Speed up - metrics for performance evaluation, Computer Engineering

Assignment Help:

Q. Speed Up - metrics for performance evaluation?

Speed up is ratio of time needed to execute a given program employing a specific algorithm on a machine with single processor (It implies that T (1) (where n=1)) to time needed to execute same program using a particular algorithm on a machine with multiple processors (It implies that T (n)). Fundamentally speed up factor helps us in knowing relative gain achieved in shifting from a sequential machine to a parallel computer. It can be noted the term T(1) denotes amount of time taken to execute a program employing the best sequential algorithm It implies that the algorithm with least time complexity. 

2366_Speed Up - metrics for performance evaluation.png

Let's take an illustration and explain practical use of speedup. Suppose we have a problem of multiplying n numbers. Time complexity of sequential algorithm for a machine with single processor is O(n) because we require one loop for reading and computing output. But in the parallel computer let every number is assigned to specific processor and computation model being used being a hypercube. In such a condition the total number of steps essential to compute result is log n it implies that time complexity is O(log n). Figure below explains the steps to be followed for achieving the required output in a parallel hypercube computer model.

As number of steps followed is equivalent to 3 it implies that log 8 where n is number of processors. Therefore complexity is O(log n). 

In view of fact sequential algorithm takes 8 steps whereas above mentioned parallel algorithm takes 3 steps speed up is as under:

1715_Speed Up - metrics for performance evaluation1.png

Because value of S(n) is inversely proportional to time needed to calculate output on a parallel number that in turn is dependent on number of processors used for performing the computation. The relation amid S(n) versus Number of processors is displayed in Figure. The speedup is directly proportional to number of processors so a linear arc is portrayed. But in situations where there is parallel overhead the arc is sub-linear.

716_Speed Up - metrics for performance evaluation3.png

Figure: Steps followed for multiplying n numbers stored on n processors

295_Speed Up - metrics for performance evaluation2.png

Figure: Speed-up vs. Number of Processors


Related Discussions:- Speed up - metrics for performance evaluation

Ending transactions - data phase, Ending transactions: Either side may...

Ending transactions: Either side may request that a burst end after the present data phase. Simple PCI component that do not support multi-word bursts will always request this

2 way staircase switch-truth table logic equation & circuit, A staircase li...

A staircase light is controlled by two switches one at the top of the stairs and another at the bottom of stairs a. Make a truth table for this system. b. Write the lo

Avantages of oopl in a programming language, Object oriented programming la...

Object oriented programming languages directly show the real life objects. The features of OOPL as inheritance, polymorphism, and encapsulation makes it strong.

Explain about magnetic disk, Q. Explain about Magnetic Disk? A disk is ...

Q. Explain about Magnetic Disk? A disk is circular platter constructed of nonmagnetic material known as substrate, coated with a magnetisable material. This is used for storing

Digital Design, Design a serial 2’s complementer with a shift register and ...

Design a serial 2’s complementer with a shift register and a flip-flop

Explain the importance of computer architecture, Explain the importance of ...

Explain the importance of Computer architecture Computer architecture courses cover application, organization, architecture, logic and transistor layers. However, four other la

What do you mean by instruction cycle, Q. What do you mean by instruction c...

Q. What do you mean by instruction cycle? We have considered the instruction execution in previous section. Now let's consider more about different types of instruction executi

Describing Random Algorithm, Suppose you''re given n numbers and asked to f...

Suppose you''re given n numbers and asked to find a number that is greater than or equal to the median a) What is the lower bound for the worst case complexity of this problem?

How do you detect if two 8-bit signals are same, By using XNOR gate if the ...

By using XNOR gate if the signals are similar then only the output will be one otherwise not.

What is disadvantage of distributed systems, What is disadvantage of Dis...

What is disadvantage of Distributed systems? Ans. Reliability is disadvantage of Distributed system.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd