  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.
