Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST model

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 Ω ( m ) bits of communication are required for any algorithm that cons...

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Bibliographic Details
Published in:Distributed computing Vol. 34; no. 4; pp. 283 - 299
Main Authors: Mashreghi, Ali, King, Valerie
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021
Springer Nature B.V
Subjects:
Algorithms
Broadcasting
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Graph theory
Messages
Nodes
Software Engineering/Programming and Operating Systems
Theory of Computation
Distributed computing
Minimum spanning tree
Broadcast tree
ISSN:0178-2770, 1432-0452
Online Access:Get full text
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Summary: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 Ω ( 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 neighbours’ 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 was 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.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-020-00387-y