Two-Sided Boundary Labeling with Adjacent Sides

  • Philipp Kindermann
  • Benjamin Niedermann
  • Ignaz Rutter
  • Marcus Schaefer
  • André Schulz
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axis-parallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by non-intersecting rectilinear paths, so-called leaders, with at most one bend.

In this paper, we study the problem Two-Sided Boundary Labeling with Adjacent Sides, where labels lie on two adjacent sides of the enclosing rectangle. We present a polynomial-time algorithm that computes a crossing-free leader layout if one exists. So far, such an algorithm has only been known for the cases that labels lie on one side or on two opposite sides of R (where a crossing-free solution always exists). For the more difficult case where labels lie on adjacent sides, we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length.


Planar Solution Full Version Adjacent Side Boundary Label Strip Condition 
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., Efrat, A., Sharir, M.: Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications. SIAM J. Comput. 29(3), 912–953 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bekos, M.A., Kaufmann, M., Nöllenburg, M., Symvonis, A.: Boundary labeling with octilinear leaders. Algorithmica 57(3), 436–461 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Area-feature boundary labeling. Comput. J. 53(6), 827–841 (2010)CrossRefGoogle Scholar
  4. 4.
    Bekos, M.A., Kaufmann, M., Symvonis, A., Wolff, A.: Boundary labeling: Models and efficient algorithms for rectangular maps. Comput. Geom. Theory Appl. 36(3), 215–236 (2007), MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Benkert, M., Haverkort, H.J., Kroll, M., Nöllenburg, M.: Algorithms for multi-criteria boundary labeling. J. Graph. Algorithms Appl. 13(3), 289–317 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chazelle, B.: 36 co-authors: The computational geometry impact task force report. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry, vol. 223, pp. 407–463. American Mathematical Society, Providence (1999)CrossRefGoogle Scholar
  7. 7.
    Fink, M., Haunert, J.H., Schulz, A., Spoerhase, J., Wolff, A.: Algorithms for labeling focus regions. IEEE Trans. Visual. Comput. Graphics 18(12), 2583–2592 (2012), CrossRefGoogle Scholar
  8. 8.
    Freeman, H., Marrinan, S., Chitalia, H.: Automated labeling of soil survey maps. In: ASPRS-ACSM Annual Convention, Baltimore, vol. 1, pp. 51–59 (1996)Google Scholar
  9. 9.
    Gemsa, A., Haunert, J.H., Nöllenburg, M.: Boundary-labeling algorithms for panorama images. In: 19th ACM SIGSPATIAL Int. Conf. Adv. Geogr. Inform. Syst., pp. 289–298 (2011)Google Scholar
  10. 10.
    Gritzmann, P., Mohar, B., Pach, J., Pollack, R.: Embedding a planar triangulation with vertices at specified positions. Amer. Math. Mon. 98, 165–166 (1991)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hirschberg, D.S.: A linear space algorithm for computing maximal common subsequences. Comm. ACM 18(6), 341–343 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Katz, B., Krug, M., Rutter, I., Wolff, A.: Manhattan-geodesic embedding of planar graphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 207–218. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Kindermann, P., Niedermann, B., Rutter, I., Schaefer, M., Schulz, A., Wolff, A.: Two-sided boundary labeling with adjacent sides. Arxiv report (May 2013),
  14. 14.
    van Kreveld, M., Strijk, T., Wolff, A.: Point labeling with sliding labels. Comput. Geom. Theory Appl. 13, 21–47 (1999), zbMATHCrossRefGoogle Scholar
  15. 15.
    Morrison, J.L.: Computer technology and cartographic change. In: Taylor, D. (ed.) The Computer in Contemporary Cartography. Johns Hopkins University Press (1980)Google Scholar
  16. 16.
    Nöllenburg, M., Polishchuk, V., Sysikaski, M.: Dynamic one-sided boundary labeling. In: 18th ACM SIGSPATIAL Int. Symp. Adv. Geogr. Inform. Syst., pp. 310–319 (2010)Google Scholar
  17. 17.
    Raghavan, R., Cohoon, J., Sahni, S.: Single bend wiring. J. Algorithms 7(2), 232–257 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Speckmann, B., Verbeek, K.: Homotopic rectilinear routing with few links and thick edges. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 468–479. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Zoraster, S.: Practical results using simulated annealing for point feature label placement. Cartography and GIS 24(4), 228–238 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Philipp Kindermann
    • 1
  • Benjamin Niedermann
    • 2
  • Ignaz Rutter
    • 2
  • Marcus Schaefer
    • 3
  • André Schulz
    • 4
  • Alexander Wolff
    • 1
  1. 1.Lehrstuhl für Informatik IUniversität WürzburgGermany
  2. 2.Fakultät für InformatikKarlsruher Institut für Technologie (KIT)Germany
  3. 3.College of Computing and Digital MediaDePaul UniversityChicagoUSA
  4. 4.Institut für Mathematische Logik und GrundlagenforschungUniversität MünsterGermany

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