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.

翻译：以公平公正的方式分配公共资源的地理分布至关重要。然而，量化这种分配的公平性较为复杂，关键因素包括到资源站点的距离、交通便利性及出行便捷度。我们采用拓扑数据分析工具——持久同调，研究投票站点的实际可用性与覆盖范围。通过持久同调提取的信息，我们能够推断投票站点分布中的空洞区域。我们对洛杉矶县及五座城市（亚特兰大、芝加哥、杰克逊维尔、纽约市、盐湖城）的投票站点覆盖率进行了分析与比较，结果表明持久同调计算是分析资源覆盖问题的合理方法。