In this exercise, we examine the effect of the interconnection network topology on the CPI of programs running on a 64-processor distributed-memory multiprocessor. The processor clock rate is 2.0 GHz, and the base CPI of an application with all references hitting in the cache is 0.75.
Assume that 0.2% of the instructions involve a remote communication reference.
The cost of a remote communication reference is (100+10 h) ns, h being the number of communication network hops that a remote reference has to make to the remote processor memory and back. Assume all communication links are bidirectional.

a. Calculate the worst-case remote communication cost when the 64 processors are arranged as a ring, as an 8 х 8 processor grid, or as a hypercube.

b. Compare the base CPI of the application with no remote communication to the CPI achieved with each of the three topologies in part (a).