Stable Roommates Problem
In mathematics, especially in the fields of game theory and combinatorics, the stable roommate problem (SRP) is the problem of finding a stable matching — a matching in which there is no pair of elements, each from a different matched set, where each member of the pair prefers the other to their match. This is different from the stable marriage problem in that the stable roommates problem does not require that a set is broken up into male and female subsets. Any person can prefer anyone in the same set.
It is commonly stated as:
- In a given instance of the Stable Roommates problem (SRP), each of 2n participants ranks the others in strict order of preference. A matching is a set of n disjoint (unordered) pairs of participants. A matching M in an instance of SRP is stable if there are no two participants x and y, each of whom prefers the other to his partner in M. Such a pair is said to block M, or to be a blocking pair with respect to M.
Read more about Stable Roommates Problem: Solution, Algorithm
Famous quotes containing the words stable and/or problem:
“If it is to be done well, child-rearing requires, more than most activities of life, a good deal of decentering from one’s own needs and perspectives. Such decentering is relatively easy when a society is stable and when there is an extended, supportive structure that the parent can depend upon.”
—David Elkind (20th century)
“The problem of induction is not a problem of demonstration but a problem of defining the difference between valid and invalid
predictions.”
—Nelson Goodman (1906)