Fast Spanning Tree Sampling in Broadcast Congested Clique

2026-03-26

AI Summary

This work addresses the problem of efficiently sampling an approximately uniform random spanning tree in the broadcast-congested clique model. We propose a novel approach that integrates probabilistic graph theory with distributed algorithm design to output a spanning tree whose distribution is within total variation distance $O(n^{-c})$ of the uniform distribution, using only $c \cdot \log^{O(1)} n$ communication rounds. This algorithm achieves high-precision sampling in polylogarithmic time—a significant improvement over prior methods—and provides the first known exponential speedup in this model, thereby substantially advancing the state-of-the-art in the efficiency of random spanning tree generation under broadcast constraints.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• spanning tree sampling
• Congested Clique
• randomized algorithms
• distributed computing
• uniform distribution

Innovation

• Spanning Tree Sampling
• Congested Clique
• Polylogarithmic Rounds
• Uniform Distribution
• Distributed Algorithms