By Lydia Kronsjö

This ebook provides a compact but entire survey of significant ends up in the computational complexity of sequential algorithms. this can be by way of a hugely informative advent to the advance of parallel algorithms, with the emphasis on non-numerical algorithms. the cloth is so chosen that the reader in lots of circumstances is ready to stick to an analogous challenge for which either sequential and parallel algorithms are mentioned - the simultaneous presentation of sequential and parallel algorithms for fixing permitting the reader to recognize their universal and detailed beneficial properties.

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**Computational Complexity of Sequential and Parallel Algorithms **

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**Extra resources for Computational Complexity of Sequential and Parallel Algorithms **

**Example text**

Solving in terms of λ, we obtain Using the fact that we obtain a quadratic equation in λ, with two real roots. The root leads to so that the point is one candidate for the maximum. The other root, , leads to another candidate, b = −a. Since ∇g ≠ 0 everywhere on the constraint set g = 3, a and b are the only two candidates for the maximum.

Use the five-step method, and model as a one-variable optimization problem. (b) Examine the sensitivity to the growth rate of the pig. Consider both the best time to sell and the resulting profit rate. (c) Examine the sensitivity to the rate at which the price for pigs is dropping. Consider both the best time to sell and the resulting profit rate. 1, but now take into account the fact that the growth rate of the pig decreases as the pig gets older. Assume that the pig will be fully grown in another five months.

We write Let y = P be the quantity we wish to maximize and x = t the independent variable. 1) over the set S = {x : x ≥ 0}. Step 4 is to solve the model, using the standard solution procedure identified in step 2. In our example we want to find the maximum of the function y = f(x) defined by Eq. 1) over the set x ≥ 0. 2 shows a graph of the function f (x). Since f is quadratic in x, the graph is a parabola. 45x versus time to sell x for the pig problem. so that f′(x) = 0 at the point x = 8. Since f is increasing on the interval (−∞, 8) and decreasing on (8, ∞), the point x = 8 is the global maximum.