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Algorithms and Parallel Computing by Fayez Gebali

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1.8 MEASURING BENEFITS OF PARALLEL COMPUTING

We review in this section some of the important results and benefits of using parallel computing. But first, we identify some of the key parameters that we will be studying in this section.

1.8.1 Speedup Factor

The potential benefit of parallel computing is typically measured by the time it takes to complete a task on a single processor versus the time it takes to complete the same task on N parallel processors. The speedup S(N) due to the use of N parallel processors is defined by

(1.6) c01e006

where Tp(1) is the algorithm processing time on a single processor and Tp(N) is the processing time on the parallel processors. In an ideal situation, for a fully parallelizable algorithm, and when the communication time between processors and memory is neglected, we have Tp (N) = Tp (1)/N, and the above equation gives

(1.7) c01e007

It is rare indeed to get this linear increase in computation domain due to several factors, as we shall see in the book.

1.8.2 Communication Overhead

For single and parallel computing systems, there is always the need to read data from memory and to write back the results of the computations. Communication with the memory takes time due to the speed mismatch between the processor and the memory [14]. Moreover, for parallel computing ...

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