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:
“One of the oddest features of western Christianized culture is its ready acceptance of the myth of the stable family and the happy marriage. We have been taught to accept the myth not as an heroic ideal, something good, brave, and nearly impossible to fulfil, but as the very fibre of normal life. Given most families and most marriages, the belief seems admirable but foolhardy.”
—Jonathan Raban (b. 1942)
“It appears that ordinary men take wives because possession is not possible without marriage, and that ordinary women accept husbands because marriage is not possible without possession; with totally differing aims the method is the same on both sides.”
—Thomas Hardy (1840–1928)
“How much atonement is enough? The bombing must be allowed as at least part-payment: those of our young people who are concerned about the moral problem posed by the Allied air offensive should at least consider the moral problem that would have been posed if the German civilian population had not suffered at all.”
—Clive James (b. 1939)