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

Determine the decimal equivalent of hexadecimal number, The hexadecimal num...

The hexadecimal number for (95.5) 10 is ? Ans. (95.5) 10 = (5F.8) 16 Integer part Fractional part 0.5x16=8.0

What is the working set of a process, What is the working set of a process?...

What is the working set of a process? The set of pages that are referred by the method in the last "n", references, where "n" is called the window of the working set of the pro

Explain crossbar exchange with all call processing steps, Explain crossbar ...

Explain crossbar exchange, with all call processing steps and diagrams. The fundamental idea of crossbar switching is to give a matrix of n x m sets of contacts with only n + m

Hat are the advantages and disadvantages of hardwired, What are the advanta...

What are the advantages and disadvantages of hardwired and micro programmed control? Advantages of hardwired control i. Operate at high speed ii Each state of this coun

Illustrate basic strategy used in raid, Q. Illustrate Basic strategy used i...

Q. Illustrate Basic strategy used in RAID? Basic strategy used in RAID is to replace large capacity disk drive with multiple smaller capacity disks. Data on these disks is dist

Flow-between matrix layout problem, Solve the problem in page 346 of the pa...

Solve the problem in page 346 of the paper on cell formation by Boctor using the MIP method.  Use 4 cells and no more than 3 machines per cell. Solve the problem using the MIP m

What is the purpose of zero (z) flag and carry (c) flag, What is the purpos...

What is the purpose of zero (z) flag and carry (c) flag? Carry flag holds the carry after addition or the borrow after subtraction. Carry flag also indicates error conditions,

What is high level formatting, Q. What is High level formatting? In any...

Q. What is High level formatting? In any disk system the space at some time in use would become discarded and therefore will be free for other application. Operating system ass

Subsequent step in karnaugh map, The subsequent step in Karnaugh map is to ...

The subsequent step in Karnaugh map is to map truth table in the map. Mapping is done by putting a 1 in respective square belonging to 1 value in truth table. This mapped map is us

What is the use of boot block, What is the use of boot block? For a com...

What is the use of boot block? For a computer to start running when powered up or rebooted it needs to have an initial program to run. This bootstrap program tends to be simple

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