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.
|Title of host publication||Proceedings 14th International Symposium on Advances in Geographic Information Systems (ACM-GIS'06, Arlington VA, USA, November 10-11, 2006)|
|Place of Publication||New York|
|Publisher||Association for Computing Machinery, Inc|
|Publication status||Published - 2006|
Berg, de, M., Mumford, E., & Speckmann, B. (2006). Optimal BSPs and rectilinear cartograms. In Proceedings 14th International Symposium on Advances in Geographic Information Systems (ACM-GIS'06, Arlington VA, USA, November 10-11, 2006) (pp. 19-26). New York: Association for Computing Machinery, Inc. https://doi.org/10.1145/1183471.1183476