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<p>Scalability has become an important consideration in parallel algorithm and machinedesigns. The word scalable, or scalability, has been widely and often used in the parallelprocessing community. However, there is no adequate, commonly accepted definition ofscalability available. Scalabilities of computer systems and programs are difficult toquantify, evaluate, and compare. In this paper, scalability is formally defined foralgorithm-machine combinations. A practical method is proposed to provide a quantitative measurement of the scalability. The relation between the newly proposed scalability and other existing parallel performance metrics is studied. A harmony between speedup and scalability has been observed. Theoretical results show that a large class ofalgorithm-machine combinations is scalable and the scalability can be predicted throughpremeasured machine parameters. Two algorithms have been studied on an nCUBE 2multicomputer and on a MasPar MP-1 computer. These case studies have shown howscalabilities can be measured, computed, and predicted. Performance instrumentation andvisualization tools also have been used and developed to understand the scalabilityrelated behavior.</p>
Index Termsparallel algorithms; parallel machines; performance evaluation; software metrics; parallelalgorithm; scalability; algorithm-machine combinations; parallel machine; quantitativemeasurement; parallel performance metrics; nCUBE 2; MasPar MP-1; case studies

X. Sun and D. Rover, "Scalability of Parallel Algorithm-Machine Combinations," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 599-613, 1994.
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