In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria (ethical, financial, legal, etc.). Such settings have motivated the following priority-respecting allocation problem: several categories, each with a quota of interchangeable items, wish to allocate the items among a set of agents. Each category has a list of eligible agents and a priority ordering over these agents; agents may be eligible in multiple categories. The goal is to select a valid allocation: one that respects quotas, eligibility, and priorities, and ensures Pareto efficiency. We provide a complete algorithmic characterization of all valid allocations, exhibiting a bijection between these allocations and maximum-weight matchings under carefully chosen rank-based weights. This recovers and extends known results in this space and enables two wide-reaching extensions: 1. Selecting valid allocations that satisfy additional criteria: Via three examples -- inclusion/exclusion of some chosen agent; agent-side Pareto efficiency vs. welfare maximization; and fairness from the perspective of allocated vs. unallocated agents -- we show that finding priority-respecting allocations subject to some secondary constraint straddles a complexity knife-edge; in each example, one problem variant can be solved efficiently, while a closely related variant is NP-hard. 2. Efficiency-envy tradeoffs in dynamic allocation: In settings where allocations must be made to $T$ agents arriving sequentially via some stochastic process, we show that while insisting on zero priority violations leads to an $\Omega(T)$ loss in efficiency, one can design allocation policies ensuring that the sum of the efficiency loss and priority violations in hindsight is $O(1)$.

翻译：在诸如医疗物资配给、大学录取及公共住房分配等众多应用中，谁获得分配的决定可由多种规范性标准（伦理、财务、法律等）加以论证。这类场景催生了以下尊重优先权的分配问题：多个类别各自拥有可互换物品的配额，需将物品分配给一组代理人。每个类别均有一个合格代理人名单及对这些代理人的优先顺序；代理人可能同时符合多个类别的资格。目标在于选择一种有效分配：即满足配额、资格与优先权约束，并确保帕累托效率。我们给出了所有有效分配的完整算法表征，证明这些分配与基于精心设计的秩加权下的最大权重匹配之间存在一一对应关系。这恢复并扩展了该领域的已知结论，并可实现两大延伸：1. 选择满足附加标准的有效分配：通过三个示例——包含/排除特定代理人、代理人侧帕累托效率与福利最大化的权衡、以及从已分配与未分配代理人视角的公平性——我们证明，在满足次要约束条件下寻找尊重优先权的分配问题处于复杂度临界状态；每个示例中，某类问题变体可高效求解，而其密切相关的变体则为NP难问题。2. 动态分配中的效率-嫉妒权衡：在必须通过某种随机过程顺序对T个到达代理人进行分配的场景中，我们证明，若坚持零优先权违反将导致Ω(T)的效率损失，但可设计出确保事后效率损失与优先权违反之和为O(1)的分配策略。