What does “Amdahl’s Law” describe in the context of parallel processing?

Correct option is A

Amdahl’s Law describes the theoretical maximum speedup of a program when a portion of its execution can be parallelized while another portion remains serial. It shows that the overall performance improvement is limited by the part of the program that cannot be parallelized, regardless of how many processors are added. If P is the fraction of execution time that can be parallelized and N is the number of processors, the speedup is given by $$\frac{1}{(1-P)+P/N}$$​. As N approaches infinity, the parallel portion approaches zero execution time, but the serial portion remains.
Information Booster
1. Amdahl’s Law Formula
​$$\boxed{S(N)=\frac{1}{(1-P)+\frac{P}{N}}}$$​​
where:
· S(N) = speedup using N processors.
· P = fraction of the program that can be parallelized.
· 1 − P = serial fraction.
· N = number of processors.
2. Theoretical Maximum Speedup
· When the number of processors approaches infinity:
​$$\lim_{N\rightarrow\infty}S(N)=\frac{1}{1-P}$$​​
· Thus, even with unlimited processors, the serial fraction places an upper bound on speedup.
3. Example
· Suppose 80% of a program is parallelizable: P = 0.8
· The maximum theoretical speedup is:
​$$S_{\max}=\frac{1}{1-0.8}=5$$​​
· Therefore, unlimited processors cannot provide more than 5× speedup under the assumptions of the basic law.
4. Effect of Increasing Processors
· Increasing the processor count improves the execution time of the parallel portion.
· However, the benefit becomes progressively smaller when the serial portion dominates.
· Therefore, simply adding more processors does not guarantee proportional performance improvement.
5. Significance in Parallel Processing
· Amdahl’s Law helps evaluate the potential benefit of parallelization before investing in additional processing resources.
· It emphasizes the importance of reducing the serial bottleneck of a program.
· It is particularly useful for understanding why parallel systems often exhibit sub-linear speedup.
Additional Knowledge
· Option (b) is incorrect: Message-passing efficiency concerns communication between processes in distributed-memory systems. It is not the primary subject of Amdahl’s Law.
· Option (c) is incorrect: Computational efficiency is a broader measure involving factors such as speedup and processor utilization. Amdahl’s Law specifically focuses on the speedup limitation caused by the serial portion.
· Option (d) is incorrect: Fault tolerance deals with maintaining system operation despite component or process failures. Reliability is not what Amdahl’s Law models.
· Important distinction: Amdahl’s Law → Fixed-size problem → Limits speedup due to serial portion.
· Related concept — Gustafson’s Law: While Amdahl’s Law emphasizes the limitation imposed by the serial fraction for a fixed workload, Gustafson’s Law considers how larger problem sizes can make parallel computing more beneficial as the number of processors increases.
· Exam trap: Amdahl’s Law does not mean that speedup is always exactly equal to the number of processors. The serial portion, and in practical systems additional overheads such as communication and synchronization, prevent ideal linear speedup.