Optimal BSPs and rectilinear cartograms

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 ...

• Type: Conference
• Year: 2006
• Where: GIS
• Authors: Mark de Berg, Elena Mumford, Bettina Speckmann
• Keywords: Database, GIS 2006, Polynomial-time Algorithm, Rectilinear Cartograms, Rectilinear Polygon