of points in the plane, and an axis-parallel rectangular label associated with each point, and the problem is to place each label with one corner at its associated point such that no two labels overlap. [KIm88, FWa91, MSh91, KRa92] This problem is known to be NP-complete. There are approximation algorithms when the problem consists of scaling the labels.


Approximation Algorithm Polynomial Time Algorithm Traditional Formulation Packing Problem Geographic Feature 
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  1. [FWa91]
    M. Formann and F. Wagner. A packing problem with applications in lettering of maps. Proceedings of the 7th ACM Symposium on Computational Geometry. (1991) 281–288.Google Scholar
  2. [KIm88]
    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), 1138. In Japanese.Google Scholar
  3. [KRa92]
    D. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM Disc. Math. (1992) 5(3), 422–427.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [ILu97a]
    C. Iturriaga and A. Lubiw. NP-hardness of some map labeling problems. Technical Report CS-97-18. University of Waterloo (1997).Google Scholar
  5. [ILu97b]
    C. Iturriaga and A. Lubiw. Elastic labels: the two-axis case. In _G. Di Battista editor, Graph Drawing (Proc. GD’97). vol. 1353 of Lecture Notes in Computer Science. Springer-Verlag. (1998), 181–192.CrossRefGoogle Scholar
  6. [MSh91]
    J. Marks and S. Shieber. The computational complexity of cartographic label placement. Technical Report CRCT-05-91. Harvard University (1991).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Claudia Iturriaga
    • 1
  • Anna Lubiw
    • 1
  1. 1.Dept.of Computer ScienceUniversity of WaterlooCanada

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