On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Floor-planning by graph dualization: 2-concave rectilinear modules
SIAM Journal on Computing
Sliceable Floorplanning by Graph Dualization
SIAM Journal on Discrete Mathematics
SIAM Journal on Computing
VISI Physical Design Automation: Theory and Practice
VISI Physical Design Automation: Theory and Practice
A fast algorithm for area minimization of slicing floorplans
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Computational Geometry: Theory and Applications
Octagonal drawings of plane graphs with prescribed face areas
Computational Geometry: Theory and Applications
Drawing slicing graphs with face areas
Theoretical Computer Science
Orthogonal drawings for plane graphs with specified face areas
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
On rectilinear duals for vertex-weighted plane graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
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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.