### Abstract

This paper presents an efficient deterministic gossip algorithm for p synchronous, crash-prone, message-passing processors. The algorithm has time complexity T = O(log^{2} p) and message complexity M = O(p^{1+ε}), for any ε > 0. This substantially improves the message complexity of the previous best algorithm that has M = O(p^{1.77}), while maintaining the same time complexity. The strength of the new algorithm is demonstrated by constructing a deterministic algorithm for performing n tasks in this distributed setting. Previous solutions used coordinator or check-pointing approaches, immediately incurring a work penalty Ω(n + f·p) for f crashes, or relied on strong communication primitives, such as reliable broadcast, or had work too close to the trivial Θ(p·n) bound of oblivious algorithms. The new algorithm uses p crash-prone processors to perform n similar and idempotent tasks so long as one processor remains active. The work of the algorithm is W = O(n + p·min{f + 1, log^{3} p}) and its message complexity is M = O(fp^{ε} + pmin{f + 1, log p}), for any ε > 0. This substantially improves the work complexity of previous solutions using simple point-to-point messaging, while "meeting or beating" the corresponding message complexity bounds. The new algorithms use communication graphs and permutations with certain combinatorial properties that are shown to exist. The algorithms are correct for any permutations, and in particular, the same expected bounds can be achieved using random permutations.

Original language | English (US) |
---|---|

Pages (from-to) | 224-238 |

Number of pages | 15 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2848 |

State | Published - Dec 1 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*2848*, 224-238.

**Efficient gossip and robust distributed computation.** / Georgiou, Chryssis; Kowalski, Dariusz R.; Shvartsman, Alex A.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2848, pp. 224-238.

}

TY - JOUR

T1 - Efficient gossip and robust distributed computation

AU - Georgiou, Chryssis

AU - Kowalski, Dariusz R.

AU - Shvartsman, Alex A.

PY - 2003/12/1

Y1 - 2003/12/1

N2 - This paper presents an efficient deterministic gossip algorithm for p synchronous, crash-prone, message-passing processors. The algorithm has time complexity T = O(log2 p) and message complexity M = O(p1+ε), for any ε > 0. This substantially improves the message complexity of the previous best algorithm that has M = O(p1.77), while maintaining the same time complexity. The strength of the new algorithm is demonstrated by constructing a deterministic algorithm for performing n tasks in this distributed setting. Previous solutions used coordinator or check-pointing approaches, immediately incurring a work penalty Ω(n + f·p) for f crashes, or relied on strong communication primitives, such as reliable broadcast, or had work too close to the trivial Θ(p·n) bound of oblivious algorithms. The new algorithm uses p crash-prone processors to perform n similar and idempotent tasks so long as one processor remains active. The work of the algorithm is W = O(n + p·min{f + 1, log3 p}) and its message complexity is M = O(fpε + pmin{f + 1, log p}), for any ε > 0. This substantially improves the work complexity of previous solutions using simple point-to-point messaging, while "meeting or beating" the corresponding message complexity bounds. The new algorithms use communication graphs and permutations with certain combinatorial properties that are shown to exist. The algorithms are correct for any permutations, and in particular, the same expected bounds can be achieved using random permutations.

AB - This paper presents an efficient deterministic gossip algorithm for p synchronous, crash-prone, message-passing processors. The algorithm has time complexity T = O(log2 p) and message complexity M = O(p1+ε), for any ε > 0. This substantially improves the message complexity of the previous best algorithm that has M = O(p1.77), while maintaining the same time complexity. The strength of the new algorithm is demonstrated by constructing a deterministic algorithm for performing n tasks in this distributed setting. Previous solutions used coordinator or check-pointing approaches, immediately incurring a work penalty Ω(n + f·p) for f crashes, or relied on strong communication primitives, such as reliable broadcast, or had work too close to the trivial Θ(p·n) bound of oblivious algorithms. The new algorithm uses p crash-prone processors to perform n similar and idempotent tasks so long as one processor remains active. The work of the algorithm is W = O(n + p·min{f + 1, log3 p}) and its message complexity is M = O(fpε + pmin{f + 1, log p}), for any ε > 0. This substantially improves the work complexity of previous solutions using simple point-to-point messaging, while "meeting or beating" the corresponding message complexity bounds. The new algorithms use communication graphs and permutations with certain combinatorial properties that are shown to exist. The algorithms are correct for any permutations, and in particular, the same expected bounds can be achieved using random permutations.

UR - http://www.scopus.com/inward/record.url?scp=35248829130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248829130&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:35248829130

VL - 2848

SP - 224

EP - 238

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -