The design and analysis of spatial data structures
The design and analysis of spatial data structures
On the optimal binary plane partition for sets of isothetic rectangles
Information Processing Letters
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
A combinatorial approach to cartograms
Computational Geometry: Theory and Applications
Introduction to Algorithms
CartoDraw: A Fast Algorithm for Generating Contiguous Cartograms
IEEE Transactions on Visualization and Computer Graphics
RecMap: Rectangular Map Approximations
INFOVIS '04 Proceedings of the IEEE Symposium on Information Visualization
On rectilinear duals for vertex-weighted plane graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Octagonal drawings of plane graphs with prescribed face areas
Computational Geometry: Theory and Applications
Optimal binary space partitions in the plane
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Orthogonal cartograms with few corners per face
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
How to visualize the k-root name server (demo)
GD'11 Proceedings of the 19th international conference on Graph Drawing
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A cartogram is a thematic map that visualizes statistical data about a set of regions like countries, states or provinces. The size of a region in a cartogram corresponds to a particular geographic variable, for example, population. We present an algorithm for constructing rectilinear cartograms (each region is represented by a rectilinear polygon) with zero cartographic error and correct region adjacencies, and we test our algorithm on various data sets. It produces regions of very small complexity---in fact, most regions are rectangles---while still ensuring both exact areas and correct adjacencies for all regions.Our algorithm uses a novel subroutine that is interesting in its own right, namely a polynomial-time algorithm for computing optimal binary space partitions (BSPs) for rectilinear maps. This algorithm works for a general class of optimality criteria, including size and depth. We use this generality in our application to computing cartograms, where we apply a dedicated cost function leading to BSP's amenable to the constructing of high-quality cartograms.