  Cartograms are popular for visualizing numerical data for map regions.
Maintaining correct adjacencies is a primary quality criterion for cartograms.
When there are multiple data values per region (over time or different
datasets) shown as animated or juxtaposed cartograms, preserving the viewer's
mental-map in terms of stability between cartograms is another important
criterion. We present a method to compute stable Demers cartograms, where each
region is shown as a square and similar data yield similar cartograms. We
enforce orthogonal separation constraints with linear programming, and measure
quality in terms of keeping adjacent regions close (cartogram quality) and
using similar positions for a region between the different data values
(stability). Our method guarantees ability to connect most lost adjacencies
with minimal leaders. Experiments show our method yields good quality and
stability.
