The Stable Matching Problem is Wes Chao’s favourite algorithm.

Consider two populations, \(A\) and \(B\), who want to form paired relationships between a person \(A\) and \(B\). \(A_i\) has a list of their ranked order matches (I want to be paired with \(B_1\) most, \(B_4\) second, etc.), and so does \(B_i\) (I want to be paired with \(A_4\) most \(A_9\) second, etc.)

We want to discover a stable matching, where pairs are most unwilling to move. We can solve it using the stable matching algorithm.

Nueva Invention Studio speed-dating noises?

## applications of the stable matching problem

- Dating
- Applying to college
- Both of these are high-stress situations, especially if you are doing asking
- You can mathematically prove that
*person doing the asking gets the best result*

Hence, it shows us that the **best possible outcomes go to the people who are willing to ask and get rejected.**

## extensions to the stable matching problem

the stable matching problem can be extended to the rural hospitals problem, which is slightly better.