Abstract
An orthogonal drawing of a plane graph is called an octagonal drawing if each inner face is drawn as a rectilinear polygon of at most eight corners and the contour of the outer face is drawn as a rectangle. A slicing graph is obtained from a rectangle by repeatedly slicing it vertically and horizontally. A slicing graph is called a good slicing graph if either the upper subrectangle or the lower one obtained by any horizontal slice will never be vertically sliced. In this paper we show that any good slicing graph has an octagonal drawing with prescribed face areas, in which the area of each inner face is equal to a prescribed value. Such a drawing has practical applications in VLSI floorplanning. We also give a linear-time algorithm to find such a drawing. We furthermore present a sufficient condition for a plane graph to be a good slicing graph, and give a linear-time algorithm to find a tree-structure of slicing paths for a graph satisfying the condition.
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References
He, X.: On floorplans of planar graphs. SIAM Journal on Computing 28(6), 2150–2167 (1999)
Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. John Wiley & Sons, Chichester (1990)
Rahman, M.S., Nakano, S., Nishizeki, T.: A linear algorithm for bend-optimal orthogonal drawings of triconnected cubic plane graphs. Journal of Graph. Alg. and Appl. 3(4), 31–62 (1999), http://jgaa.info
Shi, W.: A fast algorithm for area minimization of slicing floorplans. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 15(12), 1525–1532 (1996)
Sun, Y., Sarrafzadeh, M.: Floorplanning by graph dualization: L-shaped modules. Algorithmica 10, 429–456 (1998)
Sait, S.M., Youssef, H.: VLSI Physical Design Automation. World Scientific, Singapore (1999)
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16, 421–444 (1987)
Thomassen, C.: Plane cubic graphs with prescribed face areas. Combinatorics, Probability and Computing 1, 371–381 (1992)
Yeap, K., Sarrafzadeh, M.: Floor-planning by graph dualization: 2-concave rectilinear modules. SIAM J. Comput. 22(3), 500–526 (1993)
Yeap, K.H., Sarrafzadeh, M.: Sliceable floorplanning by graph dualization. SIAM J. Disc. Math. 8(2), 258–280 (1995)
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© 2004 Springer-Verlag Berlin Heidelberg
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Rahman, M.S., Miura, K., Nishizeki, T. (2004). Octagonal Drawings of Plane Graphs with Prescribed Face Areas. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_27
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DOI: https://doi.org/10.1007/978-3-540-30559-0_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24132-4
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