Bitonic st-orderings of Biconnected Planar Graphs

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


Vertex orderings play an important role in the design of graph drawing algorithms. Compared to canonical orderings, st-orderings lack a certain property that is required by many drawing methods. In this paper, we propose a new type of st-ordering for biconnected planar graphs that relates the ordering to the embedding. We describe a linear-time algorithm to obtain such an ordering and demonstrate its capabilities with two applications.


Planar Graph Outer Face Graph Drawing Virtual Edge Biconnected Graph 
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  1. 1.
    Alam, M.J., Biedl, T., Felsner, S., Kaufmann, M., Kobourov, S.G., Ueckerdt, T.: Computing cartograms with optimal complexity. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry, SoCG 2012, pp. 21–30. ACM (2012)Google Scholar
  2. 2.
    Badent, M., Brandes, U., Cornelsen, S.: More canonical ordering. Journal of Graph Algorithms and Applications 15(1), 97–126 (2011)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  5. 5.
    Di Battista, G., Tamassia, R.: Incremental planarity testing. In: 30th Annual Symposium on Foundations of Computer Science, pp. 436–441 (1989)Google Scholar
  6. 6.
    Even, S., Tarjan, R.E.: Computing an st-numbering. Theoretical Computer Science 2(3), 339–344 (1976)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Gutwenger, C., Mutzel, P.: Planar polyline drawings with good angular resolution. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 167–182. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Gutwenger, C., Mutzel, P.: A linear time implementation of SPQR-trees. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 77–90. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Harel, D., Sardas, M.: An algorithm for straight-line drawing of planar graphs. Algorithmica 20(2), 119–135 (1998)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16, 4–32 (1996)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    OGDF - Open Graph Drawing Framework,
  12. 12.
    Tamassia, R.: Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications). Chapman & Hall/CRC (2007)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Martin Gronemann
    • 1
  1. 1.Institut für InformatikUniversität zu KölnGermany

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