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The Complexity Gap between Consensus and Safe-Consensus

(Extended Abstract)

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8576))

Abstract

In the consensus task each process proposes a value, and all correct processes have to decide the same value. In addition, validity requires that the decided value is a proposed value. Afek, Gafni and Lieber (DISC’09) introduced the safe-consensus task, by weakening the validity requirement: if the first process to invoke the task returns before any other process invokes it, then it outputs its input; otherwise, when there is concurrency, the consensus output can be arbitrary, not even the input of any process. Surprisingly, they showed that safe-consensus is equivalent to consensus, in a system where any number of processes can crash (e.g., wait-free).

We show that safe-consensus is nevertheless a much weaker communication primitive, in the sense that any wait-free implementation of consensus requires \(\binom{n}{2}\) safe-consensus black-boxes, and this bound is tight. The lower bound proof uses connectivity arguments based on subgraphs of Johnson graphs. For the upper bound protocol that we present, we introduce the g-2coalitions-consensus task, which may be of independent interest. We work in an iterated model of computation, where the processes repeatedly: write their information to a (fresh) shared array, invoke safe-consensus boxes and snapshot the contents of the shared array.

Partially supported by PAPIIT-UNAM IN107714.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México Ciudad Universitaria, México D.F., 04510, México

    Rodolfo Conde & Sergio Rajsbaum

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  1. Rodolfo Conde
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  2. Sergio Rajsbaum
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  1. School of Computer Science, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

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Conde, R., Rajsbaum, S. (2014). The Complexity Gap between Consensus and Safe-Consensus. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-09620-9_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09619-3

  • Online ISBN: 978-3-319-09620-9

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