We present the first polylogarithmic-round algorithm for sampling a random spanning tree in the (Broadcast) Congested Clique model. For any constant $c > 0$, our algorithm outputs a sample from a distribution whose total variation distance from the uniform spanning tree distribution is at most $O(n^{-c})$ in at most $c \cdot \log^{O(1)}(n)$ rounds. The exponent hidden in $\log^{O(1)}(n)$ is an absolute constant independent of $c$ and $n$. This is an exponential improvement over the previous best algorithm of Pemmaraju, Roy, and Sobel (PODC 2025) for the Congested Clique model.

翻译：我们提出了首个在（广播）拥塞团模型中以多对数轮数进行随机生成树采样的算法。对于任意常数 $c > 0$，我们的算法最多在 $c \cdot \log^{O(1)}(n)$ 轮内输出一个样本，其分布与均匀生成树分布的总变差距离不超过 $O(n^{-c})$。$\log^{O(1)}(n)$ 中隐藏的指数是与 $c$ 和 $n$ 无关的绝对常数。与 Pemmaraju、Roy 和 Sobel（PODC 2025）在拥塞团模型上的先前最优算法相比，这是指数级的改进。