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International Computing and Combinatorics Conference

COCOON 1999: Computing and Combinatorics pp 81–91Cite as

An Approximation Algorithm for the Two-Layered Graph Drawing Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

Abstract

We present a polynomial-time approximation algorithm for the minimum edge crossings problem for two-layered graphs. We show the relationship between the approximation ratio of our algorithm and the maximum degree of the vertices in the lower layer of the input graph. When the maximum degree is not greater than four, the approximation ratio is two and this ratio monotonically increases to three as the maximum degree becomes larger. We also present our experiments, showing that our algorithm constructs better solutions than the barycenter method and the median method for dense graphs as well as sparse graphs.

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References

  1. C. Batini, L. Furlani, and E. Nardelli: What Is a Good Diagram?: A Pragmatic Approach, Proc. of the 4th International Conference on Entity-Relationship Approach, pp. 312–319, 1985.

    Google Scholar 

  2. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis: Algorithms for Drawing Graphs: An Annotated Bibliography, Computational Geometry, 4 (1994), pp. 235–282.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Catarci: The Assignment Heuristic for Crossing Reduction, IEEE Transactions on Systems, Man, and Cybernetics, 25 (1995), 3, pp. 515–521.

    Article  Google Scholar 

  4. P. Eades, B. D. McKay, and N. Wormald: On an Edge Crossing Problem, Proc. of the 9th Australian Computer Science Conference, pp. 327–334, 1986.

    Google Scholar 

  5. P. Eades and N. Wormald: Edge Crossings in Drawings of Bipartite Graphs, Algorithmica, 11 (1994), 4, pp. 379–403.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. Esposito: Graph Graphics: Theory and Practice, Computers and Mathematics with Applications, 15 (1988), 4, pp. 247–253.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Jünger and P. Mutzel: 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms, Journal of Graph Algorithms and Applications, 1 (1997), 1, pp. 1–25.

    MathSciNet  Google Scholar 

  8. E. Mäkinen: Experiments on Drawing 2-level Hierarchical Graphs, International Journal of Computer Mathematics, 36 (1990), pp. 175–181.

    Article  MATH  Google Scholar 

  9. H. C. Purchase, R. F. Cohen, and M. James: Validating Graph Drawing Aesthetics, Proc. of Symposium on Graph Drawing, GD'95 (Lecture Notes in Computer Science, Vol. 1027), pp. 435–446, Springer, 1996.

    Chapter  Google Scholar 

  10. K. Sugiyama, S. Tagawa, and M. Toda: Methods for Visual Understanding of Hierarchical Systems, IEEE Transactions on Systems, Man, and Cybernetics, 11 (1981), 2, pp. 109–125.

    Article  MathSciNet  Google Scholar 

  11. A. Yamaguchi and A. Sugimoto: An Approximation Algorithm for the Two-layered Graph Drawing Problem, ARL Research Report, 98-001, 1999.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama, 350-0395, Japan

    Atsuko Yamaguchi & Akihiro Sugimoto

Authors
  1. Atsuko Yamaguchi
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  2. Akihiro Sugimoto
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Cite this paper

Yamaguchi, A., Sugimoto, A. (1999). An Approximation Algorithm for the Two-Layered Graph Drawing Problem. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_8

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  • DOI: https://doi.org/10.1007/3-540-48686-0_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

  • eBook Packages: Springer Book Archive

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