Algorithms [Sedgewick, Robert]

Another feature of the algorithm which seems to be biased is the order in which the men become the suitor: is it better to be the first man to propose (and therefore be engaged at least for a little while to your first choice) or the last (and therefore have a reduced chance to suffer the indignities of a broken engagement)? The answer is that this is not a bias at all: it doesn’t matter in what order the men become the suitor. As long as each man makes proposals and each woman accepts according to their lists, the same stable configuration results.

Advanced Algorithms

The two special cases that we’ve examined give some indication of how com-

for general (not necessarily bipartite) graphs; weighted matching for bipartite graphs, where edges have weights and a matching with maximum total weight is sought; and weighted matching for general graphs. Treating the many techniques that have been tried for matching on general graphs would fill an entire volume: it is one of the most extensively studied problems in graph theory.