Stable Marriage Problem

In mathematics and computer science, the stable marriage problem (SMP) is the problem of finding a stable matching between two sets of elements given a set of preferences for each element. A matching is a mapping from the elements of one set to the elements of the other set. A matching is stable whenever it is not the case that both:

  1. some given element A of the first matched set prefers some given element B of the second matched set over the element to which A is already matched, and
  2. B also prefers A over the element to which B is already matched

In other words, a matching is stable when there does not exist any alternative pairing (A, B) in which both A and B are individually better off than they would be with the element to which they are currently matched.

The stable marriage problem is commonly stated as:

Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners. If there are no such people, all the marriages are "stable".

Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical students to their first hospital appointments.

Read more about Stable Marriage Problem:  Solution, Algorithm, Optimality of The Solution, Similar Problems

Famous quotes containing the words stable, marriage and/or problem:

    “And neigh like Boanerges—
    Then—punctual as a Star
    Stop—docile and omnipotent
    At its own stable door—”
    —Emily Dickinson (1830–1886)

    “Our home has been nothing but a play-room. I’ve been your doll-wife here, just as at home I was Papa’s doll-child. And the children have been my dolls in their turn. I liked it when you came and played with me, just as they liked it when I came and played with them. That’s what our marriage has been, Torvald.”
    —Henrik Ibsen (1828–1906)

    “I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
    —Jean Giraudoux (1882–1944)