Refinement of Orthogonal Graph Drawings

  • Janet M. Six
  • Konstantinos G. Kakoulis
  • Ioannis G. Tollis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


Current orthogonal graph drawing algorithms produce drawings which are generally good. However, many times the readability of orthogonal drawings can be significantly improved with a postprocessing technique, called refinement, which improves aesthetic qualities of a drawing such as area, bends, crossings, and total edge length. Refinement is separate from layout and works by analyzing and then fine-tuning the existing drawing in an efficient manner. In this paper we define the problem and goals of orthogonal drawing refinement and introduce a methodology which efficiently refines any orthogonal graph drawing. We have implemented our technique in C++ and conducted preliminary experiments over a set of drawings from five well known orthogonal drawing systems. Experimental analysis shows our technique to produce an average 34% improvement in area, 22% in bends, 19% in crossings, and 34% in total edge length.


Aesthetic Quality Graph Drawing Super Node Layout Algorithm Edge Segment 
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.
    T. Biedl and G. Kant, A Better Heuristic for Orthogonal Graph Drawings, Proc. ESA’94, LNCS 855, Springer-Verlag, 1994, pp. 24–35.Google Scholar
  2. 2.
    T. C. Biedl, B. P. Madden and I. G. Tollis, The Three-Phase Method: A Unified Approach to Orthogonal Graph Drawing, Proc. GD’97, LNCS 1353, Springer-Verlag, 1997, pp. 391–402.Google Scholar
  3. 3.
    S. Bridgeman, J. Fanto, A. Garg, R. Tamassia and L. Vismara, Interactive Giotto: An Algorithm for Interactive Orthogonal Graph Drawing, Proc. GD’ 97, LNCS1353, Springer-Verlag, 1997, pp. 303–308.Google Scholar
  4. 4.
    S. Bridgeman, A. Garg and R. Tamassia, A Graph Drawing and Translation Service on the WWW, Proc. GD’ 96, LNCS 1190, Springer-Verlag, 1997, pp. 45–52.Google Scholar
  5. 5.
    R. F. Cohen, G. Di Battista, R. Tamassia and I. G. Tollis, Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST-Digraphs, SIAM J. Computing, 24(5), October 1995, pp. 970–1001.Google Scholar
  6. 6.
    G. Di Battista, P. Eades, R. Tamassia and I. G. Tollis, Algorithms for Drawing Graphs: An Annotated Bibliography, Computational Geometry: Theory and Applications, 4(5), 1994, pp. 235–282.zbMATHMathSciNetGoogle Scholar
  7. 7.
    G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari and F. Vargiu, An Experimental Comparison of Four Graph Drawing Algorithms, Computational Geometry: Theory and Applications, 1997, pp. 303–325.Google Scholar
  8. 8.
    C. Ding and P. Mateti, A Framework for the Automated Drawing of Data Structure Diagrams, IEEE Transactions on Software Engineering, 16(5), 1990, pp. 543–557.CrossRefGoogle Scholar
  9. 9.
    J. Doenhardt and T. Lengauer, Algorithmic Aspects of One Dimensional Layout Compaction, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 6(5), 1987, pp. 863–879.CrossRefGoogle Scholar
  10. 10.
    C. Esposito, Graph Graphics: Theory and Practice, Computers and Mathematics with Applications, 15(4), 1988, pp. 247–253.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    S. Even and G. Granot, Rectilinear Planar Drawings with Few Bends in Each Edge, Tech. Report 797, CS Dept., Technion, Israel Inst. of Tech., 1994.Google Scholar
  12. 12.
    Jody Fanto, Postprocessing of GIOTTO drawings, people/jrf/.
  13. 13.
    U. Fößmeier, Interactive Orthogonal Graph Drawing: Algorithms and Bounds, Proc. GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 111–123.Google Scholar
  14. 14.
    U. Fößmeier and M. Kaufmann, Algorithms and Area Bounds for Nonplanar Orthogonal Drawings, Proc. GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 134–145.Google Scholar
  15. 15.
    M. Y. Hsueh, Symbolic Layout and Compaction of Integrated Circuits, Ph.D. Thesis, University of California at Berkeley, Berkeley,CA, 1979.Google Scholar
  16. 16.
    G. Kant, Drawing Planar Graphs Using the lmc-ordering, Proc. 33rd Ann. IEEE Symposium on Found. of Comp. Sci., 1992, pp. 101–110.Google Scholar
  17. 17.
    C. Kosak, J. Marks and S. Shieber, Automating the Layout of Network Diagrams with Specified Visual Organization, IEEE Transactions on Systems, Man, Cybernetics, 24(3), 1994, pp. 440–454CrossRefGoogle Scholar
  18. 18.
    Thomas Lengauer, Combinatorial Algorithms for Integrated Circuit Layout, John Wiley and Sons, 1990.Google Scholar
  19. 19.
    K. Miriyala, S. W. Hornick and R. Tamassia, An Incremental Approach to Aesthetic Graph Layout, Proc. Int. Workshop on Computer-Aided Software Engineering (Case)’ 93 ), 1993, pp. 297–308.Google Scholar
  20. 20.
    K. Misue, P. Eades, W. Lai and K. Sugiyama, Layout Adjustment and the Mental Map, J. of Visual Languages and Computing, June 1995, pp. 183–210.Google Scholar
  21. 21.
    A. Papakostas, Information Visualization: Orthogonal Drawings of Graphs, Ph.D. Thesis, University of Texas at Dallas, 1996.Google Scholar
  22. 22.
    A. Papakostas, J. M. Six and I. G. Tollis, Experimental and Theoretical Results in Interactive Orthogonal Graph Drawing, Proc. GD’ 96, LNCS 1190, Springer-Verlag, 1997, pp. 371–386.Google Scholar
  23. 23.
    A. Papakostas and I. G. Tollis, Algorithms for Area-Efficient Orthogonal Drawings, Computational Geometry: Theory and Applications, 9(1998) 1998, pp. 83–110.zbMATHMathSciNetGoogle Scholar
  24. 24.
    A. Papakostas and I. G. Tollis, Issues in Interactive Orthogonal Graph Drawing, Proc. GD’ 95, LNCS 1027, Springer-Verlag, 1995, pp. 419–430. Also available at http://www. utdallas. edu/~tollis/papers. html. Google Scholar
  25. 25.
    H. Purchase, Which Aesthetic has the Greatest Effect on Human Understanding, Proc. of GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 248–261.Google Scholar
  26. 26.
    M. Schäffter, Drawing Graphs on Rectangular Grids, Discr. Appl. Math., 63(1995), pp. 75–89.zbMATHCrossRefGoogle Scholar
  27. 27.
    R. Tamassia, On Embedding a Graph in the Grid with the Minimum Number of Bends, SIAM J. Comput., 16(1987), pp. 421–444.zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    R. Tamassia, G. Di Battista and C. Batini, Automatic Graph Drawing and Readability of Diagrams, IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 1988, pp. 61–79.CrossRefGoogle Scholar
  29. 29.
    R. Tamassia and I. G. Tollis, Planar Grid Embeddings in Linear Time, IEEE Trans. on Circuits and Systems CAS-36, 1989, pp. 1230–1234.Google Scholar
  30. 30.
    I. G. Tollis, Graph Drawing and Information Visualization, ACM Computing Surveys, 28A(4), December 1996. Also available at ~tollis/SDCR96/TollisGeometry/.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Janet M. Six
    • 1
  • Konstantinos G. Kakoulis
    • 1
  • Ioannis G. Tollis
    • 1
  1. 1.CAD & Visualization Lab Department of Computer ScienceThe University of Texas at DallasRichardson

Personalised recommendations