It is important to choose the geographical distribution 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. In this paper, 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：以公正和公平的方式选择公共资源的地理分布十分重要,但是,量化这种分配的公平性是复杂的;重要因素包括资源地点的距离、交通的可用性和旅行的方便性。在本文中,我们使用来自地形数据分析的持久性同质学工具研究投票地点的有效可用性和覆盖面。来自持久性同质学的信息使我们能够推导投票地点分布上的漏洞。我们分析和比较洛杉矶县和五个城市(亚特兰大、芝加哥、杰克逊维尔、纽约市和盐湖市)投票地点的覆盖范围。我们的结论是,计算持久性同质学似乎是分析资源覆盖面的合理方法。
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