On rectangular cartograms

M Van Kreveld, B Speckmann - Computational Geometry, 2007 - Elsevier
A rectangular cartogram is a type of map where every region is a rectangle. The size of the
rectangles is chosen such that their areas represent a geographic variable (eg, population) …

Area-universal and constrained rectangular layouts

D Eppstein, E Mumford, B Speckmann… - SIAM Journal on …, 2012 - SIAM
A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles.
These layouts are used as rectangular cartograms in cartography, as floorplans in building …

Computing cartograms with optimal complexity

MJ Alam, T Biedl, S Felsner, M Kaufmann… - Proceedings of the …, 2012 - dl.acm.org
In a rectilinear dual of a planar graph vertices are represented by simple rectilinear
polygons, while edges are represented by side-contact between the corresponding …

A linear programming approach to rectangular cartograms

B Speckmann, M Van Kreveld, S Florisson - Progress in Spatial Data …, 2006 - Springer
Abstract In [26], the first two authors of this paper presented the first algorithms to construct
rectangular cartograms. The first step is to determine a representation of all regions by …

[HTML][HTML] On rectilinear duals for vertex-weighted plane graphs

M De Berg, E Mumford, B Speckmann - Discrete Mathematics, 2009 - Elsevier
Let G=(V, E) be a plane triangulated graph where each vertex is assigned a positive weight.
A rectilinear dual of G is a partition of a rectangle into| V| simple rectilinear regions, one for …

Area-universal rectangular layouts

D Eppstein, E Mumford, B Speckmann… - Proceedings of the twenty …, 2009 - dl.acm.org
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 …

On mathematical optimization for the visualization of frequencies and adjacencies as rectangular maps

E Carrizosa, V Guerrero, DR Morales - European Journal of Operational …, 2018 - Elsevier
In this paper, we address the problem of visualizing a frequency distribution and an
adjacency relation attached to a set of individuals. We represent this information using a …

On rectilinear duals for vertex-weighted plane graphs

M De Berg, E Mumford, B Speckmann - International Symposium on Graph …, 2005 - Springer
Abstract Let \mathcalG=(V, E) be a plane triangulated graph where each vertex is assigned
a positive weight. A rectilinear dual of \mathcalG is a partition of a rectangle into| V| simple …

3D proportional contact representations of graphs

MJ Alam, SG Kobourov, G Liotta… - IISA 2014, The 5th …, 2014 - ieeexplore.ieee.org
In 3D contact representations, the vertices of a graph are represented by 3D polyhedra and
the edges are realized by non-zero-area common boundaries between corresponding …

Edge-weighted contact representations of planar graphs

M Nöllenburg, R Prutkin, I Rutter - … , Redmond, WA, USA, September 19-21 …, 2013 - Springer
We study contact representations of edge-weighted planar graphs, where vertices are
rectangles or rectilinear polygons and edges are polygon contacts whose lengths represent …