Question: Consider an omega network that connects p processors. Define a function f that maps p = [0, 1, , p-1] onto a permutation P of

"Consider an omega network that connects p processors. Define a function f that maps p = [0, 1, , p-1] onto a permutation P of P (that is, P[i] = f(P[i]) and P[i] P for all 0 i < p). Think of this function as mapping communication requests by the processors so that processor P[i] requests communication with processor P[i]."

(1) How many distinct permutation function exist?

(2) How many of these functions result in non-blocking communication?

(3) What is the probability that an arbitrary function will result in non-blocking communication?

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