### Abstract

We consider the Do-All problem: p failure-prone processors perform t similar and independent tasks. We assume that processors are synchronous, communicate by message passing, and are subject to crashes determined by an adaptive adversary restricted only by the upper bound f on the number of crashes. The performance of algorithms in this setting is normally measured in terms of work (total available processor steps) and communication (total number of point-to-point messages) complexity. We consider work and communication as comparable resources and we develop algorithms that have efficient effort defined as work + communication. We present a p-processor, t-task algorithm that has effort O(t+p^{1.77}), against the unbounded adversary (f < p). This is the first algorithm that achieves subquadratic in p effort efficiency for unbounded adversary, or even for linearly-bounded adversary that crashes up to a constant fraction of the processors.We present another algorithm that has work O(t + p log^{2} p) against f-bounded adversaries such that p−f = Ω(p^{b}) for a constant b, 0 < b < 1. We show how to achieve effort O(t + p log^{2} p) against a linearly-bounded adversary; this result is close to lower bound Ω(t + p log p/ log log p).

Original language | English (US) |
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Title of host publication | Distributed Computing - 16th International Conference, DISC 2002, Proceedings |

Editors | Dahlia Malkhi |

Publisher | Springer Verlag |

Pages | 295-310 |

Number of pages | 16 |

ISBN (Print) | 3540000739, 9783540000730 |

State | Published - Jan 1 2002 |

Externally published | Yes |

Event | 16th International Conference on Distributed Computing, DISC 2002 - Toulouse, France Duration: Oct 28 2002 → Oct 30 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2508 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th International Conference on Distributed Computing, DISC 2002 |
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Country | France |

City | Toulouse |

Period | 10/28/02 → 10/30/02 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Computing - 16th International Conference, DISC 2002, Proceedings*(pp. 295-310). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2508). Springer Verlag.