We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.

翻译：我们研究具有单边不确定性的双边稳定匹配问题，涉及两个等势的智能体集合A和B。初始状态下，集合A中智能体的偏好列表已知，而集合B中智能体的偏好未知。算法可通过查询揭示集合B中智能体的偏好信息。我们考察三种查询模型：比较查询、面试查询和集合查询。通过竞争性分析，我们的目标是设计能够最小化查询次数的算法，以解决寻找稳定匹配或验证给定匹配是否稳定（或对某一侧智能体稳定且最优）的问题。我们提出了关于最佳可能竞争比的多重上界与下界，并给出了在完全信息条件下确定最优查询集的离线问题复杂性的相关结果。