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An efficient orthogonal grid drawing algorithm for cubic graphs

  • Session 1B: Graph Drawing
  • Conference paper
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Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

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Abstract

In this paper we present a new algorithm that constructs an orthogonal drawing of a graph G with degree at most three. Even if we do not require any limitations neither to planar nor to biconnected graphs, we reach the best known results in the literarture: each edge has at most 1 bend, the total number of bends is ≤ n/2+1, and the area is ≤(n/2−1)2.

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References

  1. Aho, A., Hopcroft, J. K. Ullman, J. D.: The design and analysis of computer algorithms. Addison Wesley, Reading,MA, (1973)

    Google Scholar 

  2. Biedl, T., Kant, G.: A Better Euristic for Orthogonal Graph Drawings. Algorithms — ESA '94. Proceedings, Lectures Notes in Computer Science, Springer-Verlag 855 (1994) 24–35

    Google Scholar 

  3. Bjorken, J.D., Drell, S.D.: Quantum Electrodynamics. Mc-Graw Hill

    Google Scholar 

  4. Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to algorithms. the MIT Press, Cambridge,MA, (1990)

    Google Scholar 

  5. Di Battista, G., Liotta, G., Vargiu, F.: Spirality of Orthogonal Representations and Optimal Drawings of Series-Parallel Graphs and 3-Planar Graphs. Lectures Notes in Computer Science, Springer-Verlag 709 (1993) 151–162

    Google Scholar 

  6. Greenlaw, R., Petreschi, R.: Cubic graphs, Tech. Rep. University of New Hampshire, Durham,N.H.,USA 15 (1993)

    Google Scholar 

  7. Kant, G.: Drawing Planar Graphs Using the canonical ordering. Algorithmica — Special Issue on Graph Drawing (to appear)

    Google Scholar 

  8. Liu, Y. Marchioro, P., Petreschi, R.: At most single bend embedding of cubic graphs. Applied Mathematics (Chin. Journ.) 9/B/2 (1994) 127–142

    Google Scholar 

  9. Papakostas, A., Tollis, I.G.: Improved Algorithms and Bounds for Orthogonal Drawings. Proc.Graph Drawing '94, Lectures Notes in Computer Science, Springer-Verlag 894 (1994) 40–51

    Google Scholar 

  10. Preparata, F.P., Vuillemin, J.: The Cube-Connected Cycles: A Versatile Network for Parallel Computation. Communications of ACM 24/5 (1981) 300–309

    Article  Google Scholar 

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Ding-Zhu Du Ming Li

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© 1995 Springer-Verlag Berlin Heidelberg

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Calamoneri, T., Petreschi, R. (1995). An efficient orthogonal grid drawing algorithm for cubic graphs. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030817

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  • DOI: https://doi.org/10.1007/BFb0030817

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

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