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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| Veröffentlicht in: | Information and computation Jg. 292; S. 105035 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 105035 |
| Author | Castañeda, Armando Fraigniaud, Pierre Roy, Matthieu Rajsbaum, Sergio Paz, Ami Travers, Corentin |
| Author_xml | – sequence: 1 givenname: Armando surname: Castañeda fullname: Castañeda, Armando email: armando.castaneda@im.unam.mx organization: Instituto de Matemáticas, UNAM, Mexico – sequence: 2 givenname: Pierre surname: Fraigniaud fullname: Fraigniaud, Pierre email: pierref@irif.fr organization: IRIF, CNRS and Université Paris Cité, France – sequence: 3 givenname: Ami surname: Paz fullname: Paz, Ami email: ami.paz@lisn.fr organization: LISN, CNRS and Université Paris-Saclay, France – sequence: 4 givenname: Sergio surname: Rajsbaum fullname: Rajsbaum, Sergio email: rajsbaum@im.unam.mx organization: Instituto de Matemáticas, UNAM, Mexico – sequence: 5 givenname: Matthieu surname: Roy fullname: Roy, Matthieu email: roy@laas.fr organization: LAAS, CNRS, Toulouse, France – sequence: 6 givenname: Corentin surname: Travers fullname: Travers, Corentin email: corentin.travers@lis-lab.fr organization: LIS, Université Aix-Marseille, France |
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| Keywords | Distributed graph algorithms Combinatorial topology Crash failures Consensus |
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| SubjectTerms | Combinatorial topology Computer Science Consensus Crash failures Distributed graph algorithms Mathematics |
| Title | Synchronous t-resilient consensus in arbitrary graphs |
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