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Let $f$ be the fraction of the computation (in terms of time) that is parallelizabl$e$. $P$ the number of processors in the system, and $s_p$ the speed up achievable in comparison with sequential  execution – then the $s_p$ can be calculated using the relation:

  1. $\frac{1}{1-f-f/P}$
  2. $\frac{P}{P-f(P+1)}$
  3. $\frac{1}{1-f+f/P}$
  4. $\frac{P}{P+f(P-1)}$
in CO and Architecture by Veteran (105k points)
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answer C

  • Let execution time without parallelism is 1.
  • If f is the fraction of parallel computation (1-f) time must be spend for sequential computation.
  • f fraction of computation can be distributed among P processors; So it will take f/P time to complete computation.
  • Total time for computation with parallelism = 1-f + f/P

speed up = time without parallelism / time with parallelism

= 1/ 1-f + f/P

// Correct me if I am wrong!

by Boss (32.5k points)
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@Shiva,what basis you've used for calculation?

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