Two algorithms for finding rectangular duals of planar graphs

  • Goos Kant
  • Xin He
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 790)

Abstract

We present two linear-time algorithms for computing a regular edge labeling of 4-connected planar triangular graphs. This labeling is used to compute in linear time a rectangular dual of this class of planar graphs. The two algorithms are based on totally different frameworks, and both are conceptually simpler than the previous known algorithm and are of independent interests. The first algorithm is based on edge contraction. The second algorithm is based on the canonical ordering. This ordering can also be used to compute more compact visibility representations for this class of planar graphs.

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References

  1. 1.
    Bhasker, J., and S. Sahni, A linear algorithm to check for the existence of a rectangular dual of a planar triangulated graph, Networks 7 (1987), pp. 307–317.Google Scholar
  2. 2.
    Bhasker, J., and S. Sahni, A linear algorithm to find a rectangular dual of a planar triangulated graph, Algorithmica 3 (1988), pp. 247–178.Google Scholar
  3. 3.
    Eades, P., and R. Tamassia, Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Dept. of Comp. Science, Brown Univ., Technical Report CS-89-09, 1989.Google Scholar
  4. 4.
    Fraysseix, H. de, J. Pach and R. Pollack, How to draw a planar graph on a grid, Combinatorica 10 (1990), pp. 41–51.Google Scholar
  5. 5.
    He, X., On finding the rectangular duals of planar triangulated graphs, SIAM J. Comput., to appear.Google Scholar
  6. 6.
    He, X., Efficient Parallel Algorithms for two Graph Layout Problems, Technical Report 91-05, Dept. of Comp. Science, State Univ. of New York at Buffalo, 1991.Google Scholar
  7. 7.
    Kant, G., Drawing planar graphs using the lmc-ordering, Proc. 33th Ann. IEEE Symp. on Found. of Comp. Science, Pittsburgh, 1992, pp. 101–110.Google Scholar
  8. 8.
    Koźmiński, K., and E. Kinneñ, Rectangular dual of planar graphs, Network 5 (1985), pp. 145–157.Google Scholar
  9. 9.
    Rosenstiehl, P., and R. E. Tarjan, Rectilinear planar layouts and bipolar orientations of planar graphs, Discr. and Comp. Geometry 1 (1986), pp. 343–353.Google Scholar
  10. 10.
    Schnyder, W., Embedding planar graphs on the grid, in: Proc. 1st Annual ACM-SIAM Symp. on Discr. Alg., San Francisco, 1990, pp. 138–147.Google Scholar
  11. 11.
    Tamassia, R., and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discr. and Comp. Geometry 1 (1986), pp. 321–341.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Goos Kant
    • 1
  • Xin He
    • 2
  1. 1.Department of Computer ScienceUtrecht UniversityCH Utrechtthe Netherlands
  2. 2.Department of Computer ScienceState University of New York at BuffaloBuffaloUSA

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