According to Amdahl’s law, as the number of parallel processors increases, what does the execution time approach?
Select one: a. The execution time of the parallel fraction of the code b. The execution time of the sequential fraction of the code c. The execution time of the parallel portion of the code divided by the speedup d. The execution time of the sequential portion of the code divided by the speedup
The correct answer and explanation is:
The correct answer is b. The execution time of the sequential fraction of the code.
Explanation:
Amdahl’s Law is a formula that helps us understand the maximum improvement in execution time that can be achieved when a portion of the code is parallelized, while the rest remains sequential. The law is particularly useful for analyzing the limitations of parallel computing, especially when the non-parallelizable portion of the program becomes a bottleneck.
Amdahl’s Law is given by the following formula: S=1(1−p)+pnS = \frac{1}{(1 – p) + \frac{p}{n}}
Where:
- SS is the speedup,
- pp is the fraction of the program that can be parallelized,
- nn is the number of processors.
This law essentially states that as the number of processors increases, the speedup of the program is limited by the fraction that cannot be parallelized (denoted by 1−p1 – p).
Now, when we look at the execution time as the number of processors approaches infinity, Amdahl’s Law tells us that the execution time will tend to the execution time of the sequential fraction of the code, because the parallel fraction can be infinitely sped up, but the sequential portion remains unaffected.
For example, if 90% of a program can be parallelized and 10% cannot, no matter how many processors you use, the sequential 10% will always determine the lower bound on performance. This means that even with an infinite number of processors, the execution time will never go below the execution time of the sequential portion.
Thus, Amdahl’s Law highlights the diminishing returns of adding more processors when there is a significant sequential portion in the code. In summary, as the number of parallel processors increases, the execution time of the sequential fraction of the code dominates the overall execution time.