  It is important to choose the geographical distributions of public resources
in a fair and equitable manner. However, it is complicated to quantify the
equity of such a distribution; important factors include distances to resource
sites, availability of transportation, and ease of travel. We use persistent
homology, which is a tool from topological data analysis, to study the
effective availability and coverage of polling sites. The information from
persistent homology allows us to infer holes in the distribution of polling
sites. We analyze and compare the coverage of polling sites in Los Angeles
County and five cities (Atlanta, Chicago, Jacksonville, New York City, and Salt
Lake City), and we conclude that computation of persistent homology appears to
be a reasonable approach to analyzing resource coverage.
