NDLI: Work-Competitive Scheduling for Cooperative Computing with Dynamic Groups

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Work-Competitive Scheduling for Cooperative Computing with Dynamic Groups

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Georgiou, Chryssis Russell, Alexander Shvartsman, Alexander A.
Copyright Year	2005
Abstract	The problem of cooperatively performing a set of t tasks in a decentralized computing environment subject to failures is one of the fundamental problems in distributed computing. The setting with partitionable networks is especially challenging, as algorithmic solutions must accommodate the possibility that groups of processors become disconnected (and, perhaps, reconnected) during the computation. The efficiency of task-performing algorithms is often assessed in terms of work: the total number of tasks, counting multiplicities, performed by all of the processors during the computation. In general, the scenario where the processors are partitioned into g disconnected components causes any task-performing algorithm to have work $\Omega(t\cdot g)$ even if each group of processors performs no more than the optimal number of $\Theta(t)$ tasks. Given that such pessimistic lower bounds apply to any scheduling algorithm, we pursue a competitive analysis. Specifically, this paper studies a simple randomized scheduling algorithm for p asynchronous processors, connected by a dynamically changing communication medium, to complete t known tasks. The performance of this algorithm is compared against that of an omniscient off-line algorithm with full knowledge of the future changes in the communication medium. The paper describes a notion of computation width, which associates a natural number with a history of changes in the communication medium, and shows both upper and lower bounds on work-competitiveness in terms of this quantity. Specifically, it is shown that the simple randomized algorithm obtains the competitive ratio $(1+\mathbf{cw}/e)$, where $\mathbf{cw}$ is the computation width and e is the base of the natural logarithm ($e=2.7182\ldots$); this competitive ratio is then shown to be tight.
Starting Page	848
Ending Page	862
Page Count	15
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539704440442
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity partitionable networks independent tasks randomized algorithms on-line algorithms distributed computation Randomized algorithms work complexity Models and methods for concurrent and distributed computing Analysis of algorithms Distributed algorithms competitive analysis
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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