Using Sifting for k-Layer Straightline Crossing Minimization

  • Christian Matuszewski
  • Robby Schönfeld
  • Paul Molitor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)


We present a new algorithm for k-layer straightline crossing minimization which is based on sifting that is a heuristic for dynamic reordering of decision diagrams used during logic synthesis and formal verification of logic circuits. The experiments prove sifting to be very efficient. In particular it outperforms the traditional layer by layer sweep based heuristics known from literature by far when applied to k-layered graphs with k ≥ 3.


  1. EK86.
    P. Eades and D. Kelly. Heuristics for reducing crossings in 2-layered networks. Ars Combin., 21.A:89–98, 1986.MathSciNetGoogle Scholar
  2. EW94a.
    P. Eades and S. Whitesides. Drawing graphs in two layers. Theoretical Computer Science, 131:361–374, 1994.MATHCrossRefMathSciNetGoogle Scholar
  3. EW94b.
    P. Eades and N. C. Wormald. Edge crossings in drawings of bipartite graphs. Algorithmica, 11(4):379–403, 1994.MATHCrossRefMathSciNetGoogle Scholar
  4. GJ83.
    M. R. Garey and D. S. Johnson. Crossing number is NP-complete. SIAM Journal on Algebraic and Discrete Methods, 4:312–316, 1983.MATHCrossRefMathSciNetGoogle Scholar
  5. JM97.
    M. Jünger and P. Mutzel. 2-Layer straightline crossing minimization: Performance of exact and heuristic algorithms. J. Graph Algorithms Appl., 1(1):1–25, 1997.Google Scholar
  6. Knu93.
    D. E. Knuth. The Stanford GraphBase: A Platform for Combinatorial Computing. Addison-Wesley, Reading, MA, 1993.Google Scholar
  7. Mäk90.
    E. Mäkinen. Experiments on drawing 2-level hierarchical graphs. Internat. J. Comput. Math., 36:175–181, 1990.CrossRefMATHGoogle Scholar
  8. MGB+98.
    P. Mutzel, C. Gutwenger, R. Brockenauer, S. Fialko, G. W. Klau, M. Krüger, 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 S. H. Whitesides, editor, Proceedings of the 6th International Symposium on Graph Drawing (GD’ 98), volume 1547 of Lecture Notes in Computer Science, pages 456–457. Springer, 1998. Project home page at Scholar
  9. MN99.
    K. Mehlhorn and S. Näher. The Leda Platform of Combinatorial and Geometric Computing. Cambridge University Press, 1999. Project home page at
  10. Rud93.
    R. Rudell. Dynamic variable ordering for ordered binary decision diagrams. In Proc. International Conf. on Computer-Aided Design (ICCAD), pages 42–47, November 1993.Google Scholar
  11. STT81.
    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, February 1981.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christian Matuszewski
    • 1
  • Robby Schönfeld
    • 1
  • Paul Molitor
    • 1
  1. 1.Institute for Computer Science, University Halle-WittenbergHalle(Saale)Germany

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