Stable marriage problemIn mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if: In other words, a matching is stable when there does not exist any pair (A, B) which both prefer each other to their current partner under the matching.
MarriageMarriage, also called matrimony or wedlock, is a culturally and often legally recognized union between people called spouses. It establishes rights and obligations between them, as well as between them and their children (if any), and between them and their in-laws. It is nearly a cultural universal, but the definition of marriage varies between cultures and religions, and over time. Typically, it is an institution in which interpersonal relationships, usually sexual, are acknowledged or sanctioned.
Child marriageChild marriage is a marriage, similar union, formal or informal, between a child under a certain age – typically 18 years – and an adult or another child. The vast majority of child marriages are between a female child and a male adult, and are rooted in gender inequality. Although the age of majority (legal adulthood) and marriageable age are usually designated at age 18, both vary across countries, and therefore the marriageable age may be older or younger in a given country.
Civil marriageA civil marriage is a marriage performed, recorded, and recognized by a government official. Such a marriage may be performed by a religious body and recognized by the state, or it may be entirely secular. Every country maintaining a population registry of its residents keeps track of marital status, and all UN Member countries except Iran, Somalia, South Sudan, Sudan, and Tonga have signed or ratified either the United Nations Convention on Consent to Marriage, Minimum Age for Marriage, and Registration of Marriages (1962) or the United Nations Convention on the Elimination of All Forms of Discrimination against Women (1979) which carry a responsibility to register marriages.
Matching (graph theory)In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated as a network flow problem. Given a graph G = (V, E), a matching M in G is a set of pairwise non-adjacent edges, none of which are loops; that is, no two edges share common vertices.
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