分数线性拟阵匹配属于 quasi-NC
Fractional Linear Matroid Matching is in quasi-NC
AI总结：
针对线性拟阵匹配缺乏 quasi-NC 并行算法的问题，论文借助分数拟阵匹配与非交换 Edmonds 问题的联系，给出分数线性拟阵匹配的 quasi-NC 算法，并解决一类黑盒非交换 Edmonds 问题。
摘要：
匹配与线性拟阵交问题可在 quasi-NC 中求解，这意味着存在确定性算法，能在多对数时间内运行，并使用拟多项式数量的并行处理器。然而，对于推广了这两个问题的线性拟阵匹配，这样的并行算法尚属未知。本文提出一种用于分数线性拟阵匹配的 quasi-NC 算法；该问题是线性拟阵匹配的松弛，并共同推广了分数匹配和线性拟阵交。我们的算法建立在 Oki 和 Soma（2023）最近揭示的分数拟阵匹配与非交换 Edmonds 问题之间联系的基础上。作为推论，我们还解决了系数为二阶斜对称矩阵的黑盒非交换 Edmonds 问题。
英文摘要：
The matching and linear matroid intersection problems are solvable in quasi-NC, meaning that there exist deterministic algorithms that run in polylogarithmic time and use quasi-polynomially many parallel processors. However, such a parallel algorithm is unknown for linear matroid matching, which generalizes both of these problems. In this work, we propose a quasi-NC algorithm for fractional linear matroid matching, which is a relaxation of linear matroid matching and commonly generalizes fractional matching and linear matroid intersection. Our algorithm builds upon the connection of fractional matroid matching to non-commutative Edmonds' problem recently revealed by Oki and Soma~(2023). As a corollary, we also solve black-box non-commutative Edmonds' problem with rank-two skew-symmetric coefficients.
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。
