Ilya O. Ryzhov, John Gunnar Carlsson, Yinchu Zhu
arXiv 24 Nov 2025 · Econometrics
arXiv:2511.19722 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Dvoretzky, A. and Wald, A. and Wolfowitz, J (1951) Relations among certain ranges of vector measures | 0.928 | 4 | 4 | 100% |
| 2 | Carlsson, J. G. and Carlsson, E. and Devulapalli, R (2016) Shadow prices in territory division self | 0.843 | 3 | 3 | 100% |
| 3 | Hartmann, V. and Schuhmacher, D (2020) Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case | 0.843 | 3 | 3 | 100% |
| 4 | Pasupathy, R. and Kim, S (2011) The stochastic root-finding problem: Overview, solutions, and open questions | 0.843 | 3 | 3 | 100% |
| 5 | Zhu, Y. and Ryzhov, I. O (2025) Optimal data-driven hiring with equity for underrepresented groups self | 0.843 | 3 | 3 | 100% |
| 6 | Dwork, C. and Hardt, M. and Pitassi, T. and Reingold, O. and Zemel, R (2012) Fairness through awareness | 0.737 | 3 | 2 | 100% |
| 7 | Aurenhammer, F (1991) Voronoi diagrams – a survey of a fundamental geometric data structure | 0.644 | 2 | 2 | 100% |
| 8 | Carlsson, J. G. and Devulapalli, R (2013) Dividing a territory among several facilities self | 0.644 | 2 | 2 | 100% |
| 9 | Chzhen, E. and Denis, C. and Hebiri, M. and Oneto, L. and Pontil, M (2020) Fair regression with Wasserstein barycenters | 0.644 | 2 | 2 | 100% |
| 10 | Genevay, A. and Cuturi, M. and Peyré, G. and Bach, F (2016) Stochastic optimization for large-scale optimal transport | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 60 scored citations.