The speedup is the measure that displays the benefit of solving a problem in parallel. It is defined as the ratio of the time taken to solve a problem on a single processing element (Ts) to the time required to solve the same problem on p identical processing elements (Tp).

We denote speedup as follows:

We have a linear speedup, where if S=p, then it means that the speed of execution increases with the number of processors. Of course, this is an ideal case. While the speedup is absolute when Ts is the execution time of the best sequential algorithm, the speedup is relative when Ts is the execution time of the parallel algorithm for a single processor.

Let's recap these conditions:

• S = p is a linear or ideal speedup.
• S < p is a real speedup.
• S > p is a superlinear speedup.