We give a $\widetilde{O}(n)$ time almost uniform sampler for independent sets of a matroid, whose ground set has $n$ elements and is given by an independence oracle. As a consequence, one can sample connected spanning subgraphs of a given graph $G=(V,E)$ in $\widetilde{O}(|E|)$ time. This leads to improved running time on estimating all-terminal network reliability. Furthermore, we generalise this near-linear time sampler to the random cluster model with $q\le 1$.

翻译：我们提出了一种时间复杂度为 $\widetilde{O}(n)$ 的几乎均匀采样器，用于采样拟阵的独立集，其中基础集合包含 $n$ 个元素，并通过独立性预言机给出。由此，对于给定图 $G=(V,E)$ 的连通生成子图，可以在 $\widetilde{O}(|E|)$ 时间内完成采样。这一结果改进了全端网络可靠性的估计运行时间。此外，我们将这种近线性时间采样器推广到参数 $q\le 1$ 的随机簇模型。