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Symmetric Layout of Disconnected Graphs

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Algorithms and Computation (ISAAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

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Abstract

We present a linear time algorithm for drawing disconnected planar graphs with maximum number of symmetries. Our algorithm can be generalized to making symmetric arrangements of bounded disjoint objects in the plane.

This research has been supported by a grant from the Australian Research Council. In this extended abstract, proofs are omitted.

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References

  1. Abelson, D., Hong, S., Taylor, D.E.: A Group-Theoretic Method for Drawing Graphs Symmetrically. In: Graph Drawing 2002. LNCS, pp. 86–97. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Buchheim, C., Junger, M.: Detecting Symmetries by Branch and Cut. In: Graph Drawing 2001. LNCS, pp. 178–188. Springer, Heidelberg (2001)

    Google Scholar 

  3. Eades, P.: Symmetry Finding Algorithms. In: Computational Morphology, Machine Intelligence and Pattern Recognition, pp. 41–51. North Holland, Amsterdam (1988)

    Google Scholar 

  4. Eades, P., Lin, X.: Spring Algorithms and Symmetries. Theoretical Computer Science 240, 379–405 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. de Fraysseix, H.: An Heuristic for Graph Symmetry Detection. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 276–285. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Freivalds, K., Dogrusoz, U., Kikusts, P.: Disconnected Graph Layout and the Polyomino Packing Approach. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 378–391. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Hong, S., Eades, P., Lee, S.: Drawing Series Parallel Digraphs Symmetrically. Computational Geometry: Theory and Applicatons 17(3-4), 165–188 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hong, S., McKay, B., Eades, P.: Symmetric Drawings of Triconnected Planar Graphs. In: Proc. of SODA 2002, pp. 356–365 (2002)

    Google Scholar 

  9. Hong, S., Eades, P.: Drawing Planar Graphs Symmetrically II: Biconnected Graphs, Technical Report CS-IVG-2001-01, School of IT, University of Sydney (2001)

    Google Scholar 

  10. Hong, S., Eades, P.: Drawing Planar Graphs Symmetrically III: One-connected Graphs, Technical Report CS-IVG-2001-02, School of IT, University of Sydney (2001)

    Google Scholar 

  11. Hopcroft, J.E., Wong, J.K.: Linear Time Algorithm for Isomorphism of Planar Graphs. In: Proc. of STOC, pp. 172–184 (1974)

    Google Scholar 

  12. Mani, P.: Automorphismen von Polyedrischen Graphen. Math. Annalen 192, 279–303 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  13. Manning, J.: Geometric Symmetry in Graphs, Ph.D. Thesis, Purdue Univ. (1990)

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Hong, SH., Eades, P. (2003). Symmetric Layout of Disconnected Graphs . In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_42

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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