Discrete Mathematics
Floor-planning by graph dualization: 2-concave rectilinear modules
SIAM Journal on Computing
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Contact graphs of line segments are NP-complete
Discrete Mathematics
RecMap: Rectangular Map Approximations
INFOVIS '04 Proceedings of the IEEE Symposium on Information Visualization
Computational Geometry: Theory and Applications
Rectangular layouts and contact graphs
ACM Transactions on Algorithms (TALG)
GD'10 Proceedings of the 18th international conference on Graph drawing
Triangle contact representations and duality
GD'10 Proceedings of the 18th international conference on Graph drawing
Contact representations of planar graphs with cubes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Optimal polygonal representation of planar graphs
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Computing cartograms with optimal complexity
Proceedings of the twenty-eighth annual symposium on Computational geometry
GD'12 Proceedings of the 20th international conference on Graph Drawing
Proportional contact representations of 4-connected planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.