SIAM Review, Volume 66, Issue 3, Page 481-500, May 2024.
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 availability and coverage of polling sites. The information from persistent homology allows us to infer holes in a 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.

中文翻译：

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资源覆盖范围的持久同源性：访问投票站的案例研究


《SIAM 评论》，第 66 卷，第 3 期，第 481-500 页，2024 年 5 月。

公平合理地选择公共资源的地域分配很重要。然而，量化这种分配的公平性是很复杂的；重要因素包括距资源地点的距离、交通的可用性以及旅行的便利性。我们使用持久同源性（拓扑数据分析的工具）来研究投票站的可用性和覆盖范围。来自持久同源性的信息使我们能够推断投票站点分布中的漏洞。我们分析和比较了洛杉矶县和五个城市（亚特兰大、芝加哥、杰克逊维尔、纽约市和盐湖城）的投票站的覆盖范围，我们得出结论，持久同源性的计算似乎是分析资源的合理方法覆盖范围。