An efficient algorithm for computing the choropleth map classification scheme known as equal area breaks or geographical quantiles is introduced. An equal area breaks classification aims to obtain a coloring for the map such that the area associated with each of the colors is approximately equal. This is meant to be an alternative to an approach that assigns an equal number of regions with a particular range of property values to each color, called quantiles, which could result in the mapped area being dominated by one or a few colors. Moreover, it is possible that the other colors are barely discernible. This is the case when some regions are much larger than others (e.g., compare Switzerland with Russia). A number of algorithms of varying computational complexity are presented to achieve an equal area assignment to regions. They include a pair of greedy algorithms, as well as an optimal algorithm that is based on dynamic programming. The classification obtained from the optimal equal area algorithm is compared with the quantiles and Jenks natural breaks algorithms and found to be superior from a visual standpoint by a user study. Finally, a modified approach is presented which enables users to vary the extent to which the coloring algorithm satisfies the conflicting goals of equal area for each color with that of assigning an equal number of regions to each color.
