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:
- 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
- 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:
“This stable is a Prince’s court.
This crib His chair of state;
The beasts are parcel of His pomp,
The wooden dish His plate.”
—Robert Southwell (1561?–1595)
“The parent who loves his child dearly but asks for nothing in return might qualify as a saint, but he will not qualify as a parent. For a child who can claim love without meeting any of the obligations of love will be a self-centered child and many such children have grown up in our time to become petulant lovers and sullen marriage partners because the promise of unconditional love has not been fulfilled.”
—Selma H. Fraiberg (20th century)
“The problem of culture is seldom grasped correctly. The goal of a culture is not the greatest possible happiness of a people, nor is it the unhindered development of all their talents; instead, culture shows itself in the correct proportion of these developments. Its aim points beyond earthly happiness: the production of great works is the aim of culture.”
—Friedrich Nietzsche (1844–1900)