Height-Preserving Transformations of Planar Graph Drawings

  • Therese Biedl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

There are numerous styles of planar graph drawings, such as straight-line drawings, poly-line drawings, orthogonal graph drawings and visibility representations. Given a planar drawing in one of these styles, can it be converted it to another style while keeping the height unchanged? This paper answers this question for (nearly) all pairs of these styles, as well as for related styles that additionally restrict edges to be y-monotone and/or vertices to be horizontal line segments. These transformations can be used to develop new graph drawing results, especially for height-optimal drawings.

Keywords

Planar graph drawing poly-line drawing straight-line drawing orthogonal drawing visibility representation minimizing height 

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References

  1. 1.
    Babu, J., Basavaraju, M., Chandran Leela, S., Rajendraprasad, D.: 2-connecting outerplanar graphs without blowing up the pathwidth. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 626–637. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Biedl, T.: A 4-approximation for the height of drawing 2-connected outer-planar graphs. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 272–285. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Biedl, T., Lubiw, A., Petrick, M., Spriggs, M.J.: Morphing orthogonal planar graph drawings. ACM Transactions on Algorithms 9(4), 29 (2013)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Biedl, T., Bläsius, T., Niedermann, B., Nöllenburg, M., Prutkin, R., Rutter, I.: Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 460–471. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Chimani, M., Zeranski, R.: Upward planarity testing via SAT. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 248–259. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Dujmovic, V., Fellows, M., Kitching, M., Liotta, G., McCartin, C., Nishimura, N., Ragde, P., Rosamond, F., Whitesides, S., Wood, D.: On the parameterized complexity of layered graph drawing. Algorithmica 52, 267–292 (2008)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Felsner, S., Liotta, G., Wismath, S.: Straight-line drawings on restricted integer grids in two and three dimensions. Journal of Graph Algorithms and Applications 7(4), 335–362 (2003)CrossRefMathSciNetGoogle Scholar
  8. 8.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10, 41–51 (1990)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    He, X., Wang, J., Zhang, H.: Compact visibility representation of 4-connected plane graphs. Theor. Comput. Sci. 447, 62–73 (2012)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Hoffmann, M., van Kreveld, M., Kusters, V., Rote, G.: Quality ratios of measures for graph drawing styles. In: Canadian Conference on Computational Geometry, CCCG 2014 (to appear, 2014)Google Scholar
  12. 12.
    Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16, 4–32 (1996)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. Teubner/Wiley & Sons, Stuttgart/Chicester (1990)Google Scholar
  14. 14.
    Miura, K., Nakano, S., Nishizeki, T.: Convex grid drawings of four-connected plane graphs. Int. J. Found. Comput. Sci. 17(5), 1031–1060 (2006)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Pach, J., Tóth, G.: Monotone drawings of planar graphs. Journal of Graph Theory 46(1), 39–47 (2004)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Rosenstiehl, P., Tarjan, R.E.: Rectilinear planar layouts and bipolar orientation of planar graphs. Discrete Computational Geometry 1, 343–353 (1986)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Schnyder, W.: Embedding planar graphs on the grid. In: ACM-SIAM Symposium on Discrete Algorithms (SODA 1990), pp. 138–148 (1990)Google Scholar
  18. 18.
    Biedl, T., Kant, G.: A better heuristic for orthogonal graph drawings. Computational Geometry: Theory and Applications 9, 159–180 (1998)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Biedl, T., Kaufmann, M., Mutzel, P.: Drawing planar partitions II: HH-drawings. In: Hromkovič, J., Sýkora, O. (eds.) WG 1998. LNCS, vol. 1517, pp. 124–136. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  20. 20.
    Tamassia, R., Tollis, I.: A unified approach to visibility representations of planar graphs. Discrete Computational Geometry 1, 321–341 (1986)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Wismath, S.: Characterizing bar line-of-sight graphs. In: ACM Symposium on Computational Geometry (SoCG 1985), pp. 147–152 (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Therese Biedl
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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