By Sanguthevar Rajasekaran

The power of parallel computing to procedure huge facts units and deal with time-consuming operations has led to unparalleled advances in organic and medical computing, modeling, and simulations. Exploring those contemporary advancements, the guide of Parallel Computing: types, Algorithms, and functions offers entire insurance on all features of this box.

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Extra resources for Handbook of Parallel Computing: Models, Algorithms and Applications (Chapman & Hall CRC Computer & Information Science Series)

Example text

Xn−1 ). Similarly, the sequential approach cannot update the variables of S properly: once x0 has received its new value, setting x1 disturbs x0 unpredictably. 4 Parallel Approach A parallel computer with n processors, by contrast, will measure all the variables x0 , x1 , . . , xn−1 simultaneously (one value per processor), and therefore obtain an accurate reading of the state of the system within the given time frame. Consequently, 1. A snapshot of the state of the system that satisfies G (x0 , x1 , .

It is clear in this case that S(i) = 2i−1 , for i ≥ 1. It follows that the total number of operations performed when executing all stages, from stage 1 up to and including stage i, is i 2j−1 = 2i − 1. j=1 It is interesting to note that while C(t ) is a linear function of the time variable t , the quantity S(i) grows exponentially with i − 1, where i is the number of stages executed so far. The effect of this behavior on the total number of operations performed is appreciated by considering the following example.

3. , oblivious to external circumstances), a stage (as required by an algorithm) is exactly the same thing as a step (as executed by a computer). In unconventional computing (the subject of this chapter), computational complexity is affected by its environment and is therefore variable. Under such conditions, one or more steps may be needed in order to execute a stage. 1 Examples of Increasing Functions C(t) Consider the following three cases in which the number of operations required to execute a computational stage increases with time.