Question

Problem: Find the speedup and efficiency that can be obtained with parallel computing, given the values of the time needed to complete the sequential part of the task (denoted by T_s), the time needed to complete the parallelizable part of the task with one processor (denoted by T_p), and the number of processors (denoted by N) in the first three columns of the following table, and report them in the last two columns of the table.

Tsin seconds	Tpin seconds	N	Speedup	Efficiency
100	900	2
100	900	5
100	900	10

Answer 1

• Speedup = number of processors/(1+(no. of processors -1)* f ) where f is a fraction of the program that is run sequentially.
• Efficiency= time taken to do sequential task / (time taken to do parallel task * no of processors)
• In this case, a fraction of sequential task f= 100/(900+100)=0.1
• number of processors varies in all the cases.
  Case -1 : Number of Processors =2; time to run sequential task = 100; time to run parallel task = 900
  i. Speedup = 2/(1+(2-1)*.1)= 2/1.1=1.81
  ii. Efficiency = 100/(2*900)=100/1800 = .055
  Case -2 : Number of Processors =5; time to run sequential task = 100; time to run parallel task = 900
  i. Speedup = 5/(1+(5-1)*.1)= 5/1.4 = 3.57
  ii. Efficiency = 100/(5*900)= 0.022
  Case -3 : Number of Processors =10; time to run sequential task = 100; time to run parallel task = 900
  i. Speedup = 10/(1+(10-1)*0.1)=10/1.9 = 5.26
  ii. Efficiency = 100/(10*900)=0.011

Friend, this was a really nice question to answer. If you find my answer helpful, please like it. Thanks.