Algorithms and area bounds for nonplanar orthogonal drawings

  • Ulrich Föβmeier
  • Michael Kaufmann
Left and Right Turns
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)


We report on some extensions of the Kandinsky model: A new and highly nontrivial technique to incorporate nonplanar drawings into the Kandinsky model in the same way as in the GIOTTO approach is presented. This means a major step towards the practical usability of our approach. The used technique even gives new insights for the solvability of network flow problems. Another variant of Kandinsky ensures a minimal size of the vertices removing the requirement of uniform size of each vertex. We present a new technique to evaluate our approach with respect to the area and the number of bends, and to perform a reasonable comparison with the GIOTTO approach.


  1. 1.
    Bertolazzi, P., G. Di Battista, W. Didimo, Computing Orthogonal Drawings with the Minimum Number of Bends, Proc. of WADS'97, to appear.Google Scholar
  2. 2.
    Biedl, T.C., Orthogonal Graph Drawing, Algorithms and Lower Bounds, Diplomarbeit TU Berlin, 1995.Google Scholar
  3. 3.
    Biedl, T.C., M. Kaufmann, Area-Efficient Static and Incremental Drawings of High-Degree Graphs. to appear in ESA 1997.Google Scholar
  4. 4.
    Di Battista, G., P. Eades, R. Tamassia, I.G.Tollis, Algorithms for Drawing Graphs: An Annotated Bibliography, Computational Geometry: Theory & Applications, 235–282,1994.Google Scholar
  5. 5.
    Di Battista, G., A. Garg, G. Liotta, R. Tamassia, E. Tassinari, F. Vargiu, An Experimental Comparison of Three Graph Drawing Algorithms, Computational Geometry: Theory & Applications, 1996.Google Scholar
  6. 6.
    CPLEX optimization, Inc., Using the CPLEX Base System.Google Scholar
  7. 7.
    Eades, P., J. Marks, Graph-Drawing Contest Report, Proceedings on GD'94, Princeton, LNCS 894, 143–146, 1995.Google Scholar
  8. 8.
    Fößmeier U., M. Kaufmann, Drawing High Degree Graphs with Low Bend Numbers, Proceedings on GD'95, Passau, LNCS 1027, 254–266, 1995.Google Scholar
  9. 9.
    Fößmeier U., G. Kant, M. Kaufmann, 2-Visibility Drawings of Planar Graphs, Proceedings on GD'96, Berkeley, LNCS 1190, 155–168, 1996.Google Scholar
  10. 10.
    Garey, M.R., D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, New York, 1979.Google Scholar
  11. 11.
    Kleinschmidt, P., personal communication.Google Scholar
  12. 12.
    Lawler, E.L., Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976, Chapter 4.Google Scholar
  13. 13.
    Papakostas A., I.G. Tollis, High-degree orthogonal drawings with small grid-size and few bends. Technical report, University of Texas at Dallas, Richardson, TX 75083, December 1996.Google Scholar
  14. 14.
    Tarnassia, R. On Embedding a Graph in the Grid with the Minimum Number of Bends, SIAM Journal of Computing, vol. 16, No. 3, 421–444, 1987.CrossRefGoogle Scholar
  15. 15.
    Tamassia, R., G. Di Battista, C. Batini, Automatic Graph Drawing and Readability of Diagrams, IEEE Trans. Systems, Man and Cybernetics, 61–79, 1988.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ulrich Föβmeier
    • 1
  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

Personalised recommendations