Drawing Outer-Planar Graphs in O(n log n )Area

  • Therese Biedl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

In this paper,we study drawings of outer-planar graphs in various models.We showthat O (n log n )area can be achieved for such drawings if edges are allowed to have bends or if vertices may be represented by boxes.The question of straight-line grid-drawings of outer- planar graphs in o (n 2 )area remains open.

References

  1. BCDB + 94.
    P. Bertolazzi, R.F. Cohen, G. DiBattista, R. Tamassia,and I.G. Tollis. How to drawa series-parallel digraph.Intl.J.Comput.Geom.Appl., 4:385–402,1994.MATHCrossRefGoogle Scholar
  2. BMT98.
    T. Biedl, B. Madden, and I. Tollis.The three-phase method:A unified approach to orthogonal graph drawing.In Graph Drawing (GD’ 97),volume 1353of Lecture Notes in Computer Science,pages 391–402.Springer-Verlag,1998.CrossRefGoogle Scholar
  3. CU96.
    N. Castañeda and J. Urrutia. Straight line embeddings of planar graphs on point sets. In Canadian Conference on Computational Geometry (CCCG’ 96),pages 312–318,1996.Google Scholar
  4. DBETT98.
    G. DiBattista, P. Eades, R. Tamassia,and I. Tollis.Graph Drawing: Algorithms for Geometric Representations of Graphs.Prentice-Hall,1998.Google Scholar
  5. Fár48.
    I.Fáry.On straight line representation of planar graphs. Acta.Sci.Math. Szeged,11:229–233,1948.Google Scholar
  6. FK96.
    U. Föβmeier and M. Kaufmann.Drawing high degree graphs with low bend numbers.In F. Brandenburg,editor,Symposium on Graph Drawing 95,volume 1027of Lecture Notes in Computer Science, pages 254–266. Springer-Verlag,1996.Google Scholar
  7. FKK97.
    U. Föβmeier, G. Kant,and M. Kaufmann.2-visibility drawings of planar graphs.In S. North,editor,Symposium on Graph Drawing,GD 96,volume 1190 of Lecture Notes in Computer Science, pages 155–168.Springer-Verlag,1997.Google Scholar
  8. FPP88.
    H. deFraysseix, J. Pach,and R. Pollack.Small sets supporting fary embeddings of planar graphs.In Twentieth Annual ACM Symposium on Theory of Computing,pages 426–433,1988.Google Scholar
  9. FPP90.
    H. deFraysseix, J. Pach,and R. Pollack.How to drawa planar graph on a grid.Combinatorica,10:41–51,1990.MATHCrossRefMathSciNetGoogle Scholar
  10. GGT96.
    A. Garg, M.T. Goodrich,and R. Tamassia.Planar upward tree drawings with optimal area. International J.Computational Geometry Applications,6:333–356,1996.MATHCrossRefMathSciNetGoogle Scholar
  11. Kan96.
    G. Kant.Drawing planar graphs using the canonical ordering.Algorithmica,16:4–32,1996.Google Scholar
  12. Lei80.
    C. Leiserson. Area-efficient graph layouts (for VLSI). In 21st IEEE Symposium on Foundations of Computer Science, pages 270–281,1980.Google Scholar
  13. Sch90.
    W. Schnyder.Embedding planar graphs on the grid. In 1st Annual ACM-SIAM Symposium on Discrete Algorithms,pages 138–148,1990.Google Scholar
  14. Shi76.
    Y. Shiloach. Arrangements of Planar Graphs on the Planar Lattice. PhD thesis,Weizmann Institute of Science,1976.Google Scholar
  15. Ste51.
    S. Stein.Convex maps.In Amer.Math.Soc.,volume 2, pages 464–466,1951.Google Scholar
  16. Ull83.
    J.D. Ullman.Computational Aspects of VLSI.Computer Science Press, 1983.Google Scholar
  17. Wag36.
    K. Wagner.Bemerkungen zum Vierfarbenproblem. Jahresbericht der Deutschen Mathematiker-Vereinigung,46:26–32,1936.Google Scholar
  18. Wis85.
    S. Wismath.Characterizing bar line-of-sight graphs.In 1st ACM Symposium on Computational Geometry,pages 147–152,Baltimore,Maryland, USA,1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Therese Biedl
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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