Talk:Stable matching problem: Difference between revisions

Revision as of 00:48, 6 May 2022

Revision as of 00:49, 6 May 2022

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== Other Algorithms? ==

The Gale-Shapley method seems pretty lopsided. Aren't there other algorithms known, particularly ones that treat both groups symmetrically? It doesn't seem too difficult to think of one. For instance, one method would be: (a) sort all pairs of uncommitted individuals in decreasing order of mutual preference (e.g. one if A has a #m on their list, and a has A as #n on their list, then the total preference might be m + n or some other monotonic symmetric function of m and n); and set up a tie-breaking convention to handle ties (or select amongst ties randomly); (b) find the first stable pair on the list and commit the individuals to each other; (c) repeat (a) for the remaining uncommitted individuals. By construction, the result is stable; and the method is symmetric, subject to the symmetry of the tie-breaking convention. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2603:6000:AA4D:C5B8:0:3361:EAF8:97B7|2603:6000:AA4D:C5B8:0:3361:EAF8:97B7]] ([[User talk:2603:6000:AA4D:C5B8:0:3361:EAF8:97B7#top|talk]]) 00:48, 6 May 2022 (UTC)</small> <!--Autosigned by SineBot-->

== Uniqueness of solution ==