Devise a parallel algorithm to solve the primality problem for the positive integer n. At the end of the algorithm, every processor should know whether or not n is prime. Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume that no list of primes is initially stored in memory. Assuming [n"² ] processors, provide an analysis of the number of parallel operations used by your algorithm on the following. a. CREW PRAM b. EREW PRAM c. Mesh d. Hypercube

Devise a parallel algorithm to solve the primality problem for the positive integer n. At the end of the algorithm, every processor should know whether or not n is prime. Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume that no list of primes is initially stored in memory. Assuming [n"² ] processors, provide an analysis of the number of parallel operations used by your algorithm on the following. a. CREW PRAM b. EREW PRAM c. Mesh d. Hypercube

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Make or invent a parallel algorithm to solve the primality problem for the positive integer n.At the end of the algorithm, every processor should know whether or not n is prime.Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume that no list of primes is initially stored in memory. Assuming [n1/2] processors, provide an analysis of the number of parallel operations used by your algorithm on the following. CREW PRAM EREW PRAM Mesh Hypercube
A) In pseudocode, implement and explain the time complexity analysis of the quicksort algorithm, detailing the best-case, worst-case, and average-case scenarios. Additionally, discuss the factors that influence these scenarios and how they impact the overall efficiency of the algorithm. B) In pseudocode, implement and explain the time complexity analysis of the merge sort algorithm, detailing the best-case, worst-case, and average-case scenarios. Additionally, discuss the factors that influence these scenarios and how they impact the overall efficiency of the algorithm.
Please answer questions A-D
Make or invent a parallel algorithm to solve the primality problem for the positive integer n.At the end of the algorithm, every processor should know whether or not n is prime.Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume that no list of primes is initially stored in memory. Assuming [n1/2] processors, provide an analysis of the number of parallel operations used by your algorithm on the following. CREW PRAM EREW PRAM Mesh Hypercube
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Write pseudo code for it & what conditions) what else should change in Semigroup computation on a PRAM algorithm? to avoid the final broadcasting phase which essentially doubles the execution time of the semigroup computation algorithm in the EREW PRAM, it has been suggested that we replace the indices j + s in the algorithm with j + s mod p (i.e., allow the computations to wrap around). And under what conditions would this method yield correct results in all processors? (Write pseudo code for it)
make python implement parallel matrix multiplication by row-partitioning using theProcess object of multiprocessing module. The input matrices A and B are small3×3 matrices and each of 3 processes receives its row and matrix B from the masterprocess, multiplies its row with matrix B to form the row of product matrix C. Aworker then sends its associated row of matrixC to the master.We need to consider thefollowing for this algorithm: when a process is spawned using the Process module,it has all of the data of the parent process but the modifications it makes are notreflected in the parent process. In order to have the product matrix C shared betweenthe processes, we need to use the Manager object of the multiprocessing module anddefine C as an array to be shared from this object. Each worker process performsmultiplication and stores the result in its row entry of matrix C.
(b) Consider the two sorting algorithms below, which each take as input array A] indexed from s to f. SwapSort2(A, s, f) SwapSort1(A, s, f) swapped = true while (swapped) swapped = false for i = s to f-2 swapped = true while (swapped) swapped = false for i = s to f-2 if A[i] > A[i+2] Swap A[i] and A[i+2] swapped = true if A[i] > Ali+2] Swap A[i] and A[i+2] swapped = true swapped = true while (swapped) swapped = false for i = s to f-1 if A[i] > A[i+1] Swap A[i] and A[i+1] swapped = true • Execute SwapSort1 on array A = [7,6, 5, 4, 3, 2, 1] indexed from s = 1 to f = 7. • Which of the above two algorithms is correct?. Justify your answer. • What is the worst-case number of comparisons are made by SwapSort2 when the input array A has length n and is sorted in reverse order? • Does your result from above represent the worst-case number of comparisons made by SwapSort2? Justify your answer. • Justify that the worst-case runtime of SwapSort2 is of the form T(n) a, b, c. = an? + bn +c for…
Three major steps of a divide-and-conquer algorithm are: • Divide the problem in to two or more parts. • Solve each part separately. • Combine the partial solution. In the Quicksort algorithm, which of these steps represent most of the work. Please explain
What is the best case scenario? What is the exact number of operations for the best case scenario in terms of n and m? What is the big-oh for the best case scenario? What is the worst case scenario? What is the exact number of operations for the worst case scenario in terms of n and m? What is the big-oh for the worst case scenario? Consider the following algorithm tha finds a row where every entry is x in a 2-D array. Assume that (a) the array has n rows and m columns, and that (b) the comparison on line 3 counts towards the running time.