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.

see signal temporal logic

\begin{align} v+(-1)v &= (1+(-1))v \\ &= 0v \\ &= 0 \end{align}

As \((-1)v=0\), \((-1)v\) is the additive identity of \(v\) which we defined as \(-v\) \(\blacksquare\).