We sharpen run‐time analysis for algorithms under the partial rejection sampling framework. Our method yields improved bounds for: the cluster‐popping algorithm for approximating all‐terminal network reliability; the cycle‐popping algorithm for sampling rooted spanning trees; and the sink‐popping algorithm for sampling sink‐free orientations. In all three applications, our bounds are not only tight in order, but also optimal in30 constants.

中文翻译：

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弹出算法的紧界

我们在部分拒绝采样框架下优化了算法的运行时分析。我们的方法在以下方面产生了改进的界限：用于近似所有终端网络可靠性的簇弹出算法；用于采样生根生成树的循环弹出算法；以及用于提取无下沉方向的下沉弹出算法。在所有三个应用程序中，我们的边界不仅有序有序，而且在30个常量中也是最优的。