One-sided matching problems with ordinal preferences, such as hostel room allocation, are commonly solved using the Top Trading Cycles (TTC) mechanism, which guarantees Pareto-optimal (PO) outcomes. However, TTC does not yield a unique solution: multiple PO allocations may exist, and many distinct initial endowments can converge to the same outcome. Focusing on a single TTC result obscures the structure of the Pareto-efficient frontier and limits principled secondary optimization over fairness or welfare objectives. Therefore, the goal is to find the entire set of PO allocations for a given preference profile. We propose the Inverse Top Trading Cycles Enumeration Algorithm (ITEA), a novel method that efficiently computes the complete set of Pareto-optimal allocations in one-sided matching problems. We prove the soundness and completeness of the proposed algorithm and analyze its computational complexity. Although in the worst case, there can be $n!$ PO allocations; however, compared to the brute-force approach, our algorithm reduces time complexity when there are fewer PO allocations. Empirical results demonstrate substantial reductions in redundant TTC computations compared to brute-force enumeration, enabling efficient characterization of the Pareto frontier.

翻译：针对具有序数偏好的单边匹配问题（如宿舍房间分配），通常采用顶级交易循环（TTC）机制来解决，该机制能保证帕累托最优（PO）结果。然而，TTC并不产生唯一解：可能存在多个PO分配方案，且多种不同的初始禀赋可能收敛于相同结果。仅关注单一TTC结果会模糊帕累托有效前沿的结构，并限制基于公平或福利目标的二次优化。因此，目标是在给定偏好分布下找出完整的PO分配集合。我们提出逆顶级交易循环枚举算法（ITEA），这是一种能高效计算单边匹配问题中所有帕累托最优分配集合的新方法。我们证明了所提算法的正确性与完备性，并分析了其计算复杂度。尽管最坏情况下可能存在$n!$个PO分配，但与暴力枚举方法相比，当PO分配数量较少时，我们的算法能够降低时间复杂度。实验结果表明，相比暴力枚举，该方法能大幅减少冗余的TTC计算，从而高效表征帕累托前沿。