Abstract
The rectangular grid drawing of a plane graph G is a drawing of G such that each vertex is located on a grid point, each edge is drawn as a horizontal or vertical line segment, and the contour of each face is drawn as a rectangle. In this paper we give a simple linear-time algorithm to find a rectangular grid drawing of G if it exists. We also give an upper bound \(W + H \leqslant \frac{n}{2}\)on the sum of required width W and height H and a bound \(W + H \leqslant \frac{{n^2 }}{{16}}\)on the area of a rectangular grid drawing of G, where n is the number of vertices in G. These bounds are best possible, and hold for any compact rectangular grid drawing.
The full version of this paper is at http://www.nishizeki.ecei.tohoku.ac.jp/nszk/saidur/fv.html
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
J. Bhasker and S. Sahni, A linear algorithm to find a rectangular dual of a planar triangulated graph, Algorithmica, 3 (1988), pp. 247–278.
N. Chiba, K. Onoguchi, and T. Nishizeki, Drawing planar graphs nicely, Acta Informatica, 22 (1985), pp. 187–201.
M. Chiobak and S. Nakano, Minimum-width grid drawings of plane graphs, Technical Report, UCR-CS-94-5, Department of Computer Science, University of California at Riverside, 1994.
G. de Battista, P. Eades, R. Tamassia and I. G. Tollis, Algorithms for drawing graphs: an annotated bibliography, Comp. Geom. Theory Appl., to appear.
H. de Fraysseix, J. Pach and R. Pollack, How to draw a planar graph on a grid, Combinatorica, 10 (1990), pp. 41–51.
X. He, An efficient parallel algorithm for finding rectangular duals of plane triangulated graphs, Algorithmica 13 (1995), pp. 553–572.
X. He, On finding the rectangular duals of planar triangulated graphs, SIAM J. Comput., 22(6) (1993), pp. 1218–1226.
G. Kant and X. He, Two algorithms for finding rectangular duals of planar graphs, Graph-Theoretic Concepts in Computer Science, 19th International Workshop, WG'93 Proceedings, (1994), pp. 396–410.
K. Kozminski and E. Kinnen, An algorithm for finding a rectangular dual of a planar graph for use in area planning for VLSI integrated circuits, Proc. 21st DAC, Albuquerque, June (1984), pp. 655–656.
T. Nishizeki and N. Chiba, Planar Graphs: Theory and Algorithms, North-Holland, Amsterdam, 1988.
W. Schnyder, Embedding planar graphs in the grid, Proc. first ACM-SIAM Symp. on Discrete Algorithms, San Francisco, (1990), pp. 138–147.
K. Tani, S. Tsukiyama, S. Shinoda and I. Shirakawa, On area-efficent drawings of rectangular duals for VLSI floor-plan, Mathematical Programming 52 (1991), pp. 29–43.
C. Thomassen, Plane representations of graphs, (Eds.) J.A. Bondy and U.S.R. Murty, Progress in Graph Theory, Academic Press Canada, (1984), pp. 43–69.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rahman, S., Nakano, Si., Nishizeki, T. (1996). Rectangular grid drawings of plane graphs. In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_142
Download citation
DOI: https://doi.org/10.1007/3-540-61332-3_142
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61332-9
Online ISBN: 978-3-540-68461-9
eBook Packages: Springer Book Archive