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A New Heuristic Layout Algorithm for DAGs

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Part of the book series: Operations Research Proceedings ((ORP,volume 1994))

Summary

Directed acyclic graphs (DAGs) are a common representation of hierarchical relationships and are widely used in software and information engineering, system theory, and others. The usefulness depends on a readable, understandable and easy to remember layout. The key problem in making such a good layout is the reduction of numbers of arc crossings. We focus on the two layer problem and make a fresh attempt at a heuristic method of arc crossing reduction based on a stochastic approach. The “stochastic” heuristic is described in detail. The results of the approach are analyzed. A comparison of these results with the mostly used methods of barycentering and median-ordering is given. The “stochastic” heuristic is shown to be preferable in terms of Warfield’s generating matrices.

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References

  1. G. Di Battista, P. Eades, R. Tamassia, I. G. Tollis, “Algorithms for Drawing Graphs: an Annotated Bibliography”, Technical Report CS-89-09 (Revised Version), Department of Computer Science, Brown University, Jun. 1994.

    Google Scholar 

  2. M. J. Carpano, “Automatic Display of Hierarchized Graphs for Computer Aided Decision Analysis”, IEEE Trans. Syst. Man, Cybern., SMC-1 [ Nov. 1980 ] 11, 705–715.

    Article  Google Scholar 

  3. P. Eades and D. Kelly, “Heuristics for Reducing Crossings in 2-Layered Networks”, Ars Combinatoria, 21-A [ 1986 ], 89–98.

    Google Scholar 

  4. P. Eades and N. C. Wormald, “The median heuristic for drawing 2-layers networks”, Technical Report 69, Department of Computer Science, University of Queensland, 1986.

    Google Scholar 

  5. P. Eades and N. C. Wormald, “Edge Crossings in Draings of Bipartite Graphs”, Technical Report 108, Department of Computer Science, University of Queensland, 1991.

    Google Scholar 

  6. S. E. Elmaghraby, “Activity Networks: Project Planning and Control by Network Models”, New York: Wiley 1977.

    Google Scholar 

  7. E. R. Gansner, E. Koutsofios, S. C. North, and K. P. Vo, “A Technique for Drawing Directed Graphs”, IEEE Trans, on Software Engineering, 19 [ Mar. 1993 ] 3, 214–229.

    Article  Google Scholar 

  8. E. R. Gansner, S. C. North, and K. P. Vo, “DAG — A Program that Draws Directed Graphs”, Software—Practice and Experience, 18 [ Nov. 1988 ] 11, 1047–1062.

    Article  Google Scholar 

  9. M. R. Garey and D. S. Johnson, Crossing Number is NP-Complete, SIAMJ. on Algebraic and Discrete Methods, 4 [ 1983 ] 3, 312–316.

    Article  Google Scholar 

  10. F. N. Paulisch, The Design of an Exendible Graph Editor, Berlin: Springer 1993.

    Book  Google Scholar 

  11. K. Sugiyama, S. Tagawa, and M. Toda, “Methods for Visual Understanding of Hierarchical System Structures”, IEEE Trans. Syst. Man, Cybern., SMC-11 [ Feb. 1981 ] 2, 109–125.

    Article  Google Scholar 

  12. K. Sugiyama and M. Toda, “Structuring Information for Understanding of Complex Systems: A Basis for Decision Making”, FUJITSU Sei. Tech J., 21 [ Jun. 1985 ] 2, 144–166.

    Google Scholar 

  13. R. Tamassia, G. Di Battista, and C. Batini, “Automatic Graph Drawing and Readability of Diagrams”, IEEE Trans. Syst. Man, Cybern., 18 [Jan./Feb. 1988 ] 1, 61–79.

    Article  Google Scholar 

  14. J. N. Warfield, “Societal Systems”, New York: Wiley 1976.

    Google Scholar 

  15. J. N. Warfield, “Crossing Theory and Hierarchy Mapping”, IEEE Trans. Syst. Man, Cybern., SMC-1 [ Jul. 1977 ] 7, 505–523.

    Article  Google Scholar 

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© 1995 Springer-Verlag Berlin Heidelberg

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Dresbach, S. (1995). A New Heuristic Layout Algorithm for DAGs. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_23

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  • DOI: https://doi.org/10.1007/978-3-642-79459-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58793-4

  • Online ISBN: 978-3-642-79459-9

  • eBook Packages: Springer Book Archive

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