The TopDown Algorithm (TDA) first produces differentially private counts at
the nation and then produces counts at lower geolevels (e.g.: state, county,
etc.) subject to the constraint that all query answers in lower geolevels are
consistent with those at previously estimated geolevels. This paper describes
the three sets of definitions of these geolevels, or the geographic spines,
that are implemented within TDA. These include the standard Census geographic
spine and two other spines that improve accuracy in geographic areas that are
far from the standard Census spine, such as cities, towns, and/or AIAN areas.
The third such spine, which is called the optimized spine, also modifies the
privacy-loss budget allocated to the entities within the geolevels, or the
geounits, to ensure the privacy-loss budget is used efficiently within TDA.