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Question 10: Finding the sum of 16 numbers can be represented by the binary-tree computation graph of Figure 2 mentioned bellow with T(1) = W(1) = 15. Assume unit-time additions and ignore all else. Sum Figure 2: Computation graph for finding the sum of 16 numbers. 16 numbers to be added Suppose, we have total number of processors, p=8. And essentially, the 8 processors perform all of the additions at the same tree level in each time unit, beginning with the leaf nodes and ending at the root. The relatively low efficiency is the result of limited parallelism near the root of the tree. a) Now redraw the Figure 2 for the following conditions: Assuming that addition operations that are vertically aligned in Figure 2 are to be performed by the same processor and that each inter-processor transfer, represented by an oblique arrow, also requires one unit of work (time), the number of processors are same as p = 8. i. W(p) ii. T(p) iii. S(p) iv. E(p) b) Applying the formulas or rules of the effectiveness of parallel processing, algorithm, and architecture define the following, where, p=Number of processors. v. R(p) vi. U(p) vii. Q(p) Work performed by p processors Execution time with p processors, where T(1) = W(1); T(p) ≤W(p) Speedup Efficiency Redundancy Utilization, and Quality

Question 10: Finding the sum of 16 numbers can be represented by the binary-tree computation graph of Figure 2 mentioned bellow with T(1) = W(1) = 15. Assume unit-time additions and ignore all else. Sum Figure 2: Computation graph for finding the sum of 16 numbers. 16 numbers to be added Suppose, we have total number of processors, p=8. And essentially, the 8 processors perform all of the additions at the same tree level in each time unit, beginning with the leaf nodes and ending at the root. The relatively low efficiency is the result of limited parallelism near the root of the tree. a) Now redraw the Figure 2 for the following conditions: Assuming that addition operations that are vertically aligned in Figure 2 are to be performed by the same processor and that each inter-processor transfer, represented by an oblique arrow, also requires one unit of work (time), the number of processors are same as p = 8. i. W(p) ii. T(p) iii. S(p) iv. E(p) b) Applying the formulas or rules of the effectiveness of parallel processing, algorithm, and architecture define the following, where, p=Number of processors. v. R(p) vi. U(p) vii. Q(p) Work performed by p processors Execution time with p processors, where T(1) = W(1); T(p) ≤W(p) Speedup Efficiency Redundancy Utilization, and Quality

Database System Concepts
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
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Question 10: Finding the sum of 16 numbers can be represented by the binary-tree computation graph of Figure 2 mentioned bellow with T(1) = W(1) = 15. Assume unit-time additions and ignore all else. On Sum 16 numbers to be added Figure 2: Computation graph for finding the sum of 16 numbers. i. W(p) ii. T(p) iii. S(p) iv. E(p) + Suppose, we have total number of processors, p=8. And essentially, the 8 processors perform all of the additions at the same tree level in each time unit, beginning with the leaf nodes and ending at the root. The relatively low efficiency is the result of limited parallelism near the root of the tree. v. R(p) vi. U(p) vii. Q(p) a) Now redraw the Figure 2 for the following conditions: Assuming that addition operations that are vertically aligned in Figure 2 are to be performed by the same processor and that each inter-processor transfer, represented by an oblique arrow, also requires one unit of work (time), the number of processors are same as p = 8. b) Applying the formulas or rules of the effectiveness of parallel processing, algorithm, and architecture define the following, where, p=Number of processors. Efficiency Redundancy Utilization, and Quality Work performed by p processors Execution time with p processors, where T(1) = W(1); T(p) ≤W(p) Speedup
Transcribed Image Text:Question 10: Finding the sum of 16 numbers can be represented by the binary-tree computation graph of Figure 2 mentioned bellow with T(1) = W(1) = 15. Assume unit-time additions and ignore all else. On Sum 16 numbers to be added Figure 2: Computation graph for finding the sum of 16 numbers. i. W(p) ii. T(p) iii. S(p) iv. E(p) + Suppose, we have total number of processors, p=8. And essentially, the 8 processors perform all of the additions at the same tree level in each time unit, beginning with the leaf nodes and ending at the root. The relatively low efficiency is the result of limited parallelism near the root of the tree. v. R(p) vi. U(p) vii. Q(p) a) Now redraw the Figure 2 for the following conditions: Assuming that addition operations that are vertically aligned in Figure 2 are to be performed by the same processor and that each inter-processor transfer, represented by an oblique arrow, also requires one unit of work (time), the number of processors are same as p = 8. b) Applying the formulas or rules of the effectiveness of parallel processing, algorithm, and architecture define the following, where, p=Number of processors. Efficiency Redundancy Utilization, and Quality Work performed by p processors Execution time with p processors, where T(1) = W(1); T(p) ≤W(p) Speedup
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