Work-Competitive Scheduling for Cooperative Computing with Dynamic Groups

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 possibil...

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Veröffentlicht in:SIAM journal on computing Jg. 34; H. 4; S. 848 - 862
Hauptverfasser: Georgiou, Chryssis, Russell, Alexander, Shvartsman, Alexander A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2005
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Communication
Competition
Computer science
Computer science; control theory; systems
Computer systems performance. Reliability
Distributed processing
Exact sciences and technology
Knowledge
Scheduling
Software
Theoretical computing
68W20
Lower bound
68Q25
68W40
Task complexity
partitionable networks
independent tasks
Competitiveness
on-line algorithms
distributed computation
Scheduling
Independent task
Computing
Distributed computing
Competitive algorithms
Upper bound
Partitioning
Algorithm performance
Multiplicity
randomized algorithms
work complexity 68W15
Counting
68Q85
competitive analysis
ISSN:0097-5397, 1095-7111
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539704440442