Stable Marriage Problem (Stable Matching Problem)

Description

Given $n$ men and $n$ women, where each person has ranked all members of the opposite sex 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. When there are no such pairs of people, the set of marriages is deemed stable.

Related Problems

Generalizations: Stable Roommates Problem

Subproblem: Almost Stable Marriage Problem, Boolean d-Attribute Stable Matching, Stable Matching Verification, Stable Pair Checking

Related: Boolean d-Attribute Stable Matching, Stable Matching Verification, Stable Pair Checking

Parameters

$n$: number of men and number of women

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Valentin Polishchuk, and Jukka Suomela	2008	$O({1})$	$O({1})$	2 + \epsilon	Parallel	Time
Gale–Shapley algorithm	1962	$O(n^{2})$	$O(n)$	Exact	Deterministic	Time
Manlove; Malley	2005	$O(n^{2})$	$O(n^{2})$?	Exact	Deterministic	Time
Unsworth; C.; Prosser; P	2005	$O(n^{2})$	$O(n^{2})$?	Exact	Deterministic	Time
Gent; I.P.; Irving; R.W.; Manlove; D.F.; Prosser; P.; Smith; B.M.	2001	$O(n^{2})$	$O(n^{2})$?	Exact	Deterministic	Time
S. S. TSENG and R. C. T. LEE	1984	$O(n^{2})$	$O(n)$ per processor?	Exact	Parallel	Time
[[Tomas Feder, Nimrod Megiddoy, Serge A� Plotki (Stable Marriage Problem Stable Matching Problem)|Tomas Feder, Nimrod Megiddoy, Serge A� Plotki]]	1994	$O(n^{0.5})$	$O(n^{0.5})$ auxiliary per processor?	Exact	Parallel	Time

Time Complexity Graph

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Space Complexity Graph

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Time-Space Tradeoff

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References/Citation

http://www.dcs.gla.ac.uk/~davidm/pubs/7981.pdf