发表机构
Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究肯德尔tau距离下受拟阵或标志拟阵前缀约束的排序与秩聚合，给出多项式时间算法找最接近可行排序，证明其最优性，还表明固定数量输入排序时拟阵约束的秩聚合NP难。
AI 中文摘要
我们研究在肯德尔tau距离下的排序和秩聚合问题，输出排序的前缀受到拟阵或标志拟阵的约束。在拟阵情况下，前k个前缀需构成拟阵的一个基；在标志拟阵情况下，几个规定前缀需构成由商关系相连的一系列拟阵的基。此框架包含先前研究的k公平性和块公平性概念，还涵盖更一般的分层和分配型上下配额约束。我们给出一个多项式时间算法，在标志拟阵前缀约束下找到给定单个输入排序的最接近可行排序。该算法是自然的贪心过程，通过对称群上的布鲁哈特序论证证明其最优性。结果，现有的公平秩聚合近似框架可推广到拟阵设置。我们还证明，对于每个固定的输入排序数m≥2，即使在划分拟阵约束下，具有拟阵约束的秩聚合也是NP难的。
英文摘要
We study ranking and rank aggregation under the Kendall tau distance, subject to matroid or flag matroid constraints on prefixes of the output ranking. In the matroid case, the top-$k$ prefix is required to form a base of a matroid; in the flag matroid case, several prescribed prefixes are required to form bases of a sequence of matroids linked by quotient relations. This framework contains the previously studied notions of $k$-fairness and block-fairness as special cases, and also captures more general hierarchical and assignment-type lower- and upper-quota constraints. We provide a polynomial-time algorithm for finding, given a single input ranking, a closest feasible ranking under flag matroid prefix constraints. The algorithm is a natural greedy procedure, and its optimality is proved via a Bruhat order argument on the symmetric group. As a consequence, existing approximation frameworks for fair rank aggregation carry over to the matroidal setting. We also prove that rank aggregation with matroid constraints is NP-hard for every fixed number $m\ge 2$ of input rankings, even under partition matroid constraints.
Commentsv2: Minor revisions from v1. To appear in ISAAC 2026
