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Although the present study showed a speeding up and a slowing down for valid and invalid exogenous cues, respectively, it is important to note that the relative speeding up and slowing down for valid and invalid exogenous cues can only be perceived in relationship to each other.
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In further studies the authors would like to show relative speed-ups and trade-offs in parallelizing this step of the algorithm.
In contrast, the relative speed-up for the synchronous algorithm is low for 50 processors, while the relative speed-up remains high for the asynchronous algorithm.
The absolute speed-up is not as striking as the relative speed-up, but it is also a far more stringent measure of algorithm efficiency.
We can thus calculate the theoretical limits of the algorithm's relative speed-up by dividing the speed of the serial algorithm by the number of islands Nisl.
That the relative speed-up is high for the synchronous algorithm is a direct result of the highly (almost embarrassingly) parallel nature of the serial algorithm, and the asynchronous algorithm improves on this even further to give a nearly perfect relative speed-up for up to 50 processors.
We estimated 95% confidence intervals on absolute and relative speed-up using Fieller's theorem [ 37] for confidence intervals on ratios of Gaussians.
The relative speed-up for both parallel implementations is close to perfect for 10 and 20 processors, and the efficiency of the two algorithms is largely indistinguishable.
The relative speed-up is defined as (11) and represents a measure of the efficiency of the parallelisation in terms of communication overhead (if the relative speed-up is equal to the number of processors, then the algorithm does not loose speed due to communication overhead).
As expected, the absolute speed-up is generally lower than the relative speed-up: these two measures increasingly diverge as the number of processors increases, reflecting the negative effect of adding islands beyond the optimum.
Note that this is a much more stringent definition of parallel efficiency than the relative speed-up (which is the value more often given for parallel algorithms), but it is also the measure most often required for practical decision making, as it puts a value on exactly how much extra speed will be gained by moving to a parallel algorithm, assuming you are using an optimal serial algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com