Straight-Line Drawing of Quadrangulations

  • Éric Fusy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

This article introduces a straight-line drawing algorithm for quadrangulations, in the family of the face-counting algorithms. It outputs in linear time a drawing on a regular W×H grid such that W + H = n − 1 − Δ, where n is the number of vertices and Δ is an explicit combinatorial parameter of the quadrangulation.

References

  1. 1.
    Biedl, T., Brandenburg, F.J.: Drawing planar bipartite graphs with small area. In: Proceedings of CCCG, Windsor, pp. 105–108 (2005)Google Scholar
  2. 2.
    Bonichon, N., Felsner, S., Mosbah, M.: Convex drawings of 3-connected plane graphs. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 287–299. Springer, Heidelberg (2004)Google Scholar
  3. 3.
    de Fraysseix, H., Ossona de Mendez, P., Pach, J.: A left-first search algorithm for planar graphs. Discrete Comput. Geom. 13, 459–468 (1995)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    de Fraysseix, H., Ossona de Mendez, P., Rosenstiehl, P.: Bipolar orientations revisited. Discrete Appl. Math. 56(2-3), 157–179 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fusy, E.: Transversal structures on triangulations, with application to straight-line drawing. In: Cointe, P. (ed.) ECOOP 1996. LNCS, vol. 1098, pp. 177–188. Springer, Heidelberg (1996), Full paper with proofs available at, http://arxiv.org/abs/math.CO/0602163 Google Scholar
  7. 7.
    Huemer, C., Kappes, S.: A binary labelling for plane laman graphs and quadrangulations. In: Proceedings of EWCG, Delphi, pp. 83–86 (2006)Google Scholar
  8. 8.
    Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16(1), 4–32 (1996)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Kant, G., He, X.: Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems. Theoretical Computer Science 172(1-2), 175–193 (1997)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Miura, K., Nakano, S., Nishizeki, T.: Grid drawings of four-connected plane graphs. Disc. Comput. Geometry 26(2), 73–87 (2001)MATHMathSciNetGoogle Scholar
  11. 11.
    Schnyder, W.: Embedding planar graphs on the grid. In: Proceedings of the first annual ACM-SIAM Symposium on Discrete Algorithms, pp. 138–148. ACM Press, New York (1990)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Éric Fusy
    • 1
  1. 1.Algorithms Project (INRIA Rocquencourt) and LIX (École Polytechnique) 

Personalised recommendations