k-Layer Straightline Crossing Minimization by Speeding Up Sifting

  • Wolfgang Günther
  • Robby Schönfeld
  • Bernd Becker
  • Paul Molitor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)


Recently, a technique called sifting has been proposed for k-layer straightline crossing minimization. This approach outperforms the traditional layer by layer sweep based heuristics by far when applied to k-layered graphs with k≥3. In this paper, we present two methods to speed up sifting. First, it is shown how the crossing matrix can be computed and updated efficiently. Then, we study lower bounds which can be incorporated in the sifting algorithm, allowing to prune large parts of the search space. Experimental results show that it is possible to speed up sifting by more than a factor of 20 using the new methods.


  1. 1.
    R.E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Trans. on Comp., 35(8):677–691, 1986.MATHCrossRefGoogle Scholar
  2. 2.
    R. Drechsler and W. Günther. Using lower bounds during dynamic BDD minimization. In Design Automation Conf., pages 29–32, 1999.Google Scholar
  3. 3.
    P. Eades and S. Whitesides. Drawing graphs in two layers. Theoretical Computer Science, 131:361–374, 1994.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Jünger and P. Mutzel. 2-layer straightline crossing minimization: Performance of exact and heuristic algorithms. Journal of Graph Algorithms and Applications, 1(1):1–25, 1997.MathSciNetGoogle Scholar
  5. 5.
    M. Laguna, R. Martí,, and V. Valls. Arc crossing minimization in hierarchical digraphs with tabu search. Computers and Operations Research, 24(12):1175–1186, 1997.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C. Matuszewski, R. Schönfeld, and P. Molitor. Using sifting for k-layer straightline crossing minimization. In Graph Drawing Conference, LNCS 1731, pages 217–224, 1999.Google Scholar
  7. 7.
    K. Mehlhorn and S. Näher. The Leda Platform of Combinatorial and Geometric Computing. Cambridge University Press, 1999. Project home page at http://www.mpi-sb.mpg.de/LEDA/.
  8. 8.
    P. Mutzel, T. Ziegler, S. Näher, D. Alberts, D. Ambras, G. Koch, M. Jünger, C. Buchheim, and S. Leipert. A library of algorithms for graph drawing. In International Symposium on Graph Drawing, LNCS 1547, pages 456–457, 1998. Project home page at http://www.mpi-sb.mpg.de/AGD/.Google Scholar
  9. 9.
    S. Panda and F. Somenzi. Who are the variables in your neighborhood. In Int’l Conf. on CAD, pages 74–77, 1995.Google Scholar
  10. 10.
    R. Rudell. Dynamic variable ordering for ordered binary decision diagrams. In Int’l Conf. on CAD, pages 42–47, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Wolfgang Günther
    • 1
  • Robby Schönfeld
    • 2
  • Bernd Becker
    • 1
  • Paul Molitor
    • 2
  1. 1.Institute for Computer ScienceAlbert-Ludwigs-UniversityFreiburgGermany
  2. 2.Institute for Computer Science Martin-Luther-UniversityHalle-WittenbergGermany

Personalised recommendations