Prove that the mens courtship algorithm terminates

Reference no: EM131333789

In this exercise we consider a situation with n men and n women.

(a) Prove that if in stage t of the men's courtship algorithm, a particular man is dismissed for the (n - 1)-th time, then the algorithm terminates at stage (t + 1).

(b) Prove that the men's courtship algorithm terminates after at most (n - 1)² + 1 stages.

(c) Find preference relations under which the algorithm terminates after precisely (n - 1)² + 1 stages (hence this is the lowest bound for the length of the algorithm).

Reference no: EM131333789

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