### Abstract

We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of workcomplexity and communication complexity. When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work O(t+plogp(plogp+tlogt)) and a nonconstructive algorithm that has work O(t+plog^{2}p). The latter result is close to the lower bound Ω(t+plogp/loglogp) on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by c p, for some positive constant c<1. We also present a nonconstructive algorithm that has effort O(t+p^{1.77}).

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

Pages (from-to) | 1-40 |

Number of pages | 40 |

Journal | Information and Computation |

Volume | 254 |

DOIs | |

State | Published - Jun 1 2017 |

Externally published | Yes |

### Fingerprint

### Keywords

- Crash failures
- Distributed algorithm
- Load balancing
- Message passing
- Ramanujan graphs
- Scheduling tasks

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Information and Computation*,

*254*, 1-40. https://doi.org/10.1016/j.ic.2017.02.003

**Doing-it-All with bounded work and communication.** / Chlebus, Bogdan S.; Gąsieniec, Leszek; Kowalski, Dariusz R.; Schwarzmann, Alexander Allister.

Research output: Contribution to journal › Article

*Information and Computation*, vol. 254, pp. 1-40. https://doi.org/10.1016/j.ic.2017.02.003

}

TY - JOUR

T1 - Doing-it-All with bounded work and communication

AU - Chlebus, Bogdan S.

AU - Gąsieniec, Leszek

AU - Kowalski, Dariusz R.

AU - Schwarzmann, Alexander Allister

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of workcomplexity and communication complexity. When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work O(t+plogp(plogp+tlogt)) and a nonconstructive algorithm that has work O(t+plog2p). The latter result is close to the lower bound Ω(t+plogp/loglogp) on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by c p, for some positive constant c<1. We also present a nonconstructive algorithm that has effort O(t+p1.77).

AB - We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of workcomplexity and communication complexity. When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work O(t+plogp(plogp+tlogt)) and a nonconstructive algorithm that has work O(t+plog2p). The latter result is close to the lower bound Ω(t+plogp/loglogp) on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by c p, for some positive constant c<1. We also present a nonconstructive algorithm that has effort O(t+p1.77).

KW - Crash failures

KW - Distributed algorithm

KW - Load balancing

KW - Message passing

KW - Ramanujan graphs

KW - Scheduling tasks

UR - http://www.scopus.com/inward/record.url?scp=85018414006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018414006&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2017.02.003

DO - 10.1016/j.ic.2017.02.003

M3 - Article

AN - SCOPUS:85018414006

VL - 254

SP - 1

EP - 40

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

ER -