Mixed Upward Planarization – Fast and Robust

  • Martin Siebenhaller
  • Michael Kaufmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


In a mixed upward drawing of a graph G = (V,E) all directed edges ED ⊆ E are represented by monotonically increasing curves. Mixed upward drawings arise in applications like UML diagrams where such edges denote a hierarchical structure. The mixed upward planarization is an important subtask for computing such drawings. We outline a fast and simple heuristic approach that provides a good quality and can be applied to larger graphs as before in reasonable time. Unlike other Sugiyama-style [4] approaches, the quality is comparable to the GT based approach [2] even if there are only few directed edges. Furthermore, the new approach is particularly suitable for extensions like clustering and swimlanes.


  1. 1.
    Brandes, U., Köpf, B.: Fast and Simple Horizontal Coordinate Assignment. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 31–44. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Eiglsperger, M., Kaufmann, M., Eppinger, F.: An Approach for Mixed Upward Planarization. J. Graph Algorithms Appl. 7(2), 203–220 (2003)MathSciNetGoogle Scholar
  3. 3.
    Eiglsperger, M., Siebenhaller, M., Kaufmann, M.: An Efficient Implementation of Sugiyama’s Algorithm for Layered Graph Drawing. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 155–166. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Sugiyama, K., Tagawa, S., Toda, M.: Methods for Visual Understanding of Hierarchical System Structures. IEEE Transactions on Systems, Man and Cybernetics, SMC-11(2), 109–125 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Siebenhaller
    • 1
  • Michael Kaufmann
    • 1
  1. 1.Universität Tübingen, WSITübingenGermany

Personalised recommendations