A parallel simulated annealing algorithm for generating 3D layouts of undirected graphs

  • Burkhard Monien
  • Friedhelm Ramme
  • Helmut Salmen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)

Abstract

In this paper, we introduce a parallel simulated annealing algorithm for generating aesthetically pleasing straight-line drawings. The proposed algorithm calculates high quality 3D layouts of arbitrary undirected graphs. Due to the 3D layouts, structure information is presented to the human viewer at a glance. The computing time of the algorithm is reduced by a new parallel method for exploiting promising intermediate configurations. As the algorithm avoids running into a local minimum of the cost function, it is applicable for the animation of graphs of reasonably larger size than it was possible before.

Subsequent to the discussion of the algorithm, empirical data for the performance of the algorithm and the quality of the generated layouts are presented.

Keywords

3D graph layout straight-line drawing parallel simulated annealing 

References

  1. [BETT94]
    G.D. Battista, P. Eades, R. Tamassia, I.G. Tollis: Algorithms for drawing graphs: An annotated bibliography, Report, Brown University, June 1994Google Scholar
  2. [CELR94]
    R.F. Cohen, P. Eades, T. Lin, F. Ruskey: Three-Dimensional Graph Drawing, Proc. of Graph Drawing '94, LNCS Springer, Vol. 894, pp. 1–11Google Scholar
  3. [DH93]
    R. Davidson, D, Harel: Drawing graphs nicely using simulated annealing, Technical Report CS89-13, Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Israel 1989, revised July 1993, to appear in Communications of the ACMGoogle Scholar
  4. [DLS93]
    R. Diekmann, R. Lüling, J. Simon: Problem Independent Distributed Simulated Annealing and its Applications, in: R.V.V. Vidal (ed.): Applied Simulated Annealing, Lecture Notes in Economics and Mathematical Systems, Springer 1993, No. 396, pp. 17–44.Google Scholar
  5. [Ea84]
    P. Eades: A heuristic for graph drawing, Congressus Numerantium, 1984, Vol. 42, pp. 149–160Google Scholar
  6. [FPS94]
    P.W. Fowler, T. Pisanski, J. Shawe-Taylor: Molecular Graph Eigenvectors for Molecular Coordinates, Proc. of Graph Drawing '94, LNCS Springer, Vol. 894, pp. 282–285Google Scholar
  7. [FLM94]
    A. Frick, A. Ludwig, H. Mehldau: A Fast Adaptive Layout Algorithm for Undirected Graphs, Proc. of Graph Drawing '94, LNCS Springer, Vol. 894, pp. 388–403Google Scholar
  8. [FR91]
    T.M.J. Fruchtermann, E.M. Reingold: Graph drawing by force-directed placement, Software-Practice and Experience, 1991, Vol. 21, No. 11, pp. 1129–1164Google Scholar
  9. [HS93]
    D. Harel, M. Sardas: Randomized Graph Drawing with Heavy-Duty Preprocessing, Technical Report CS93-16, Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Israel Oct. 1993Google Scholar
  10. [HRS86]
    M.D. Huang, F. Romeo, A. Sangiovanni-Vincentelli: An Efficient General Cooling Schedule for Simulated Annealing, IEEE Int. Conf. on Computer Aided Design 1986, pp. 381–384Google Scholar
  11. [JAMS89-91]
    D.S. Johnson, C.R. Aragon, L. A. McGeoch, C. Schevon: Optimization by Simulated Annealing: An Experimental Evaluation, Part I, ”Graph Partitioning”, Operations Research Vol.37, No.6, pp.865–892, 1989; Optimization by Simulated Annealing: An Experimental Evaluation, Part II, ”Graph Coloring and Number Partitioning”, Operations Research Vol.39, No. 3, pp. 378–406, 1991Google Scholar
  12. [KK89]
    T. Kamada, S. Kawai: An algorithm for drawing general undirected graphs, Information Processing Letters, North-Holland 1989, Vol. 31, pp. 7–15Google Scholar
  13. [KMS94]
    C. Kosak, J. Marks, S. Shieber: Automating the Layout of Network Diagrams with Specified Visual Organization, IEEE Trans. on Systems, Man, and Cybernetics, Vol. 24, No. 3, pp. 440–454Google Scholar
  14. [OG89]
    O.E. Otten, L. van Ginneken: The Annealing Algorithm, Kluwer Academic Publishers 1989Google Scholar
  15. [Parix]
    Parsytec Computer Ltd.: Parix 1.3: Software Documentation, AachenGoogle Scholar
  16. [Sa95]
    H. Salmen: Dreidimensionale Auslegung beliebiger Graphen mittels parallelem Simulated Annealing Methoden, Master Thesis, Univ. of Paderborn, 1995Google Scholar
  17. [Tu93]
    D. Tunkelang: A layout algorithm for undirected graphs, In Graph Drawing '93, ALCOM Int. Workshop, Paris 1993Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Burkhard Monien
    • 1
  • Friedhelm Ramme
    • 2
  • Helmut Salmen
    • 1
  1. 1.Department of Computer ScienceUniversity of PaderbornGermany
  2. 2.Paderborn Center for Parallel Computing (PC2)University of PaderbornGermany

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