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Spirality of orthogonal representations and optimal drawings of series-parallel graphs and 3-planar graphs (extended abstract)

  • Giuseppe Di Battista
  • Giuseppe Liotta
  • Francesco Vargiu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)

Abstract

An orthogonal drawing of a graph is a planar drawing such that all the edges are polygonal chains of horizontal and vertical segments. Finding the planar embedding of a planar graph such that its orthogonal drawing has the minimum number of bends is a fundamental open problem in graph drawing. This paper provides the first partial solution to the problem. It gives a new combinatorial characterization of orthogonal drawings based on the concept of spirality and provides a polynomial-time algorithm for series-parallel graphs and biconnected 3-planar graphs.

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References

  1. [1]
    P. Bertolazzi, R.F. Cohen, G. Di Battista, R. Tamassia, and I.G. Tollis, “How to Draw a Series-Parallel Digraph,” Proc. 3rd Scandinavian Workshop on Algorithm Theory, 1992.Google Scholar
  2. [2]
    G. Di Battista and R. Tamassia “Algorithms for Plane Representations of Acyclic Digraphs,” Theoretical Computer Science, vol. 61, pp. 175–198, 1988.CrossRefGoogle Scholar
  3. [3]
    G. Di Battista and R. Tamassia “Incremental Planarity Testing,” Proc. 30th IEEE Symp. on Foundations of Computer Sciene, pp. 436–441, 1989.Google Scholar
  4. [4]
    G. Di Battista and R. Tamassia “On Line Planarity Testing,” Technical Report CS-89-31, Dept. of Computer Science, Brown Univ. 1989.Google Scholar
  5. [5]
    P. Eades and R. Tamassia, “Algorithms for Automatic Graph Drawing: An Annotated Bibliography,” Technical Report CS-89-09, Dept. of Computer Science, Brown Univ. 1989.Google Scholar
  6. [6]
    S. Even “Graph Algoritms,” Computer Science Press, Potomac, MD, 1979.Google Scholar
  7. [7]
    G. Kant “A New Method for Planar Graph Drawings on a Grid,” Proc. IEEE Symp. on Foundations of Computer Science, 1992.Google Scholar
  8. [8]
    E. L. Lawler “Combinatorial Optimization: Networks and Matroids,” Holt, Rinehart and Winston, New York, Chapt. 4, 1976.Google Scholar
  9. [9]
    T. Nishizeki and N. Chiba, “Planar Graphs: Theory and Algorithms,” Annals of Discrete Mathematics 32, North-Holland, 1988.Google Scholar
  10. [10]
    J. A. Storer “On Minimal Node-Cost Planar Embeddings,” Networks, vol. 14, pp. 181–212, 1984.Google Scholar
  11. [11]
    R. Tamassia “On Embedding a Graph in the Grid with the Minimum Number of Bends,” SIAM J. Computing, vol. 16, no. 3, pp. 421–444, 1987.CrossRefGoogle Scholar
  12. [12]
    R. Tamassia, “Planar Orthogonal Drawings of Graphs,” Proc. IEEE Int. Symp. on Circuits and Systems, 1990.Google Scholar
  13. [13]
    R. Tamassia and I.G. Tollis “Efficient Embedding of Planar Graphs in Linear Time,” Proc. IEEE Int. Symp. on Circuits and Systems, Philadelphia, pp. 495–498, 1987.Google Scholar
  14. [14]
    R. Tamassia and I.G. Tollis “Planar Grid Embedding in Linear Time,” IEEE Trans. on Circuits and Systems, vol. CAS-36, no. 9, pp. 1230–1234, 1989.CrossRefGoogle Scholar
  15. [15]
    R. Tamassia, I. G. Tollis, and J. S. Vitter “Lower Bounds and Parallel Algorithms for Planar Orthogonal Grid Drawings,” Proc. IEEE Symp. on Parallel and Distributed Processing, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Giuseppe Liotta
    • 1
  • Francesco Vargiu
    • 1
    • 2
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItalia
  2. 2.Data-base Informatica Spa.Italy

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