| Abstract: |
| Ideally, all public resources (e.g. hospitals, grocery stores, vaccination clinics, etc.) should be distributed in a way that is fair and equitable to everyone. However, this is not always the case. Quantifying how much (or little) access individuals have to certain resources is a complex problem. Previous work has shown that tools from topological data analysis (TDA) can be useful in determining holes in the locations of resource locations based on geographic locations and travel times [Hickok et al., Persistent homology for resource coverage: a case study of access to polling sites, SIAM Review, 2024]. Some resources may necessitate incorporation a notion of quality. We develop a framework for studying the coverage of resources of heterogeneous quality. As a case study, we look at public parks to determine how equitably green space is distributed. This topological framework for studying the coverage heterogeneous resources can be extended in many application areas. For example, it could be used to analyze the coverage of nuisances, or sites that one wants to avoid. |
|