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  "path": "/abs/2603.25018v1",
  "publishedAt": "2026-03-27T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Nima Anari",
    "Alireza Haqi"
  ],
  "textContent": "**Authors:** Nima Anari, Alireza Haqi\n\nWe 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.",
  "title": "Fast Spanning Tree Sampling in Broadcast Congested Clique"
}