I would argue that "every proposal involves a new pair" isn't quite true.
If a man, m, proposes to a woman who is already engaged and prefers her
assigned partner over m, no new pair is formed
+석상주 I think he means that whenever a man is unpaired and begins proposing down his list of woman, he will eventually find a woman who will accept (either prefers him or is unpaired) and a new pair is formed. There has to be an unpaired women if there is an unpaired man, since there is equal number of men and women.
Gale-Shapley Stable Matching Algorithm
Submission by rm1791 : A tutorial on GS stable matching algorithm. Apologies for my poorly made animation and amusingly disturbing voice/accent.
Best Marriage Proposal from a Boy to a Girl
Best Marriage Proposal from a Boy to a Girl.
TCP 2013 - A Proposal of Algorithm for Solving P Median Problem
Technical Computing Prague 2013 //www.humusoft.cz/akce/matlab13/ Medviď, V. A Proposal of Algorithm for Solving P-Median Problem.