Practical Level Planarity Testing and Layout with Embedding Constraints

  • Martin Harrigan
  • Patrick Healy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


We describe a practical method to test a leveled graph for level planarity and provide a level planar layout of the graph if the test succeeds, all in quadratic running-time. Embedding constraints restricting the order of incident edges around the vertices are allowed.


  1. 1.
    Chiba, N., Nishizeki, T., Abe, S., Ozawa, T.: A Linear Algorithm for Embedding Planar Graphs using PQ-Trees. Journal of Comp. and Sys. Sci. 30(1), 54–76 (1985)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Di Battista, G., Nardelli, E.: Hierarchies and Planarity Theory. IEEE Trans. Sys., Man and Cybern. 18(6), 1035–1046 (1988)MATHCrossRefGoogle Scholar
  3. 3.
    Gutwenger, C., Klein, K., Mutzel, P.: Planarity Testing and Optimal Edge Insertion with Embedding Constraints. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 126–137. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Healy, P., Kuusik, A.: Algorithms for Multi-Level Graph Planarity Testing and Layout. Theor. Comp. Sci. 320(2-3), 331–344 (2004)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Heath, L., Pemmaraju, S.: Recognizing Leveled-Planar DAGs in Linear Time. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 300–311. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  6. 6.
    Jünger, M., Leipert, S.: Level Planar Embedding in Linear Time. Journal of Graph Alg. and App. 6(1), 67–113 (2002)MATHGoogle Scholar
  7. 7.
    Randerath, B., Speckenmeyer, E., Boros, E., Hammer, P., Kogan, A., Makino, K., Simeone, B., Cepek, O.: A Satisfiability Formulation of Problems on Level Graphs. Technical report 40-2001, Rutgers Center for Operations Research, Rutgers University (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Martin Harrigan
    • 1
  • Patrick Healy
    • 1
  1. 1.Department of Computer Science and Information SystemsUniversity of LimerickIreland

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