Consider a program for multiplying two large-scale N N matrices, where N is the matrix size. The sequential multiply time on a single server is T₁ = cN³ minutes, where c is a constant determined by the server used. An MPI-code parallel program requires T_n = cN³/n + dN²/n^0.5 minutes to complete execution on an n-server cluster system, where d is a constant determined by the MPI version used. Assume the program has a zero sequential bottleneck (? = 0).

Answer the following questions for a given cluster configuration with n = 128 servers, c = 0.8, and d = 0.1.

Using Amdahls law, calculate the speedup of the n-server cluster configuration for running a fixed workload corresponding to the matrix size N=15,000. What is the efficiency of running this n-server cluster?

Using Gustafsons law, calculate the speedup of the n-server cluster configuration for running a scaled workload corresponding with an enlarged matrix size N = n^1/3N. What is the efficiency of running this n-server cluster?

Compare both the results in Part (i) and (ii), and comment on their implications with respect to the speedup and efficiency of the n-cluster configuration.