Minimum Segment Drawings of Series-Parallel Graphs with the Maximum Degree Three

(Extended Abstract)
  • Md. Abul Hassan Samee
  • Md. Jawaherul Alam
  • Muhammad Abdullah Adnan
  • Md. Saidur Rahman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

A minimum segment drawing Γ of a planar graph G is a straight line drawing of G that has the minimum number of segments among all straight line drawings of G. In this paper, we give a linear-time algorithm for computing a minimum segment drawing of a series-parallel graph with the maximum degree three. To the best of our knowledge, this is the first algorithm for computing minimum segment drawings of an important subclass of planar graphs.

References

  1. 1.
    Dujmović, V., Eppstein, D., Suderman, M., Wood, D.R.: Drawings of planar graphs with few slopes and segments. Comput. Geom. 38(3), 194–212 (2007)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Fáry, I.: On straight line representation of planar graphs. Acta Sci. Math. Szeged 11, 229–233 (1948)MATHGoogle Scholar
  3. 3.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Nishizeki, T., Rahman, M.S.: Planar Graph Drawing. Lecture Notes Series on Computing, vol. 12. World Scientific Publishing Co., Singapore (2004)MATHGoogle Scholar
  5. 5.
    Purchase, H.C.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Rahman, M.S., Egi, N., Nishizeki, T.: No-bend orthogonal drawings of series-parallel graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 409–420. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Samee, M.A.H.: Minimum Segment Drawings of Series-Parallel Graphs with the Maximum Degree Three. M.Sc. Engineering Thesis, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (July 2008)Google Scholar
  8. 8.
    Schnyder, W.: Embedding planar graphs on the grid. In: First ACM-SIAM Symp. on Discrete Algorithms, pp. 138–148 (1990)Google Scholar
  9. 9.
    Stein, K.S.: Convex maps. Amer. Math. Soc. 2, 464–466 (1951)CrossRefMATHGoogle Scholar
  10. 10.
    Wagner, K.: Bemerkungen zum vierfarbenproblem. Jahresber. Deutsch. Math-Verein. 46, 26–32 (1936)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Md. Abul Hassan Samee
    • 1
  • Md. Jawaherul Alam
    • 2
  • Muhammad Abdullah Adnan
    • 2
  • Md. Saidur Rahman
    • 2
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUSA
  2. 2.Department of Computer Science and EngineeringBangladesh University of Engineering and TechnologyDhakaBangladesh

Personalised recommendations