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Broadcast in Almost Mixing Time

Authors Anton Paramonov , Roger Wattenhofer

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LIPIcs.STACS.2026.71.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Random network models
  • Theory of computation → Random walks and Markov chains
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Distributed algorithms
  • Expander Graphs
  • Random graphs
  • Broadcast
  • Branching random walks
  • Tree packing
  • CONGEST model

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Abstract

We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node s possesses a set M of messages with every message of size O(log n) where n is the total number of nodes. The objective is to ensure that every node in the network learns all messages in M. The execution of an algorithm progresses in rounds, and we focus on optimizing the round complexity of broadcasting multiple messages. 
Our primary contribution is a randomized algorithm for networks with expander topology. The algorithm succeeds with high probability and achieves a round complexity that is optimal up to a factor of the network’s mixing time and polylogarithmic terms. It leverages a multi-COBRA primitive, which uses multiple branching random walks running in parallel. A crucial aspect of our method is the use of these branching random walks to construct an optimal (up to a polylogarithmic factor) tree packing of a random graph, which is then used for efficient broadcasting.
We also prove the problem to be NP-hard in a centralized setting and provide insights into why lower bounds that can be matched in expanders, namely graph diameter and |M|/minCut, cannot be tight in general graphs.

Cite As Get BibTex

Anton Paramonov and Roger Wattenhofer. Broadcast in Almost Mixing Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 71:1-71:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.71

Author Details

Anton Paramonov
  • ETH Zurich, Switzerland
Roger Wattenhofer
  • ETH Zurich, Switzerland

Acknowledgements

The authors thank Diana Ghinea and Bernhard Haeupler for their helpful feedback, which helped improve this paper.

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