Doing-it-All with bounded work and communication

Bogdan S. Chlebus, Leszek Gąsieniec, Dariusz R. Kowalski, Alexander A. Schwarzmann

Research output: Contribution to journalArticle

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+plog⁡p(plog⁡p+tlog⁡t)) and a nonconstructive algorithm that has work O(t+plog2⁡p). The latter result is close to the lower bound Ω(t+plog⁡p/log⁡log⁡p) 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).

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalInformation and Computation
Volume254
DOIs
StatePublished - Jun 1 2017

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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

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