Question

A program run on a parallel machine is measured to have the following efficiency values for increasing numbers of processors, P.

P 1 2 3 4 5 6 7
E 100 90 85 80 70 60 50

Using the above results, plot the speedup graph.

Use the graph to explain whether or not the program has been successfully parallelized.

P E    Speedup
1 100% 1
2  90% 1.8
3  85% 2.55
4  80% 3.2
5  70% 3.5
6  60% 3.6
7  50% 3.5

This is a past year exam question, and I know how to calculate the speedup & plot the graph. However I don’t know how to tell a program is successfully parallelized.

Answer 1

Amdahl’s law

I think the idea here is that not all portion can be parallelized.

For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours (95%) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour. Hence the speedup is limited up to 20×

In this example, the speedup reached maximum 3.6 with 6 processors. So the parallel portion is about 1-1/3.6 is about 72.2%.