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International Colloquium on Structural Information and Communication Complexity

SIROCCO 2016: Structural Information and Communication Complexity pp 177–191Cite as

t-Resilient Immediate Snapshot Is Impossible

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9988))

Abstract

An immediate snapshot object is a high level communication object, built on top of a read/write distributed system in which all except one processes may crash. It allows each process to write a value and obtains a set of pairs (process id, value) such that, despite process crashes and asynchrony, the sets obtained by the processes satisfy noteworthy inclusion properties.

Considering an n-process model in which up to t processes are allowed to crash (t-crash system model), this paper is on the construction of t-resilient immediate snapshot objects. In the t-crash system model, a process can obtain values from at least \((n-t)\) processes, and, consequently, t-immediate snapshot is assumed to have the properties of the basic \((n-1)\)-resilient immediate snapshot plus the additional property stating that each process obtains values from at least \((n-t)\) processes. The main result of the paper is the following. While there is a (deterministic) \((n-1)\)-resilient algorithm implementing the basic \((n-1)\)-immediate snapshot in an \((n-1)\)-crash read/write system, there is no t-resilient algorithm in a t-crash read/write model when \(t\in [1\ldots (n-2)]\). This means that, when \(t<n-1\), the notion of t-resilience is inoperative when one has to implement t-immediate snapshot for these values of t: the model assumption “at most \(t<n-1\) processes may crash” does not provide us with additional computational power allowing for the design of a genuine t-resilient algorithm (genuine meaning that such an algorithm would work in the t-crash model, but not in the \((t+1)\)-crash model). To show these results, the paper relies on well-known distributed computing agreement problems such as consensus and k-set agreement.

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Notes

  1. 1.

    From a terminology point of view, we say t-failure model (in the present case t-crash model) if the model allows up to t processes to fail. We keep the term t-resilience for algorithms. The \((n-1)\)-crash model is also called wait-free model [16]. Several progress conditions have been associated with (n-1)-resilient algorithms: wait-freedom [16], non-blocking [22], or obstruction-freedom [18]. (See a unified presentation in Chap. 5 of [31].).

  2. 2.

    A is equivalent to B if A can be (computationally) reduced to B and reciprocally.

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Acknowledgments

The authors want to thank the referees for their constructive comments. This work was been partially supported by the French ANR project DISPLEXITY devoted to the study of Computability and Complexity in distributed computing, and the UNAM-PAPIIT project IN107714.

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Authors and Affiliations

  1. IRIF/GANG, Université Paris Diderot, Paris, France

    Carole Delporte & Hugues Fauconnier

  2. Instituto de Matemáticas, UNAM, 04510, México D.F., Mexico

    Sergio Rajsbaum

  3. IUF, IRISA (Université de Rennes), Rennes, France

    Michel Raynal

Authors
  1. Carole Delporte
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  2. Hugues Fauconnier
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  3. Sergio Rajsbaum
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  4. Michel Raynal
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Correspondence to Michel Raynal .

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Editors and Affiliations

  1. Aalto University, Espoo, Finland

    Jukka Suomela

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Delporte, C., Fauconnier, H., Rajsbaum, S., Raynal, M. (2016). t-Resilient Immediate Snapshot Is Impossible. In: Suomela, J. (eds) Structural Information and Communication Complexity. SIROCCO 2016. Lecture Notes in Computer Science(), vol 9988. Springer, Cham. https://doi.org/10.1007/978-3-319-48314-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-48314-6_12

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