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arXiv · 2603.25018

Fast Spanning Tree Sampling in Broadcast Congested Clique

Nima Anari·Alireza Haqi
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Abstract

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.

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Nima Anari, Alireza Haqi. 2026-03-26. Fast Spanning Tree Sampling in Broadcast Congested Clique. https://arxiv.org/abs/2603.25018

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