Question: 1. For a parallel program with p processors on a problem of dimension n, the communication time grows as c + np for some constant

1. For a parallel program with p processors on a problem of dimension n, the communication time grows as c + np for some constant c, while the computation time equals n 3/p, so the total time equals T (n, p) = c + np + n 3/p. (a) For a fixed, constant dimension n and for an increasing number of processors p, find the optimal number of processors for which T (n, p) is minimal. (b) What is the efficiency at the optimal number of processors?

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