高效面试调度实现稳定匹配
Efficient Interview Scheduling for Stable Matching
AI总结：
针对偏好不确定且需通过面试揭示的市场，提出两种自适应算法（顺序和混合）以最小化面试次数和轮数，实现临时稳定匹配，并证明每代理平均2次面试的必要性。
摘要：
稳定匹配的研究通常依赖于代理人对另一方的偏好是完整且已知的假设。然而，在许多真实市场中，偏好可能是不确定的，并且只能通过昂贵的互动（如面试）来揭示。我们展示了如何达到临时稳定匹配，在这种匹配下，所有匹配的对必须已经面试过，并且当真实值仍然未知时，代理人使用期望效用，同时最小化预期的面试次数和预期的面试轮数。我们引入了两种产生临时稳定匹配的自适应算法：一种顺序运行，另一种是混合算法，它首先并行安排一些面试，然后继续顺序进行。关注代理人对另一方事前无差异的情况，我们证明顺序算法每代理平均进行2次面试。我们通过证明任何每代理面试次数少于2次的算法并不总是保证临时稳定性来补充这一点。我们还证明，混合算法只需要对数期望轮数，同时每代理平均仍只进行约2次面试。此外，我们的算法安排的面试保证了在延迟接受算法在所有面试完成后运行时的临时稳定匹配。
英文摘要：
The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
