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Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model

Authors Ali Mashreghi, Valerie King

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Author Details

Ali Mashreghi
  • Department of Computer Science, University of Victoria, BC, Canada
Valerie King
  • Department of Computer Science, University of Victoria, BC, Canada

Funding

  • Mashreghi, Ali: Funded with an NSERC grant.
  • King, Valerie: Funded with an NSERC grant.

Cite AsGet BibTex

Ali Mashreghi and Valerie King. Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.DISC.2018.37

Abstract

We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Omega(m) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1 model where nodes have initial knowledge of their neighbors' identities it is possible to construct MST in O~(n) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O(log n). However, no algorithm with o(m) messages were known for the asynchronous case. Here, we provide an algorithm that uses O(n^{3/2} log^{3/2} n) messages to find MST in the asynchronous CONGEST model. Our algorithm is randomized Monte Carlo and outputs MST with high probability. We will provide an algorithm for computing a spanning tree with O(n^{3/2} log^{3/2} n) messages. Given a spanning tree, we can compute MST with O~(n) messages.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Distributed Computing
  • Minimum Spanning Tree
  • Broadcast Tree

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