### 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 language | English (US) |
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Title of host publication | SPAA'09 - Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures |

Pages | 290-299 |

Number of pages | 10 |

DOIs | |

State | Published - Nov 23 2009 |

Externally published | Yes |

Event | 21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA'09 - Calgary, AB, Canada Duration: Aug 11 2009 → Aug 13 2009 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
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### Conference

Conference | 21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA'09 |
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Country | Canada |

City | Calgary, AB |

Period | 8/11/09 → 8/13/09 |

### 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

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## Cite this

*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