Abstract
In this paper we introduce a new drawing style of a plane graph G, called a “box-rectangular drawing.” It is defined to be a drawing of G on an integer grid such that every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. We establish a necessary and sufficient condition for the existence of a box-rectangular drawing of G. We also give a simple lineartime algorithm to find a box-rectangular drawing of G if it exists.
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References
T. C. Biedl, Optimal orthogonal drawings of triconnected plane graphs, Proc. SWAT’96, Lect. Notes in Compute Science, Springer, 1097 (1996), pp. 333–344.
T. C. Biedl and M. Kaufmann, Area-efficient static and incremental graph drawings, Proc. of 5th European Symposium on Algorithms, Lect. Notes in Computer Science, Springer, 1284 (1997), pp. 37–52.
T. Calamoneri and R. Petreschi, Orthogonally drawing cubic graphs in parallel, Journal of Parallel and Distributed Comp., 55 (1998), pp. 94–108.
G. de Battista, P. Eades, R. Tamassia and I. G. Tollis, Algorithms for drawing graphs: an annotated bibliography, Comp. Geom. Theory Appl., 4 (1994), pp. 235–282.
U. Fößmeier, G. Kant and M. Kaufmann, 2-visibility drawings of plane graphs, Proc. of Graph Drawing’ 96, Lect. Notes in Compute Science, Springer, 1190 (1997), pp. 155–168.
R. L. Francis and J. A. White, Facility Layout and Location, Prentice-Hall, Inc, New Jersey, 1974.
G. Kant, Drawing planar graphs using the canonical ordering, Algorithmica (1996) 16, pp. 4–32.
G. Kant and X. He, Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems, Theoretical Computer Science, 172 (1997), pp. 175–193.
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. of 21st DAC, (1984), pp. 655–656.
T. Lengauer, Combinatirial Algorithms for Integrated Circuit Layout, John Wiley & Sons, Chichester, 1990.
O. Ore, The Four Color Problem, Academic press, New York, 1967.
A. Papakostas and I. G. Tollis, Orthogonal drawings of high degree graphs with small area and few bends, Proc. of 5th Workshop on Algorithms and Data Structures, Lect. Notes in Computer Science, Springer, 1272 (1998), pp. 354–367.
M. S. Rahman, S. Nakano and T. Nishizeki, Rectangular grid drawings of plane graphs, Comp. Geom. Theo. Appl. 10 (3) (1998), pp. 203–220.
M. S. Rahman, S. Nakano and T. Nishizeki, A linear algorithm for optimal orthogonal drawings of triconnected cubic plane graphs, Proc. of Graph Drawing’97, Lect. Notes in Computer Science, Springer, 1353 (1998), pp. 99–110. Also, Journal of Graph Alg. Appl., to appear.
N. Sherwani, Algorithms for VLSI Physical Design Automation, 2nd edition, Kluwer Academic Publishers, Boston, 1995.
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.
R. Tamassia, On embedding a graph in the grid with the minimum number of bends, SIAM J. Comput. 16 (1987), pp. 421–444.
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Rahman, M.S., Nakano, Si., Nishizeki, T. (1999). Box-Rectangular Drawings of Plane Graphs. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_25
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DOI: https://doi.org/10.1007/3-540-46784-X_25
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