a) Describe an algorithm to produce a stable many-to-many matching for any instance

of this polygamous marriage problem.

c) Give a small example instance where a man is unmarried at the end of running

your algorithm.

d) Give a proof that at termination of your algorithm, if a man is unmarried, he

cannot possibly have a wife in any stable matching and remains forever alone.

Suppose we have n men and n women, where the men propose to the women. Each man mi has a preference list containing the n women, and a number 0?km,