Gale–Shapley algorithm

E612744

The Gale–Shapley algorithm is a foundational procedure in mathematics and computer science that computes stable matchings between two equally sized sets, such as students and schools or men and women in the stable marriage problem.

All labels observed (4)

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Statements (49)

Predicate Object
instanceOf algorithm ⓘ
algorithm in computer science ⓘ
algorithm in mathematics ⓘ
matching algorithm ⓘ
stable matching algorithm ⓘ
alsoKnownAs deferred acceptance algorithm ⓘ
appliedTo college admissions ⓘ
kidney exchange matching ⓘ
matching medical residents to hospitals ⓘ
matching men and women in marriage markets ⓘ
matching students to schools ⓘ
school choice mechanisms ⓘ
coreIdea iterative proposals from one side to the other ⓘ
tentative acceptance and possible later rejection of proposals ⓘ
field algorithmic game theory ⓘ
computer science ⓘ
game theory ⓘ
market design ⓘ
mathematics ⓘ
guarantees existence of a stable matching for any complete strict preferences ⓘ
no blocking pairs in the resulting matching ⓘ
proposer-optimal stable matching ⓘ
receiver-pessimal stable matching ⓘ
termination in finite time ⓘ
input strict preference lists of agents over the opposite set ⓘ
two equally sized sets of agents ⓘ
inspired design of many school choice systems worldwide ⓘ
design of the National Resident Matching Program mechanisms ⓘ
namedAfter David Gale ⓘ
Lloyd Shapley ⓘ
output stable matching ⓘ
property lattice structure of stable matchings underlies its optimality ⓘ
not strategy-proof for the receiving side ⓘ
produces a matching in the core of the associated marriage market ⓘ
strategy-proof for the proposing side under strict preferences ⓘ
publishedIn American Mathematical Monthly ⓘ
relatedConcept blocking pair ⓘ
core of a matching market ⓘ
deferred acceptance mechanism ⓘ
lattice of stable matchings ⓘ
stable matching ⓘ
solvesProblem stable marriage problem ⓘ
stable matching problem ⓘ
spaceComplexity O(n^2) ⓘ
terminationCondition no unmatched proposer has someone left to propose to ⓘ
timeComplexity O(n^2) ⓘ
usedIn matching theory ⓘ
mechanism design ⓘ
yearProposed 1962 ⓘ

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Referenced by (10)

Full triples — surface form annotated when it differs from this entity's canonical label.

David Gale → notableWork → Gale–Shapley algorithm ⓘ
Gale–Shapley algorithm → alsoKnownAs → deferred acceptance algorithm ⓘ
linked to: Gale–Shapley algorithm
Shapley–Gale theorem → relatedTo → Gale–Shapley algorithm ⓘ
Gale’s top trading cycles algorithm → relatedTo → Gale–Shapley deferred acceptance algorithm ⓘ
linked to: Gale–Shapley algorithm
Gale’s top trading cycles algorithm → contrastWith → deferred acceptance algorithm ⓘ
linked to: Gale–Shapley algorithm
Lloyd Shapley → knownFor → Gale–Shapley algorithm ⓘ
Lloyd Shapley → notableWork → College admissions and the stability of marriage ⓘ
linked to: Gale–Shapley algorithm
Lloyd Shapley → notableConcept → Gale–Shapley deferred acceptance algorithm ⓘ
linked to: Gale–Shapley algorithm
Lloyd Shapley → knownFor → Gale–Shapley algorithm ⓘ
subject linked to: Shapley