Synchronous t-resilient consensus in arbitrary graphs

We study the number of rounds needed to solve consensus in a synchronous network G where at most t nodes may fail by crashing. This problem has been thoroughly studied when G is a complete graph, but very little is known when G is arbitrary. We define a notion of radius(G,t), that extends the standa...

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Bibliographic Details
Published in:Information and computation Vol. 292; p. 105035
Main Authors: Castañeda, Armando, Fraigniaud, Pierre, Paz, Ami, Rajsbaum, Sergio, Roy, Matthieu, Travers, Corentin
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2023
Elsevier
Subjects:
Combinatorial topology
Computer Science
Consensus
Crash failures
Distributed graph algorithms
Mathematics
Distributed graph algorithms
Combinatorial topology
Crash failures
Consensus
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We study the number of rounds needed to solve consensus in a synchronous network G where at most t nodes may fail by crashing. This problem has been thoroughly studied when G is a complete graph, but very little is known when G is arbitrary. We define a notion of radius(G,t), that extends the standard graph theoretical notion of radius, for considering all the ways in which t nodes may crash, and we present an algorithm that solves consensus in radius(G,t) rounds. Then we derive a lower bound showing that, among oblivious algorithms, our algorithm is optimal for a large family of graphs including all vertex-transitive graphs.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2023.105035