解决地理分区中的群体公平问题，确保各群体在不同设施中代表性均衡。
Individual and group fairness in geographical partitioning
- 提出基于加权的新型Voronoi图，实现多群体公平分区。
- 算法高效求解，案例中处理7个群体与78个办公点。
- 适用于教育区划、公共服务分配等需要公平性的场景。
社会经济隔离常出现在学区划分等情境中，导致某些群体在特定区域内被过度或不足代表，进而引发机会与结果的不平等。本文提出一类新的地理分区问题，人口具有异质性，需确保每个群体在每个设施中获得公平代表。证明最优解是加性加权Voronoi图的新推广，并提出一种简单高效的计算算法，解决了自Dvoretzky等（1951）以来的开放问题。在包含7个族裔群体和78个区级办公点的真实案例研究中验证了方法的有效性与实践潜力。
原文摘要 · Abstract (English)
Socioeconomic segregation often arises in school districting and other contexts, causing some groups to be over- or under-represented within a particular district. This phenomenon is closely linked with disparities in opportunities and outcomes. We formulate a new class of geographical partitioning problems in which the population is heterogeneous, and it is necessary to ensure fair representation for each group at each facility. We prove that the optimal solution is a novel generalization of the additively weighted Voronoi diagram, and we propose a simple and efficient algorithm to compute it, thus resolving an open question dating back to Dvoretzky et al. (1951). The efficacy and potential for practical insight of the approach are demonstrated in a realistic case study involving seven demographic groups and $78$ district offices.
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