We address a general housing market problem with a set of agents and a set of houses. Each agent has a weak ordinal preference list that allows ties on houses as well as an initial endowment; moreover, each agent wishes to reallocate to a better house on the housing market. In this work, we reduces the complexity of the family of top trading cycles algorithms by selecting a specific house from the preferred set during the trading phase. The rule of construction digraphs is used to select an appropriate house. Based on these digraphs, we propose an extended top trading cycles algorithm with complexity \(O(n^{2} r)\), where \(n\) is the number of agents and \(r\) is the maximum length of ties in the preference lists. The algorithm complexity is lower than that of the state-of-the-art algorithms. We show that the proposed algorithm is individually rational, Pareto efficient, and strategy-proof. It thus overcomes the limitations of a classic top trading cycles algorithm, and features Pareto efficiency and strategy-proofness on the weak preference domain.

我们通过一组代理商和一组房屋来解决一般的住房市场问题。每个代理人的序数偏好列表都很薄弱，它允许在房屋上建立纽带以及获得最初的;赋；此外，每个代理商都希望在住房市场上重新分配到更好的住房。在这项工作中，我们通过在交易阶段从首选集合中选择一所特定的房屋，降低了顶级交易周期算法族的复杂性。建筑有向图的规则用于选择合适的房屋。基于这些图，我们提出了一个扩展的顶部交易周期算法，其复杂度为\（O（n ^ {2} r）\），其中\（n \）是代理商数量，\（r \）是首选项列表中关系的最大长度。该算法的复杂度低于最新技术。我们证明了所提出的算法是个体合理的，帕累托有效的并且是策略证明的。因此，它克服了经典的最高交易周期算法的局限性，并在弱偏好域上具有帕累托效率和策略证明性。