The stable marriage problem is a famous computational problem with applications in matching kidney donors to recipients, medical residents to hospitals, etc. The problem $($as stated in Wikipedia$)$ is this:

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.