By Russ Miller, Laurence Boxer

With multi-core processors changing conventional processors and the move to multiprocessor workstations and servers, parallel computing has moved from a area of expertise region to the middle of desktop technology. on the way to offer effective and cost-efficient ideas to difficulties, algorithms needs to be designed for multiprocessor structures. Algorithms Sequential and Parallel: A Unified procedure 2/E offers a state of the art method of an algorithms path. The ebook considers algorithms, paradigms, and the research of ideas to severe difficulties for sequential and parallel versions of computation in a unified type. this provides practising engineers and scientists, undergraduates, and starting graduate scholars a history in algorithms for sequential and parallel algorithms inside of one textual content. must haves contain basics of information buildings, discrete arithmetic, and calculus.

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**Example text**

We now continue with an example that uses logarithms. 14 Chapter 1 Asymptotic Analysis EXAMPLE Let f (n) = ln n and g(n) = n. Then, by applying L’Hopital’s Rule, we have lim nqh n 1 = lim , n qh ln n 1/ n which evaluates as lim nqh 1 = lim n = h. 1 / n nqh Therefore, ln n = O (n). We remind the reader that log b x = (log b a)(log a x), for positive a, b, and x with a | 1 | b . Therefore, because log b a is a constant, log b x = 6(log a x). That is, the base of a logarithm is irrelevant inside asymptotic notation, except that we assume a, b > 1 (so that the logarithms are positive, because we generally have x > 1 in such contexts).

B) What is the worst-case running time for a generic instance of the Insert step? c) Show that the algorithm has a worst-case running time of 6(n2). d) Although both the array-based and linked-list-based implementations of InsertionSort have worst case running times of 6(n2), in practice, we usually find that the linked-list-based implementation (assuming the same data, in the same input order) is faster. Why should this be? ) 10. Array implementations of both InsertionSort and SelectionSort have 6(n2) worst case running times.

Some of these are considerably faster than others. Yet, sometimes the asymptotically slower algorithms are useful because, for example, they may be very fast on relatively small data sets or they may be very fast on sets of data that exhibit certain characteristics. We will present several sorting algorithms in this book and examine such issues. In the previous section, we presented an analysis of InsertionSort. In one of the exercises at the end of this chapter, we present SelectionSort, a fairly straightforward, useful sorting routine that exhibits the same worst case 6(n2) running time as InsertionSort.