A Fast Multi-scale Method for Drawing Large Graphs

  • David Harel
  • Yehuda Koren
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)

Abstract

We present a multi-scale layout algorithm for the aesthetic drawing of undirected graphs with straight-line edges. The algorithm is extremely fast, and is capable of drawing graphs of substantially larger size than any other algorithm we are aware of. For example, the algorithm achieves optimal drawings of 1000 vertex graphs in about 2 seconds. The paper contains graphs with over 6000 nodes. The proposed algorithm embodies a new multi-scale scheme for drawing graphs, which was motivated by the recently published multi-scale algorithm of Hadany and Harel [7]. It can significantly improve the speed of essentially any force-directed method (regardless of that method’s ability of drawing weighted graphs or the continuity of its cost-function).

References

  1. 1.
    Brandenburg, F.J., Himsolt, M., and Rohrer, C., “An Experimental Comparison of Force-Directed and Randomized Graph Drawing Algorithms”, Proceedings of Graph Drawing’ 95, Lecture Notes in Computer Science, Vol. 1027, pp. 76–87, Springer Verlag, 1995.Google Scholar
  2. 2.
    Di Battista, G., Eades, P., Tamassia, R. and Tollis, I.G., Algorithms for the Visualization of Graphs, Prentice-Hall, 1999.Google Scholar
  3. 3.
    Davidson, R., and Harel, D., “Drawing Graphs Nicely Using Simulated Annealing”, ACM Trans. on Graphics 15 (1996), 301–331.CrossRefGoogle Scholar
  4. 4.
    Eades, P., “A Heuristic for Graph Drawing”, Congressus Numerantium 42 (1984), 149–160.MathSciNetGoogle Scholar
  5. 5.
    Fruchterman, T.M.G., and Reingold, E., “Graph Drawing by Force-Directed Placement”, Software-Practice and Experience 21 (1991), 1129–1164.CrossRefGoogle Scholar
  6. 6.
    Gonzalez, T., “Clustering to Minimize the Maximum Inter-Cluster Distance”, Theoretical Computer Science 38 (1985), 293–306.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hadany, R., and Harel, D., “A Multi-Scale Method for Drawing Graphs Nicely”, Discrete Applied Mathematics, in press, 2000. (Also, Proc. 25th Inter. Workshop on Graph-Theoretic Concepts in Computer Science (WG’ 99), Lecture Notes in Computer Science, Vol. 1665, pp. 262-277, Springer Verlag, 1999.)Google Scholar
  8. 8.
    Hochbaum, D. S. (ed.), Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996.Google Scholar
  9. 9.
    Hochbaum, D.S., and Shmoys, D. B, “A Unified Approach to Approximation Algorithms for Bottleneck Problems”, J. Assoc. Comput. Mach. 33 (1986), 533–550.MathSciNetGoogle Scholar
  10. 10.
    Kamada, T., and Kawai, S., “An Algorithm for Drawing General Undirected Graphs”, Information Processing Letters 31 (1989), 7–15.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • David Harel
    • 1
  • Yehuda Koren
    • 1
  1. 1.Dept. of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

Personalised recommendations