Question

What is the parallel efficiency(Eff) of an algorithm? Where a task takes time T in uniprocessor system, P is number of processors, M is time taken by each processor.
(a) Eff = (T*P)/M
(b) Eff = T*(M/P)
(c) Eff = T/(P*M)
(d) Eff = T*P*M

Answer 1

The parallel efficiency (Eff) of an algorithm is defined as the overall ratio required to speed up the total number of processors working in that system.

On the other hand, speed up refers to the run time taken for an algorithm in order to execute the solution of any problem as compared with that of the parallel algorithm that could be used effectively to execute the given problem by taking the help of a total of P number of processors.

By following the above, the formula would be:

Eff= T X (M/P).

So, the second option i.e. "b" is correct here.

Answer 2

$\bold{E f f=\frac{T}{P \times M}}$ is the parallel efficiency(Eff) of an algorithm  

Option (c)  

Explanation:  

• Efficiency is determined as the speed-up ratio of the number of processing items.  
• Speedup is determined as the ratio of the time taken to resolve a question on a 'single processing' element to the time needed to solve the same problem on a 'parallel computer' with p similar processing elements.  
• The speedup we denote by the 'symbol' S. So, Efficiency formula is $\bold{E=\frac{S}{P}}$.  
• In our case $\bold{Efficiency=\frac{T}{P \times M}}$

To know more

What is the parallel efficiency(Eff) of an algorithm? Where a task takes time T in uniprocessor system, P is number of processors, M is time taken by each processor.

(a) Eff = (T*P)/M

(b) Eff = T*(M/P)

(c) Eff = T/(P*M)

(d) Eff = T*P*M

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