By Russ Miller, Laurence Boxer
With multi-core processors changing conventional processors and the circulation to multiprocessor workstations and servers, parallel computing has moved from a forte region to the middle of desktop technology. so that it will supply effective and competitively priced options to difficulties, algorithms needs to be designed for multiprocessor platforms. Algorithms Sequential and Parallel: A Unified process 2/E presents a cutting-edge method of an algorithms path. The e-book considers algorithms, paradigms, and the research of suggestions to severe difficulties for sequential and parallel versions of computation in a unified model. this provides working towards engineers and scientists, undergraduates, and starting graduate scholars a historical past in algorithms for sequential and parallel algorithms inside of one textual content. necessities comprise basics of knowledge constructions, discrete arithmetic, and calculus.
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Extra resources for Algorithms Sequential & Parallel: A Unified Approach (Electrical and Computer Engineering Series)
H(n) h(n) h(1) h(1) 1 2 ... n 01 ... 8 ¨ h(i) by the integral of i=1 the nondecreasing function h(t). On the left, we demonstrate how to use the integral µ n +1 1 h( t )dt to derive an upper bound on the summation by aligning the recn tangles to the right. Notice that to use the integral µ n 0 µ 0 n h(t)dt f ¨ h(i) f µ i=1 h(t)dt . On the right, we show how h(t)dt to derive a lower bound on the summation by align- n +1 1 1 i=1 ing the rectangles to the left. Notice that n n +1 ¨ h(i) f µ µ n 0 n h(t)dt f ¨ h(i) .
EXAMPLE Let f ( n) = n( n + 1) 2 and g(n) = n2. Then we can show that f (n) = 6(g(n)) because lim nqh f ( n) n2 + n = lim = g ( n) nqh 2 n2 (dividing both numerator and denominator by n2) 1 n = 1. lim nqh 2 2 1+ Asymptotic Relationships 13 EXAMPLE If P(n) is a polynomial of degree d, then P(n) = 6(nd ). The proof is left to the reader as an exercise. EXAMPLE Compare n100 and 2 n . We remind the reader of a useful result. d f (x) e = e f ( x ) f '( x ). dx We have n 2n eln 2 e n ln 2 lim 100 = lim 100 = lim 1000 .
10. Array implementations of both InsertionSort and SelectionSort have 6(n2) worst case running times. Which is likely to be faster if we time both in the same hardware/software environment for the same input data? Why? 2 Induction and Recursion Mathematical Induction Induction Examples Recursion Binary Search Merging and MergeSort Summary Chapter Notes Exercises 34 n this chapter, we present some fundamental mathematical techniques that are used throughout the book. Many of these techniques, including recursion and mathematical induction, are taught in courses such as calculus and discrete mathematics.