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.
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.
Interfaith marriageInterfaith marriage, sometimes called a "mixed marriage", is marriage between spouses professing different religions. Although interfaith marriages are often established as civil marriages, in some instances they may be established as a religious marriage. This depends on religious doctrine of each of the two parties' religions; some prohibit interfaith marriage, and among others there are varying degrees of permissibility. Several major religions are mute on the issue, and still others allow it with requirements for ceremony and custom.
Christian views on marriageFrom the earliest days of the Christian faith, Christians have viewed marriage as a divinely blessed, lifelong, monogamous union between a man and a woman. However, while many Christians might agree with the traditional definition, the terminology and theological views of marriage have varied through time in different countries, and among Christian denominations. Many Protestants consider marriage to be a sacred institution or "holy ordinance" of God. Catholic and Eastern Orthodox Christians consider marriage as a holy sacrament or sacred mystery.
Open marriageOpen marriage is a form of non-monogamy in which the partners of a dyadic marriage agree that each may engage in extramarital sexual relationships, without this being regarded by them as infidelity, and consider or establish an open relationship despite the implied monogamy of marriage. There are variant forms of open marriage such as swinging and polyamory, each with the partners having varying levels of input into their spouse's activities.
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.
Fractional matchingIn graph theory, a fractional matching is a generalization of a matching in which, intuitively, each vertex may be broken into fractions that are matched to different neighbor vertices. Given a graph G = (V, E), a fractional matching in G is a function that assigns, to each edge e in E, a fraction f(e) in [0, 1], such that for every vertex v in V, the sum of fractions of edges adjacent to v is at most 1: A matching in the traditional sense is a special case of a fractional matching, in which the fraction of every edge is either 0 or 1: f(e) = 1 if e is in the matching, and f(e) = 0 if it is not.
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.
