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Majority and Unanimity in Synchronous Networks with Ubiquitous Dynamic Faults

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Structural Information and Communication Complexity (SIROCCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3499))

Abstract

In this paper we are interested in synchronous distributed systems subject to transient and ubiquitous failures. This includes systems where failures will occur on any communication link, systems where every processor will fail at one time or another, etc., and, following a failure, normal functioning can resume after a finite (although unpredictable) amount of time. Notice that these cases cannot be handled by the traditional component failure models.

The model we use is the transmission failure model, known also as the dynamic faults model. Using this model, we study the fundamental problem of agreement in synchronous systems of arbitrary topology.We establish bounds on the number of dynamic faults that make any non-trivial form of agreement (even strong majority) impossible; in turn, these bounds express connectivity requirements which must be met to achieve any meaningful form of agreement. We also provide, constructively, bounds on the number of dynamic faults in spite of which any non-trivial form of agreement (even unanimity) is possible.

These bounds are shown to be tight for a large class of networks, that includes hypercubes, toruses, rings, and complete graphs; incidentally, we close the existing gap between possibility and impossibility of non-trivial agreement in complete graphs in presence of dynamic Byzantine faults.

None of these results is derivable in the component failure models; in particular, all our possibility results hold in situations for which those models indicate impossibility.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Canada

    Nicola Santoro

  2. Institut for Theoretical Informatics, ETH Zurich, Switzerland

    Peter Widmayer

Authors
  1. Nicola Santoro
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  2. Peter Widmayer
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Editor information

Editors and Affiliations

  1. Département d’informatique, Université du Québec en Outaouais, J8X 3X7, Gatineau, Québec, Canada

    Andrzej Pelc

  2. IRISA, Université de Rennes, France

    Michel Raynal

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© 2005 Springer-Verlag Berlin Heidelberg

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Santoro, N., Widmayer, P. (2005). Majority and Unanimity in Synchronous Networks with Ubiquitous Dynamic Faults. In: Pelc, A., Raynal, M. (eds) Structural Information and Communication Complexity. SIROCCO 2005. Lecture Notes in Computer Science, vol 3499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11429647_21

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  • DOI: https://doi.org/10.1007/11429647_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26052-3

  • Online ISBN: 978-3-540-32073-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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