We introduce the problem of ranking with slot constraints, which can be used to model a wide range of application problems -- from college admission with limited slots for different majors, to composing a stratified cohort of eligible participants in a medical trial. We show that the conventional Probability Ranking Principle (PRP) can be highly sub-optimal for slot-constrained ranking problems, and we devise a new ranking algorithm, called MatchRank. The goal of MatchRank is to produce rankings that maximize the number of filled slots if candidates are evaluated by a human decision maker in the order of the ranking. In this way, MatchRank generalizes the PRP, and it subsumes the PRP as a special case when there are no slot constraints. Our theoretical analysis shows that MatchRank has a strong approximation guarantee without any independence assumptions between slots or candidates. Furthermore, we show how MatchRank can be implemented efficiently. Beyond the theoretical guarantees, empirical evaluations show that MatchRank can provide substantial improvements over a range of synthetic and real-world tasks.

翻译：我们提出了一种带槽位约束的排序问题，可建模广泛的应用场景——从限制各专业招生名额的大学录取，到构建医学试验中分层合格参与者队列。研究表明，传统概率排序原则（PRP）在槽位约束排序问题中可能存在高度次优性，为此我们设计了一种新型排序算法MatchRank。该算法的目标是在人工决策者按排序顺序评估候选人时，最大化实际填满的槽位数量。通过这种方式，MatchRank实现了对PRP的推广，并在无槽位约束时退化为PRP特例。理论分析表明，该算法在无需对槽位或候选者进行独立性假设的情况下具有强近似保证。此外，我们证明了MatchRank的高效实现方法。除理论保证外，实证评估显示MatchRank在合成任务与真实场景中均能带来显著性能提升。