CS575 Discussion Three
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3a. Consider adding n numbers on a p processor square 2D mesh. The input numbers
    are equally distributed over the processors. Answer the following questions.

    i.   Assuming it takes one time step to add two numbers in one processor
         and one time step to communicate a number between two adjacent
         processors derive (approximate, see book chapter 5.4) expressions
         in n and p for Tp, S and E. 

         Build a table for efficiency E as a function of n = n1, n2, n3  and p = 4,
         16 and 64, such that E(n1,4) = E(n2,16) = E(n3,64) = 80 %

    ii.  Do the same as in i, but now assuming that it takes one time step to add
         two numbers in one processor and 127 time steps to communicate a number
         between two adjacent processors.

    iii. Compute the iso-efficiencies of scenarios a and b and answer the question:
         if the number of processors increases by a factor of K, what factor does
         the input need to go up in order to keep the same efficiency. Discuss.

3b. Respond to someone else's solution, and generate a consensus solution to
    be posted on the main discussion board.