Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
Sliceable Floorplanning by Graph Dualization
SIAM Journal on Discrete Mathematics
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Slicible rectangular graphs and their optimal floorplans
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Transversal structures on triangulations, with application to straight-line drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Rectangular cartograms: the game
Proceedings of the twenty-fifth annual symposium on Computational geometry
Orientation-Constrained Rectangular Layouts
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Steinitz theorems for orthogonal polyhedra
Proceedings of the twenty-sixth annual symposium on Computational geometry
Optimizing regular edge labelings
GD'10 Proceedings of the 18th international conference on Graph drawing
Orthogonal cartograms with few corners per face
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Adjacency-preserving spatial treemaps
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Drawing planar 3-trees with given face-areas
GD'09 Proceedings of the 17th international conference on Graph Drawing
Computing cartograms with optimal complexity
Proceedings of the twenty-eighth annual symposium on Computational geometry
Drawing planar 3-trees with given face areas
Computational Geometry: Theory and Applications
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A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. They are used as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it is desirable for one rectangular layout to represent several area assignments. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whenever such a layout exists.