Orthogonal Drawings of Plane Graphs without Bends

Extended Abstract
  • Md. Saidur Rahman
  • Mahmuda Naznin
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)

Abstract

In an orthogonal drawing of a plane graph G each vertex is drawn as a point and each edge is drawn as a sequence of vertical and horizontal line segments. A point at which the drawing of an edge changes its direction is called a bend. Every plane graph of the maximum degree at most four has an orthogonal drawing, but may need bends. A simple necessary and sufficient condition has not been known for a plane graph to have an orthogonal drawing without bends. In this paper we obtain a necessary and sufficient condition for a plane graph G of the maximum degree three to have an orthogonal drawing without bends. We also give a linear-time algorithm to find such a drawing of G if it exists.

Keywords

Graph Algorithm Graph Drawing Orthogonal Drawing Bend 

References

  1. [DETT99]
    G. Di. Battista, P. Eades, R. Tamassia, I. G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice-Hall Inc., Upper Saddle River, New Jersey, 19MATHGoogle Scholar
  2. [GT95]
    A. Garg and R. Tamassia, On the computational complexity of upward and rectilinear planarity testing, Proc. of Graph Drawing’94, Lect. Notes in Computer Science, 894, pp. 99–110, 1995.Google Scholar
  3. [GT97]
    A. Garg and R. Tamassia, A new minimum cost flow algorithm with applications to graph drawing, Proc. of Graph Drawing’96, Lect. Notes in Computer Science, 1190, pp. 201–206, 1997.Google Scholar
  4. [L90]
    T. Lengauer, Combinatorial Algorithms for Integrated Circuit Layout, Wiley, Chichester, 1990.Google Scholar
  5. [RNN00a]
    M. S. Rahman, S. Nakano and T. Nishizeki, Box-rectangular drawings of plane graphs, Journal of Algorithms, 37, pp. 363–398, 2000.MATHCrossRefMathSciNetGoogle Scholar
  6. [RNN00b]
    M. S. Rahman, S. Nakano and T. Nishizeki, Rectangular drawings of plane graphs without designated corners, Proc. of COCOON’2000, Lect. Notes in Computer Science, 1858, pp. 85–94, 2000, also Comp. Geom. Theo. Appl., to appear.Google Scholar
  7. [RNN98]
    M. S. Rahman, S. Nakano and T. Nishizeki, Rectangular grid drawings of plane graphs, Comp. Geom. Theo. Appl., 10(3), pp. 203–220, 1998.MATHMathSciNetGoogle Scholar
  8. [RNN99]
    M. S. Rahman, S. Nakano and T. Nishizeki, A linear algorithm for bendoptimal orthogonal drawings of triconnected cubic plane graphs, Journal of Graph Alg. and Appl., http://www.cs.brown.edu/publications/jgaa/, 3(4), pp. 31–62, 1999.MATHMathSciNetGoogle Scholar
  9. [T84]
    C. Thomassen, Plane representations of graphs, (Eds.) J.A. Bondy and U.S.R. Murty, Progress in Graph Theory, Academic Press Canada, pp. 43–69, 1984.Google Scholar
  10. [T87]
    R. Tamassia, On embedding a graph in the grid with the minimum number of bends, SIAM J. Comput., 16, pp. 421–444, 1987.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Md. Saidur Rahman
    • 1
  • Mahmuda Naznin
    • 1
  • Takao Nishizeki
    • 2
  1. 1.Department of computer Science and EngineeringBangladesh University of Engineering and Technology (BUET)DhakaBangladesh
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Personalised recommendations