Drawing Algorithms for Series-Parallel Digraphs in Two and Three Dimensions

  • Seok-Hee Hong
  • Peter Eades
  • Aaron Quigley
  • Sang-Ho Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


In this paper we have introduced two algorithms for drawing series parallel digraphs. One constructs two dimensional drawings which display symmetries, the other constructs three dimensional drawings with a footprint of minimum size.

Future work will include combinations of these two algorithms: we would like to display as much symmetry as possible in a three dimensional drawing of small footprint.


  1. 1.
    A. Aho, J. Hopcroft and J. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.Google Scholar
  2. 2.
    P. Bertolazzi, R.F. Cohen, G. D. Battista, R. Tamassia and I. G. Tollis, How to Draw a Series-Parallel Digraph, International Journal of Computational Geometry and Applications, 4(4), pp 385–402, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    R.F. Cohen, G. D. Battista, R. Tamassia and I. G. Tollis, Dynamic Graph Drawing: Trees, Series-Parallel Digraphs, and Planar st-Digraphs, SIAM Journal on Computing, 24(5), pp 970–1001, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Eades and X. Lin, Spring Algorithms and Symmetry, Computing and Combinatorics, Springer Lecture Notes in Computer Science 1276, (Ed. Jiang and Lee), 202–211.Google Scholar
  5. 5.
    P. Eades, T. Lin and X. Lin, Minimum Size h-v Drawings, Advanced Visual Interfaces (Proceedings of AVI 92, Rome, July 1992), World Scientific Series in Computer Science 36, pp. 386–394.Google Scholar
  6. 6.
    X. Lin, Analysis of Algorithms for Drawing Graphs, PhD thesis,University of Queensland 1992.Google Scholar
  7. 7.
    A. Lubiw, Some NP-Complete Problems similar to Graph Isomorphism, SIAM Journal on Computing 10(1):11–21, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Manning and M. J. Atallah, Fast Detection and Display of Symmetry in Trees, Congressus Numerantium 64, pp. 159–169, 1988.MathSciNetGoogle Scholar
  9. 9.
    J. Manning and M. J. Atallah, Fast Detection and Display of Symmetry in Outerplanar Graphs, Discrete Applied Mathematics 39, pp. 13–35, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    J. Manning, Geometric Symmetry in Graphs, PhD Thesis, Purdue University 1990.Google Scholar
  11. 11.
    R.A. Mathon, A Note on Graph Isomorphism Counting Problem, Information Processing Letters 8, 1979, pp. 131–132.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    R. Tamassia and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discr. and Comp. Geometry 1 (1986), pp. 321–341.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    J. Valdes, R. Tarjan and E. Lawler, The Recognition of Series-Parallel Digraphs, SIAM Journal on Computing 11(2), pp. 298–313, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    J. Valdes, Parsing Flowchart and Series-Parallel Graphs, Technical Report STAN-CS-78-682, Computer Science Department, Stanford University, 1978.Google Scholar
  15. 15.
    H. Wielandt, Finite permutation groups, Academic Press, 1964.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Seok-Hee Hong
    • 1
  • Peter Eades
    • 2
  • Aaron Quigley
    • 2
  • Sang-Ho Lee
    • 1
  1. 1.Department of Computer Science and EngineeringEwha Womans UniversityKorea
  2. 2.Department of Computer Science and Software EngineeringUniversity of NewcastleAustralia

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