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

ID: 3911259 • Letter: A

Question

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,

Explanation / Answer

1-make two N*N sized two dimensinal array one for men one for women
2-take one N sized one di
3-take count as 0//for counting how much men get married  
4-for(i=0;i<N;i++)
{

s=0;
for(j=0;j<N;j++)
{
if(M[i][j]==1 && W[j][i]==1 && a[i]-->0)
s=1;
}
if(s==1)
count++;
}
5-now your required unmarried mens are (N-count)
6-for eg take M[][]={{1,0,1,0},{1,1,0,0},{1,0,1,1},{1,0,0,0}} W[][]={{1,0,0,0},{1,0,1,0},{1,0,1,1},{1,0,1,1}} a[]={1,1,1,1} here (2,3) remains unmarried