If we simultaneously execute two algorithms and only take into account their best run time, we will have a performance of a new algorithm that we call the parallel algorithm, or just PA for short. Here, we can imagine that we have two independent machines or processors with multiple cores or threads, each runs an algorithm, and we only take the better result.
Moreover, if we consider that this parallel algorithm raises an exception only when both algorithms fail, then its number of exceptions should also always be lower.
We consider the parallel algorithm for two algorithms A and B on a set of three tests as an example to illustrate this idea: the first test, both A and B fail; A fails the second test and B fails the third. So the parallel algorithm only counts one exception, with the first test, whereas A and B each counts two exceptions. Obviously, we can also define a parallel algorithm for more than two algorithms.