On rectangular cartograms

Abstract

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 (for example population). Rectangular cartograms are a useful tool to visualize statistical data. However, good cartograms are generally hard to generate: The area specifications for each rectangle may make it impossible to realize correct adjacencies between the regions and so hamper the intuitive understanding of the map. Here we present the first fully automated algorithms for rectangular cartograms. Our algorithms depend on a precise formalization of region adjacencies and are building upon existing VLSI layout algorithms. Furthermore, we characterize a non-trivial class of rectangular subdivisions for which exact cartograms can be efficiently computed. An implementation of our algorithms and various tests show that in practice, visually pleasing rectangular cartograms with small cartographic error can be effectively generated.