A Split&Push Approach to 3D Orthogonal Drawing

Extended Abstract
  • Giuseppe Di Battista
  • Maurizio Patrignani
  • Francesco Vargiu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


We present a method for constructing orthogonal drawings of graphs of maximum degree six in three dimensions. Such a method is based on generating the final drawing through a sequence of steps, starting from a “degenerate” drawing. At each step the drawing “splits” into two pieces and finds a structure more similar to its final version. Also, we test the effectiveness of our approach by performing an experimental comparison with several existing algorithms.


Graph Drawing Split Operation Free Vertex Original Vertex Average Edge Length 
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]
    H. Alt, M. Godau, and S. Whitesides. Universal 3-dimensional visibility representations for graphs, in[4], pp. 8–19.CrossRefGoogle Scholar
  2. [2]
    T. C. Biedl. Heuristics for 3d-orthogonal graph drawings. In Proc. 4th Twente Workshop on Graphs and Combinatorial Optimization, pp. 41–44, 1995.Google Scholar
  3. [3]
    P. Bose, H. Everett, S. P. Fekete, A. Lubiw, H. Meijer, K. Romanik, T. Shermer, and S. Whitesides. On a visibility representation for graphs in three dimensions. In D. Avis and P. Bose, eds., Snapshots in Computational and Discrete Geometry, Vol. III, pp. 2–25. McGill Univ., July 1994. McGill tech. rep. SOCS-94.50.Google Scholar
  4. [4]
    F. J. Brandenburg, editor: Proceedings of Graph Drawing’ 95, Vol. 1027 of LNCS, Springer-Verlag, 1996.Google Scholar
  5. [5]
    I. Bruß and A. Frick. Fast interactive 3-D graph visualization, in[4], pp. 99–110.CrossRefGoogle Scholar
  6. [6]
    T. Calamoneri and A. Sterbini. Drawing 2-, 3-, and 4-colorable graphs in O(n 2) volume, in [19], pp. 53–62.Google Scholar
  7. [7]
    R. F. Cohen, P. Eades, T. Lin, and F. Ruskey. Three-dimensional graph drawing. Algorithmica, 17(2):199–208, 1996.CrossRefMathSciNetGoogle Scholar
  8. [8]
    I. F. Cruz and J. P. Twarog. 3d graph drawing with simulated annealing, in[4], pp. 162–165.CrossRefGoogle Scholar
  9. [9]
    G. Di Battista, editor: Proceedings of Graph Drawing’ 97, Vol. 1353 of LNCS, Springer-Verlag, 1998.Google Scholar
  10. [10]
    D. Dodson. COMAIDE: Information visualization using cooperative 3D diagram layout, in[4], pp. 190–201.CrossRefGoogle Scholar
  11. [11]
    P. Eades, C. Stirk, and S. Whitesides. The techniques of Kolmogorov and Bardzin for three dimensional orthogonal graph drawings. I. P. L., 60(2):97–103, 1987.MathSciNetGoogle Scholar
  12. [12]
    P. Eades, A. Symvonis, and S. Whitesides. Two algorithms for three dimensional orthogonal graph drawing, in[19], pp. 139–154.Google Scholar
  13. [13]
    S. P. Fekete, M. E. Houle, and S. Whitesides. New results on a visibility representation of graphs in 3-d, in [4] pp. 234–241.CrossRefGoogle Scholar
  14. [14]
    A. Frick, C. Keskin, and V. Vogelmann. Integration of declarative approaches, in [19], pp. 184–192.Google Scholar
  15. [15]
    A. Garg, R. Tamassia, and P. Vocca. Drawing with colors. In Proc. 4th Annu. Europ. Sympos. Algorithms, vol. 1136 of LNCS, pp. 12–26. Springer-Verlag, 1996.Google Scholar
  16. [16]
    A. N. Kolmogorov and Y. M. Bardzin. About realization of sets in 3-dimensional space. Problems in Cybernetics, pp. 261–268, 1967.Google Scholar
  17. [17]
    G. Liotta and G. Di Battista. Computing proximity drawings of trees in the 3-dimensional space. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of LNCS, pp. 239–250. Springer-Verlag, 1995.Google Scholar
  18. [18]
    B. Monien, F. Ramme, and H. Salmen. A parallel simulated annealing algorithm for generating 3D layouts of undirected graphs, in [4], pp. 396–408.CrossRefGoogle Scholar
  19. [19]
    S. North, editor: Proceedings of Graph Drawing’ 96, Vol. 1190 of LNCS, Springer-Verlag, 1997.Google Scholar
  20. [20]
    D. I. Ostry. Some Three-Dimensional Graph Drawing Algorithms. M.Sc. thesis, Dept. Comput. Sci. and Soft. Eng., Univ. Newcastle, Oct. 1996.Google Scholar
  21. [21]
    J. Pach, T. Thiele, and G. Tóth. Three-dimensional grid drawings of graphs, in [9], pp. 47–51.CrossRefGoogle Scholar
  22. [22]
    A. Papakostas and I. G. Tollis. Incremental orthogonal graph drawing in three dimensions, in[9], pp. 52–63.CrossRefGoogle Scholar
  23. [23]
    M. Patrignani and M. Pizzonia The complexity of the matching-cut problem. Tech. Rep. RT-DIA-35-1998, Dept. of Computer Sci., Univ. di Roma Tre, 1998.Google Scholar
  24. [24]
    M. Patrignani and F. Vargiu. 3DCube: A tool for three dimensional graph drawing, in [9], pp. 284-290.Google Scholar
  25. [25]
    R. Webber and A. Scott. GOVE: Grammar-Oriented Visualisation Environment, in[4], pp. 516–519.CrossRefGoogle Scholar
  26. [26]
    D. R. Wood. Two-bend three-dimensional orthogonal grid drawing of maximum degree five graphs. Technical report, School of Computer Science and Software Engineering, Monash University, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Maurizio Patrignani
    • 1
  • Francesco Vargiu
    • 2
  1. 1.Dipartimento di Informatica e AutomazioneUniversità di Roma TreRomaItaly
  2. 2.AIPARomaItaly

Personalised recommendations