2-Visibility drawings of planar graphs

  • Ulrich Fößmeier
  • Goos Kant
  • Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)

Abstract

In a 2-visibility drawing the vertices of a given graph are represented by rectangular boxes and the adjacency relations are expressed by horizontal and vertical lines drawn between the boxes. In this paper we want to emphasize this model as a practical alternative to other representations of graphs, and to demonstrate the quality of the produced drawings. We give several approaches, heuristics as well as provably good algorithms, to represent planar graphs within this model. To this, we present a polynomial time algorithm to compute a bend-minimum orthogonal drawing under the restriction that the number of bends at each edge is at most 1.

References

  1. 1.
    Biedl T. and G. Kant, A better heurisitic for orthogonal graph drawings, Proc. 2nd Ann. European Symposium on Algorithms (ESA'94), LNCS 855, Springer-Verlag, pp. 24–35, 1994.Google Scholar
  2. 2.
    Chrobak, M., and T.H. Payne, A Linear Time Algorithm for Drawing Planar Graphs on the Grid, Tech. Rep. UCR-CS-90-2, Dept. of Math. and Comp. Science, University of California at Riverside, 1990.Google Scholar
  3. 3.
    Di Battista, G., P. Eades, R. Tamassia and I.G. Tollis, Algorithms for automatic graph drawing: an annotated bibliography, Computational Geometry: Theory and Practice 4, pp. 235–282, 1994.CrossRefGoogle Scholar
  4. 4.
    Fraysseix, H. de, J. Pach and R. Pollack, How to draw a planar graph on a grid, Combinatorica 10, pp. 41–51, 1990.Google Scholar
  5. 5.
    Fößmeier, U., and M. Kaufmann, Drawing high degree graphs with low bend numbers, Proc. 4th Symposium on Graph Drawing (GD'95), LNCS 1027, Springer-Verlag, pp. 254–266, 1995.Google Scholar
  6. 6.
    Hutchinson, J.P., T. Shermer and A. Vince, On representation of some thickness-two graphs, Proc. 4th Symposium on Graph Drawing (GD'95), LNCS 1027, Springer-Verlag, pp. 324–332, 1996.Google Scholar
  7. 7.
    Kant, G., A more compact visibility representation, Proc. 19th Intern. Workshop on Graph-Theoretic Concepts in Comp. Science (WG'93), LNCS 790, Springer-Verlag, pp. 411–424, 1994.Google Scholar
  8. 8.
    Kant, G., and X. He, Two algorithms for finding rectangular duals of planar graphs, Proc. 19th Intern. Workshop on Graph-Theoretic Concepts in Comp. Science (WG'93), LNCS 790, Springer-Verlag, pp. 396–410, 1994.Google Scholar
  9. 9.
    Kirkpatrick, D.G., and S.K. Wismath, Weighted visibility graphs of bars and related flow problems, Proc. 1st Workshop Algorithms Data Structures (WADS'89), LNCS 382, Springer-Verlag, pp. 325–334, 1989.Google Scholar
  10. 10.
    Mutzel, P., The Maximum Planar Subgraph Problem, Doctoral Dissertation, Köln 1994.Google Scholar
  11. 11.
    Papakostas A. and I. Tollis, Improved algorithms and bounds for orthogonal drawings, Proc. DIMACS Workshop on Graph Drawing (GD'94), LNCS 894, Springer-Verlag, pp. 40–51, 1994.Google Scholar
  12. 12.
    Rosenstiehl, P., and R.E. Tarjan, Rectilinear planar layouts and bipolar orientations of planar graphs, Discrete Comput. Geom. 1, pp. 343–353, 1986.Google Scholar
  13. 13.
    Tamassia, R., On embedding a graph in the grid with the minimum number of bends, SIAM Journal of Computing 16, pp. 421–444, 1987.CrossRefGoogle Scholar
  14. 14.
    Tamassia, R., G. Di Battista and C. Batini, Automatic graph drawing and readability of diagrams, IEEE Trans. on Systems, Man and Cybernetics 18, pp. 61–79, 1988.Google Scholar
  15. 15.
    Tamassia, R. and I. Tollis, A unified approach to visibility representations of planar graphs, Discrete and Computational Geometry 1, pp. 321–341, 1986.Google Scholar
  16. 16.
    Tamassia, R., and I.G. Tollis, Efficient embedding of planar graphs in linear time, in: Proc. IEEE Int. Symp. on Circuits and Systems, Philadelphia, pp. 495–498, 1987.Google Scholar
  17. 17.
    Thomassen, C., Rectilinear drawings of graphs, J. Graph Theory 12, pp. 335–341, 1988.Google Scholar
  18. 18.
    Wismath, S.K., Characterizing bar line-of-sight graphs, Proc. 1st Annual ACM Symp. on Computational Geometry, pp. 147–152, 1985.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ulrich Fößmeier
    • 1
  • Goos Kant
    • 2
  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany
  2. 2.Dept. of Comp. Sci.Utrecht UniversityCH UtrechtNetherlands

Personalised recommendations