Planarization of Clustered Graphs

Extended Abstract
  • Giuseppe Di Battista
  • Walter Didimo
  • A. Marcandalli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)


We propose a planarization algorithm for clustered graphs and experimentally test its efficiency and effectiveness. Further, we integrate our planarization strategy into a complete topology-shape-metrics algorithm for drawing clustered graphs in the orthogonal drawing convention.


Span Tree Planar Graph Planarization Algorithm Dual Graph Boundary Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    AGD. A library of algorithms for graph drawing. Online.
  2. 2.
    P. Bertolazzi, G. Di Battista, and W. Didimo. Computing orthogonal drawings with the minimum numbr of bends. IEEE Transactions on Computers, 49(8), 2000.Google Scholar
  3. 3.
    U. Brandes, S. Cornelsen, and D. Wagner. How to draw the minimum cuts of a planar graph. In J. Marks, editor, Graph Drawing (Proc. GD’ 00), volume 1984of Lecture Notes Comput. Sci., pages 103–114. Springer-Verlag, 2000.Google Scholar
  4. 4.
    G. Di Battista, W. Didimo, M. Patrignani, and M. Pizzonia. Orthogonal and quasi-upward drawings with vertices of arbitrary size. In Proc. GD’ 99, volume 1731 of LNCS, pages 297–310, 2000.Google Scholar
  5. 5.
    G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing. Prentice Hall, Upper Saddle River, NJ, 1999.MATHCrossRefGoogle Scholar
  6. 6.
    G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari, and F. Vargiu. An experimental comparison of four graph drawing algorithms. Comput. Geom. TheoryAppl., 7:303–325, 1997.CrossRefMATHGoogle Scholar
  7. 7.
    H. N. Djidjev. A linear algorithm for the maximal planar subgraph problem. In Proc. 4th Workshop Algorithms Data Struct., Lecture Notes Comput. Sci. Springer-Verlag, 1995.Google Scholar
  8. 8.
    C. A. Duncan, M. T. Goodrich, and S. G. Kobourov. Planarity-preserving clustering and embedding for large planar graphs. In J. Kratochvil, editor, Graph Drawing (Proc. GD’ 99), volume 1731 of Lecture Notes Comput. Sci., pages 186–196. Springer-Verlag, 1999.Google Scholar
  9. 9.
    P. Eades and Q. W. Feng. Multilevel visualization of clustered graphs. In S. North, editor, Graph Drawing (Proc. GD’ 96), volume 1190 of Lecture Notes Comput. Sci., pages 101–112. Springer-Verlag, 1996.Google Scholar
  10. 10.
    P. Eades, Q. W. Feng, and X. Lin. Straight line drawing algorithms for hierarchical graphs and clustered graphs. In S. North, editor, Graph Drawing (Proc. GD’ 96), volume 1190 of Lecture Notes Comput. Sci., pages 113–128. Springer-Verlag, 1996.Google Scholar
  11. 11.
    P. Eades, Q. W. Feng, and H. Nagamochi. Drawing clustered graphs on an orthogonal grid. Journal of Graph Algorithms and Applications, 3(4):3–29, 2000.MathSciNetGoogle Scholar
  12. 12.
    S. Even. Graph Algorithms. Computer Science Press, Potomac, Maryland, 1979.MATHGoogle Scholar
  13. 13.
    Q. W. Feng, R. Cohen, and P. Eades. How to draw a planar clustered graph. In Computing and Combinatorics (Cocoon’ 95), volume 959 of Lecture Notes Comput. Sci., pages 21–30. Springer-Verlag, 1995.Google Scholar
  14. 14.
    Q. W. Feng, R. F. Cohen, and P. Eades. Planarity for clustered graphs. In P. Spirakis, editor, Symposium on Algorithms (Proc. ESA’ 95), volume 979 of Lecture Notes Comput. Sci., pages 213–226. Springer-Verlag, 1995.Google Scholar
  15. 15.
    U. Fößmeier and M. Kaufmann. Drawing high degree graphs with low bend numbers. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD’ 95), volume 1027 of Lecture Notes Comput. Sci., pages 254–266. Springer-Verlag, 1996.Google Scholar
  16. 16.
    GDToolkit. Graph drawing toolkit. Online.
  17. 17.
    M. L. Huang and P. Eades. A fully animated interactive system for clustering and navigating huge graphs. In S. H. Whitesides, editor, Graph Drawing (Proc. GD’ 98), volume 1547 of Lecture Notes Comput. Sci., pages 374–383. Springer-Verlag, 1998.Google Scholar
  18. 18.
    M. Jünger, E. K. Lee, P. Mutzel, and T. Odenthal. A polyhedral approach to the multi-layer crossing number problem. In G. Di Battista, editor, Graph Drawing (Proc. GD’ 97), number 1353 in Lecture Notes Comput. Sci., pages 13–24. Springer-Verlag, 1997.Google Scholar
  19. 19.
    M. Jünger and P. Mutzel. Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica, 16(1):33–59, 1996. (special issue on Graph Drawing, edited by G. Di Battista and R. Tamassia).Google Scholar
  20. 20.
    D. Lütke-Hüttmann. Knickminimales Zeichnen 4-planarer Clustergraphen. Master’s thesis, Universität des Saarlandes, 1999.Google Scholar
  21. 21.
    T. Nishizeki and N. Chiba. Planar graphs: Theory and algorithms. Ann. Discrete Math., 32, 1988.Google Scholar
  22. 22.
    B. Schieber and U. Vishkin. On finding lowest common ancestors: Simplification and parallelization. SIAM J. Comput., 17(6):1253–1262, 1988.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    K. Sugiyama and K. Misue. Visualization of structural information: Automatic drawing of compound digraphs. IEEE Trans. Softw. Eng., 21(4):876–892, 1991.MathSciNetGoogle Scholar
  24. 24.
    K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical systems. IEEE Trans. Syst. Man Cybern., SMC-11(2):109–125, 1981.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Walter Didimo
    • 1
  • A. Marcandalli
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità di Roma TreRomaItaly

Personalised recommendations