An Experimental Study of Crossing Minimization Heuristics

  • Carsten Gutwenger
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

We present an extensive experimental study of heuristics for crossing minimization. The heuristics are based on the planarization approach, so far the most successful framework for crossing minimization. We study the effects of various methods for computing a maximal planar subgraph and for edge re-insertion including post-processing and randomization.

References

  1. 1.
    Di Battista, G., Tamassia, R.: On-line planarity testing. SIAM Journal on Computing 25(5), 956–997 (1996)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bhatt, S.N., Leighton, F.T.: A framework for solving VLSI layout problems. Journal of Computer and System Sciences 28, 300–343 (1984)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bienstock, D.: Some provablyhard crossing number problems. Discrete & Computational Geometry 6, 443–459 (1991)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Brandenburg, F.J., Himsolt, M., Rohrer, C.: An experimental comparison of force-directed and randomized graph drawing algorithms. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 76–87. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  5. 5.
    Chiba, N., Nishizeki, T., Abe, S., Ozawa, T.: A linear algorithm for embedding planar graphs using PQ-trees. J. Comput. Syst. Sci. 30(1), 54–76 (1985)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Comput. Geom. Theory Appl. 7, 303–326 (1997)MATHGoogle Scholar
  7. 7.
    Eschbach, T., Günther, W., Drechsler, R., Becker, B.: Crossing reduction by windows optimization. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 285–294. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Even, G., Guha, S., Schieber, B.: Improved approximations of crossings in graph drawing and VLSI layout area. In: Proc. 32nd ACM Symp. Theory of Comp. (STOC 2000), pp. 296–305. ACM Press, New York (2000)CrossRefGoogle Scholar
  9. 9.
    Grohe, M.: Computing crossing numbers in quadratic time. In: Proc. 32nd ACM Symp. Theory of Computing (STOC 2000), pp. 231–236. ACM Press, New York (2000)Google Scholar
  10. 10.
    Gutwenger, C., Klein, K., Kupke, J., Leipert, S., Jünger, M., Mutzel, P.: Govisual software tools (2002), http://www.oreas.de
  11. 11.
    Gutwenger, C., Mutzel, P., Weiskircher, R.: Inserting an edge into a planar graph. In: Proc. Ninth Ann. ACM-SIAM Symp. Discr. Algorithms (SODA 2001), Washington, DC, pp. 246–255. ACM Press, New York (2001)Google Scholar
  12. 12.
    Jayakumar, R., Thulasiraman, K., Swamy, M.N.S.: O(n 2) algorithms for graph planarization. IEEE Trans. on Computer-Aided Design 8, 257–267 (1989)CrossRefGoogle Scholar
  13. 13.
    Johnson, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods 4(3), 312–316 (1983)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Jünger, M., Leipert, S., Mutzel, P.: A note on computing a maximal planar subgraph using PQ-trees. IEEE Trans. Computer-Aided Design 17(7) (1998)Google Scholar
  15. 15.
    Jünger, M., Mutzel, P.: Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica 16(1), 33–59 (1996)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Jünger, M., Mutzel, P.: 2-layer straightline crossing minimization: Performance of exact and heuristic algorithms. J. Gr. Alg. & Appl. (JGAA) 1(1), 1–25 (1997)Google Scholar
  17. 17.
    Leighton, F.T., Rao, S.: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. J. ACM 46(6), 787–832 (1999)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Liu, P.C., Geldmacher, R.C.: On the deletion of nonplanar edges of a graph. In: 10th. S-E Conf. Comb., Graph Theory, and Comp., pp. 727–738 (1977)Google Scholar
  19. 19.
    Mehlhorn, K., Mutzel, P.: On the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. Algorithmica 16(2), 233–242 (1996)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Mutzel, P., Ziegler, T.: The constrained crossing min. problem. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 175–185. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  21. 21.
    La Poutré, J.A.: Alpha-algorithms for incremental planaritytesting. In: Proc. 26th Annual ACM Symp. Theory of Computation (STOC), pp. 706–715 (1994)Google Scholar
  22. 22.
    Purchase, H.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  23. 23.
    Richter, R.B., Thomassen, C.: Relations between crossing numbers of complete and complete bipartite graphs. In: Amer. Math. Monthly, pp. 131–137 (1997)Google Scholar
  24. 24.
    Vismara, L., Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Vargiu, F.: Experimental studies on graph drawing algorithms. Software – Practice and Experience 30, 1235–1284 (2000)MATHCrossRefGoogle Scholar
  25. 25.
    Ziegler, T.: Crossing Minimization in Automatic Graph Drawing. PhD thesis, Max-Planck-Institut für Informatik, Saarbrücken (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Carsten Gutwenger
    • 1
  • Petra Mutzel
    • 2
  1. 1.Stiftung caesarBonnGermany
  2. 2.Vienna University of TechnologyViennaAustria

Personalised recommendations