Algorithmica

, Volume 16, Issue 2, pp 233–242

On the embedding phase of the Hopcroft and Tarjan planarity testing algorithm

  • K. Mehlhorn
  • P. Mutzel
Article

Abstract

We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be found in [MMN].

Key words

Planarity testing Topological embedding Planar embedding Combinatorial embedding 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BL]
    K. Booth and L. Lueker. Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms.J. Comput. System Sci., 13:335–379, 1976.Google Scholar
  2. [CNAO]
    N. Chiba, T. Nishizeki, S. Abe, and T. Ozawa. A linear algorithm for embedding planar graphs using PQ-trees.J. Comput. System Sci., 30(1):54–76, 1985.CrossRefGoogle Scholar
  3. [ET]
    S. Even and R. E. Tarjan. Computing an st-numbering.Theoret. Comput. Sci., 2:339–344, 1976.CrossRefGoogle Scholar
  4. [FPP]
    H. de Fraysseix, J. Pach, and R. Pollack. How to draw a planar graph on a grid.Combinatorica, 10:41–51, 1991.Google Scholar
  5. [FR]
    H. de Fraysseix and P. Rosenstiehl. A depth-first-search characterization of planarity.Ann. Discrete Math., 13:75–80, 1982.Google Scholar
  6. [HT]
    J. Hopcroft and R. Tarjan. Efficient planarity testing.J. Assoc. Comput. Mach., 21(4):549–568, 1974.Google Scholar
  7. [LEC]
    A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs.Theory of Graphs, Internat. Symp. (Rome, 1966), pages 215–232, 1967.Google Scholar
  8. [Me]
    K. Mehlhorn.Data Structures and Efficient Algorithms, Volumes I, II, III. Springer-Verlag, Berlin, 1984.Google Scholar
  9. [MMN]
    K. Mehlhorn, P. Mutzel, and St. Näher. An implementation of the Hopcroft and Tarjan planarity test and embedding algorithm. Technical Report MPI-I-93-151, Max-Planck-Institut für Informatik, Saarbrücken, 1993.Google Scholar
  10. [MN]
    K. Mehlhorn and St. Näher. LEDA: A library of efficient data types and algorithms.Comm. ACM, 38(1):96–102, 1995.CrossRefGoogle Scholar
  11. [Mu]
    P. Mutzel. A fast linear time embedding algorithm based on the Hopcroft-Tarjan planarity test. Technical Report, Universität zu Köln, 1992.Google Scholar
  12. [N]
    St. Näher. LEDA manual version 3.1. Technical Report MPI-I-95-1-002, Max-Planck-Institut für Informatik, Saarbrücken, 1995.Google Scholar
  13. [S]
    W. Schnyder. Embedding planar graphs on the grid. InProc. 1st ACM-SIAM Symp. on Discrete Algebra (SODA), San Francisco, pages 138–148, 1990.Google Scholar
  14. [W]
    S. G. Williamson. Depth-first search and Kuratowksi subgraphs.J. Assoc. Comput. Mach., 11:681–693, 1984.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • K. Mehlhorn
    • 1
  • P. Mutzel
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations