Doing-it-All with Bounded Work and Communication

• Published in: arXiv.org
• Main Authors: Chlebus, Bogdan S, Gąsieniec, Leszek, Kowalski, Dariusz R, Schwarzmann, Alexander A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 19.07.2018
• Subjects: Algorithms; Communication; Complexity; Computer Science - Distributed, Parallel, and Cluster Computing; Crashes; Lower bounds; Message passing; Microprocessors; Processors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1409.4711

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 work complexity (also known as total available processor steps) and communication complexity (total number of point-to-point messages). 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 \(O( t + p \log p\, (\sqrt{p\log p}+\sqrt{t\log t}\, ) )\) and a nonconstructive algorithm that has work \(O(t +p \log^2 p)\). The latter result is close to the lower bound \(\Omega(t + p \log p/ \log \log p)\) 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 \(O(t + p ^{1.77})\).