The Vertex-Exchange Graph: A New Concept for Multi-level Crossing Minimisation

  • Patrick Healy
  • Ago Kuusik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)

Abstract

In this paper we consider the problems of testing a multi- level graph for planarity and laying out a multi-level graph.We introduce a new abstraction that we call a vertex-exchange graph. We demonstrate how this concept can be used to solve these problems by providing clear and simple algorithms for testing a multi-level graph for planarity and laying out a multi-level graph when planar.We also show how the concept can be used to solve other problems relating to multi-level graph layout.

References

  1. 1.
    G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing, Algorithms for the Visualization of Graphs. Prentice Hall, 1999.Google Scholar
  2. 2.
    P. Eades and D. Kelly. Heuristics for drawing 2-layered networks. Ars Combinatoria, 21-A:89–98, 1986.MathSciNetGoogle Scholar
  3. 3.
    P. Eades and K. Sugiyama. How to draw a directed graph. Journal of Information Processing, 13(4):424–437, 1990.MATHGoogle Scholar
  4. 4.
    P. Eades and N. C. Wormald. Edge crossings in drawings of bipartite graphs. Algorithmica, 11:379–403, 1994.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    P. Healy and A. Kuusik. Characterisation of level non-planar graphs by minimal patterns. Technical Report UL-CSIS-98-4, University of Limerick, 1998.Google Scholar
  6. 6.
    M. Jünger, E. K. Lee, P. Mutzel, and T. Odenthal. A polyhedral approach to multi-layer crossing minimization problem. In Graph Drawing, 5th International Symposium, GD’ 97, Rome, Italy, September 1997, volume 1353 of Lecture Notes in Computer Science, pages 13–24. Springer-Verlag, 1997.CrossRefGoogle Scholar
  7. 7.
    M. Jünger and P. Mutzel. Exact and heuristic algorithms for 2-layer crossing minimization. In Graph Drawing, Symposium on Graph Drawing, GD’ 95. Passau, Germany, September 20-22, 1995, volume 1027 of Lecture Notes in Computer Science, pages 337–348. Springer-Verlag, 1995.Google Scholar
  8. 8.
    S. Leipert. Level planarity testing and embedding in linear time. PhD thesis, Institut für Informatik, Universität zu Köln, 1998.Google Scholar
  9. 9.
    K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical system structures. IEEE Transactions on Systems, Man, and Cybernetics, 11(2):109–125, 1981.CrossRefMathSciNetGoogle Scholar
  10. 10.
    J. Utech, J. Branke, H. Schmeck, and P. Eades. An evolutionary algorithm for drawing directed graphs. In Proceedings of the 1998 International Conference on Imaging Science, Systems, and Technology (CISST’98), pages 154–160, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Patrick Healy
    • 1
  • Ago Kuusik
    • 1
  1. 1.Department of Computer Science and Information SystemsUniversity of LimerickLimerickIRELAND

Personalised recommendations