In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (possibly overlapping) types and (2) hospital-doctor matching where various regional quotas are imposed. In this paper, we present a polynomial-time reduction to transform an instance of (1) to an instance of (2) and we show how the feasibility and stability of corresponding matchings are preserved under the reduction. Our reduction provides a formal connection between two important strands of work on matching with distributional constraints. We then apply the reduction in two ways. Firstly, we show that it is NP-complete to check whether a feasible and stable outcome for (1) exists. Due to our reduction, these NP-completeness results carry over to setting (2). In view of this, we help unify some of the results that have been presented in the literature. Secondly, if we have positive results for (2), then we have corresponding results for (1). One key conclusion of our results is that further developments on axiomatic and algorithmic aspects of hospital-doctor matching with regional quotas will result in corresponding results for school choice with diversity constraints.

中文翻译：

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从匹配多样性约束到匹配区域配额

在过去几年中，已经提出并研究了几种新的匹配模型，它们考虑了复杂的分布约束。相关工作包括（1）具有多样性限制的学校选择，其中学生具有（可能重叠）类型和（2）医院-医生匹配，其中施加了各种区域配额。在本文中，我们提出了多项式时间约简，将 (1) 的实例转换为 (2) 的实例，并展示了如何在约简下保持相应匹配的可行性和稳定性。我们的简化在与分布约束匹配的两个重要工作方面提供了正式联系。然后我们以两种方式应用减少。首先，我们证明检查（1）是否存在可行且稳定的结果是 NP 完全的。由于我们的减少，这些 NP 完整性结果延续到设置 (2)。有鉴于此，我们帮助统一了文献中提出的一些结果。其次，如果我们对（2）有肯定的结果，那么我们对（1）就有相应的结果。我们结果的一个关键结论是，医院-医生与区域配额匹配的公理和算法方面的进一步发展将导致具有多样性约束的学校选择的相应结果。