Locally scalable randomized consensus for synchronous crash failures

Bogdan S. Chlebus, Dariusz R. Kowalski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider bit communication complexity of binary consensus in synchronous message passing systems with processes prone to crashes. A distributed algorithm is locally scalable when each process contributes to the complexity measure an amount that is poly-logarithmic in the size n of the system, and it is globally scalable when the average contribution per process to the complexity measure is such. We show that consensus can be solved by a randomized algorithm that is locally scalable with respect to both time and bit com-munication complexities against oblivious adversaries. If a bound t on the number of crashes is a constant fraction of the number n of processes then our randomized consensus solution terminates in the expected script O(log n) time while the expected number of bits that each process sends and receives is script O(log n). Our solution uses overlay networks with topologies that are explicitly defined and have suitable connectivity and robustness properties related to graph expansion. To compare our results to deterministic consensus solutions, it is known [20] that consensus cannot be solved deterministically by an algorithm that is locally scalable with respect to message complexity and that deterministic solutions globally scalable with respect to bit communication complexity exist for any bound t < n on the number of crashes. We prove a lower bound relating the number of nonfaulty processes needed to obtain a specific message complexity of consensus of a randomized algorithm run against oblivious adversaries.

Original languageEnglish (US)
Title of host publicationSPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures
Pages290-299
Number of pages10
DOIs
StatePublished - Nov 23 2009
Externally publishedYes
Event21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA'09 - Calgary, AB, Canada
Duration: Aug 11 2009Aug 13 2009

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA'09
CountryCanada
CityCalgary, AB
Period8/11/098/13/09

Fingerprint

Crash
Message Complexity
Complexity Measure
Communication Complexity
Randomized Algorithms
Overlay networks
Communication
Message passing
Parallel algorithms
Computer systems
Overlay Networks
Topology
Terminate
Message Passing
Distributed Algorithms
Logarithmic
Connectivity
Binary
Lower bound
Robustness

Keywords

  • Bit communication complexity
  • Consensus
  • Fault tolerance
  • Graph expansion
  • Lower bound
  • Message passing
  • Randomization
  • Scalability
  • Synchrony

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

Cite this

Chlebus, B. S., & Kowalski, D. R. (2009). Locally scalable randomized consensus for synchronous crash failures. In SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures (pp. 290-299). [1584063] (Annual ACM Symposium on Parallelism in Algorithms and Architectures). https://doi.org/10.1145/1583991.1584063

Locally scalable randomized consensus for synchronous crash failures. / Chlebus, Bogdan S.; Kowalski, Dariusz R.

SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures. 2009. p. 290-299 1584063 (Annual ACM Symposium on Parallelism in Algorithms and Architectures).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chlebus, BS & Kowalski, DR 2009, Locally scalable randomized consensus for synchronous crash failures. in SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures., 1584063, Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 290-299, 21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA'09, Calgary, AB, Canada, 8/11/09. https://doi.org/10.1145/1583991.1584063
Chlebus BS, Kowalski DR. Locally scalable randomized consensus for synchronous crash failures. In SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures. 2009. p. 290-299. 1584063. (Annual ACM Symposium on Parallelism in Algorithms and Architectures). https://doi.org/10.1145/1583991.1584063
Chlebus, Bogdan S. ; Kowalski, Dariusz R. / Locally scalable randomized consensus for synchronous crash failures. SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures. 2009. pp. 290-299 (Annual ACM Symposium on Parallelism in Algorithms and Architectures).
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