When parallelizing an application, the ideal speedup is speeding up by the number of processors. This is limited by two things: percentage of the application that can be parallelized and the cost of communication. Amdahl’s law takes into account the former but not the latter.

a. What is the speedup with N processors if 80% of the application is parallelizable, ignoring the cost of communication?

b. What is the speedup with 8 processors if, for every processor added, the communication overhead is 0.5% of the original execution time.

c. What is the speedup with 8 processors if, for every time the number of processors is doubled, the communication overhead is increased by 0.5% of the original execution time?

d. What is the speedup with N processors if, for every time the number of processors is doubled, the communication overhead is increased by 0.5% of the original execution time?

e. Write the general equation that solves this question: What is the number of processors with the highest speedup in an application in which P% of the original execution time is parallelizable, and, for every time the number of processors is doubled, the communication is increased by 0.5% of the original execution time?