Download Algorithms Sequential & Parallel: A Unified Approach by Russ Miller, Laurence Boxer PDF

By Russ Miller, Laurence Boxer

With multi-core processors exchanging conventional processors and the circulate to multiprocessor workstations and servers, parallel computing has moved from a area of expertise quarter to the middle of laptop technological know-how. as a way to offer effective and within your budget ideas to difficulties, algorithms needs to be designed for multiprocessor platforms. Algorithms Sequential and Parallel: A Unified procedure 2/E presents a state of the art method of an algorithms path. The booklet considers algorithms, paradigms, and the research of suggestions to severe difficulties for sequential and parallel types of computation in a unified style. this provides working towards engineers and scientists, undergraduates, and starting graduate scholars a history in algorithms for sequential and parallel algorithms inside one textual content. must haves contain basics of knowledge constructions, discrete arithmetic, and calculus.

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Algorithms Sequential & Parallel: A Unified Approach (Electrical and Computer Engineering Series)

With multi-core processors exchanging conventional processors and the stream to multiprocessor workstations and servers, parallel computing has moved from a distinctiveness sector to the center of desktop technological know-how. so one can supply effective and reasonably-priced ideas to difficulties, algorithms has to be designed for multiprocessor structures.

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Additional resources for Algorithms Sequential & Parallel: A Unified Approach (Electrical and Computer Engineering Series)

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In this case, the performance of A followed by B takes O(f (n) + g(n)) time. Note that this analysis holds for 6, <, o, and \, as well. 22 Chapter 1 Asymptotic Analysis • Next, suppose that each application of the body of a loop requires O(f (n)) time, and the loop executes its body O (g(n)) times. The time required to execute the loop (that is, all performances of its body) is O(f (n)g(n)). A similar property holds for 6, <, o, and \. EXAMPLE (INSERTIONSORT) As an example, we consider the analysis of InsertionSort, a simple sorting technique that is introduced in many first-semester computer science courses.

Roughly speaking (we’ll give a mathematically stronger argument next), we know from step 1 that P(1) is true, and thus by step 2 that P(1 + 1) = P(2) is true, P(2 + 1) = P(3) is true, P(3 + 1) = P(4) is true, and so forth. That is, step 2 allows us to induce the truth of P(n) for every positive integer n from the truth of P(1). The assumption in step 2 that P(k) = true is called the inductive hypothesis, because it is typically used to induce the conclusion that the successor statement P(k + 1) is true.

First, assume that n is a positive integer. For n = 1, the assertion simplifies to (Calculus example) Prove that d x = 1, dx which is true. Next, consider the inductive step. Suppose the assertion is true for some positive integer k. That is, the inductive hypothesis is the statement d k x = kx k 1 . dx Now, consider the case of n = k + 1. By exploiting the product rule of calculus and the inductive hypothesis, we have ( ) d k +1 d d x = xx k = 1x k + x x k = x k + xkx k 1 = ( k + 1)xx k , dx dx dx as desired.

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