Advertisement

Bimodal Crossing Minimization

  • Christoph Buchheim
  • Michael Jünger
  • Annette Menze
  • Merijam Percan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)

Abstract

We consider the problem of drawing a directed graph in two dimensions with a minimum number of crossings such that for every node the incoming edges appear consecutively in the cyclic adjacency lists. We show how to adapt the planarization method and the recently devised exact crossing minimization approach in a simple way. We report experimental results on the increase in the number of crossings involved by this additional restriction on the set of feasible drawings. It turns out that this increase is negligible for most practical instances.

Keywords

Directed Graph Integer Linear Program Outgoing Edge Incoming Edge Incremental Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32, 474–506 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Buchheim, C., Ebner, D., Jünger, M., Klau, G.W., Mutzel, P., Weiskircher, R.: Exact Crossing Minimization. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 37–48. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Djidjev, H.N.: A linear algorithm for the maximal planar subgraph problem. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 369–380. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Faria, L., de Figueiredo, C.M.H., de Mendonça, N.C.F.X.: Splitting number is NP-complete. Discrete Applied Mathematics 108(1–2), 65–83 (2001)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM Journal on Algebraic and Discrete Methods 4(3), 312–316 (1983)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gutwenger, C., Mutzel, P., Weiskircher, R.: Inserting an edge into a planar graph. Algorithmica 41(4), 289–308 (2005)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hliněný, P.: Crossing number is hard for cubic graphs. In: MCFS 2004, pp. 772–782 (2003)Google Scholar
  8. 8.
    Jayakumar, R., Thulasiraman, K., Swamy, M.N.S.: O(n 2) algorithms for graph planarization. IEEE Transactions on Computer-Aided Design 8, 257–267 (1989)CrossRefGoogle Scholar
  9. 9.
    Jünger, M., Mutzel, P.: Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica 16(1), 33–59 (1996)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    La Poutré, J.A.: Alpha-algorithms for incremental planarity testing. In: STOC 1994, pp. 706–715 (1994)Google Scholar
  11. 11.
    Liebers, A.: Planarizing graphs – a survey and annotated bibliography. Journal of Graph Algorithms and Applications 5(1), 1–74 (2001)MathSciNetGoogle Scholar
  12. 12.
    Menze, A.: Darstellung von Nebenmetaboliten in automatisch erzeugten Zeichnungen metabolischer Netzwerke. Master’s thesis, Institute of Biochemistry, University of Cologne (June 2004)Google Scholar
  13. 13.
    Pelsmajer, M.J., Schaefer, M., Štefankovič, D.: Crossing number of graphs with rotation systems. Technical report, Department of Computer Science, DePaul University (2005)Google Scholar
  14. 14.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christoph Buchheim
    • 1
  • Michael Jünger
    • 1
  • Annette Menze
    • 1
  • Merijam Percan
    • 1
  1. 1.Institut für InformatikUniversität zu KölnKölnGermany

Personalised recommendations