# Stable Pair Checking (Stable Matching Problem)

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## Description

Verify that a given pairing is stable, given the preferences

## Related Problems

Generalizations: Stable Marriage Problem

Related: Almost Stable Marriage Problem, Stable Roommates Problem, Boolean d-Attribute Stable Matching, Stable Matching Verification

## Parameters

$n$: number of pairs of roommates

## Table of Algorithms

Currently no algorithms in our database for the given problem.

## Reductions FROM Problem

Problem | Implication | Year | Citation | Reduction |
---|---|---|---|---|

Maximum Inner Product Search | assume: OVH then: for any $\epsilon > {0}$, there is a $c$ such that determining whether a given pair is part of any or all stable matchings in the boolean $d$-attribute model with $d = c\log n$ dimensions requires time $\Omega(n^{2-\epsilon})$ |
2016 | https://arxiv.org/pdf/1510.06452.pdf | link |

Maximum Inner Product Search | assume: NSETH then: for any $\epsilon > {0}$ there is a $c$ such that determining whether a gaiven pair is part of any or all stable matching in the boolean $d$-attribute model with $d = c\log n$ dimensions requires co-nondeterministic time $\Omega(n^{2-\epsilon})$ |
2016 | https://arxiv.org/pdf/1510.06452.pdf | link |

Maximum Inner Product Search | assume: NSETH then: for any $\epsilon > {0}$ there is a $c$ such that determining whether a gaiven pair is part of any or all stable matching in the boolean $d$-attribute model with $d = c\log n$ dimensions requires nondeterministic time $\Omega(n^{2-\epsilon})$ |
2016 | https://arxiv.org/pdf/1510.06452.pdf | link |