Talk:Stable matching problem: Difference between revisions

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==Applications==

The first application given is not an application of the stable marriage problem, since a hospital may hire more than one graduate at a time. For this the college admissions algorithm of Gale and Shapley is required. An important application of the stable marriage algorithm is matching organ donors to organ recipients. Many lives have been saved by using this algorithm, also devised by Gale and Shapley.<ref>''Mariages Stable'', Donald E Knuth.</ref><ref>Gale, D.; Shapley, L. S. (1962). "College Admissions and the Stability of Marriage". American Mathematical Monthly 69: 9–14. doi:10.2307/2312726. JSTOR 2312726.</ref>

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== Optimality of the solution ==

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*[http://cran.r-project.org/web/packages/matchingMarkets/ Gale-Shapley Algorithm in R package matchingMarkets]

[[User:Mtching|Mtching]] ([[User talk:Mtching|talk]]) 19:40, 10 December 2014 (UTC)

== Dr. Klijn's comment on this article ==

Dr. Klijn has reviewed [https://en.wikipedia.org/w/index.php?title=Stable_marriage_problem&oldid=720801008 this Wikipedia page], and provided us with the following comments to improve its quality:

{{quote|text=The largest (!) part of the article is about the case of stable marriage with indifference(S?). Even though the case of indifferences is studied in the literature, the three notions of stability and their algorithms receive too much attention. Probably it is more interesting to say more about the lattice structure of the set of stable matchings (i.e., extend the section "optimality of the solution") and discuss incentives / strategic aspects of the gale-shapley algorithm (also known as the deferred acceptance algorithm!). I think it would also of interest to mention that variants of the gale-shapley algorithm are actually used in real-life applications. For instance, medical interns in the US, or school choice in Boston and New York.}}

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Klijn has published scholarly research which seems to be relevant to this Wikipedia article:

*'''Reference ''': Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.

[[User:ExpertIdeasBot|ExpertIdeasBot]] ([[User talk:ExpertIdeasBot|talk]]) 12:51, 7 June 2016 (UTC)

== Dr. Romero Medina's comment on this article ==

Dr. Romero Medina has reviewed [https://en.wikipedia.org/w/index.php?title=Stable_marriage_problem&oldid=733328992 this Wikipedia page], and provided us with the following comments to improve its quality:

{{quote|text=<<The stable marriage problem has been stated as follows:>>

Reference Gale, D.; Shapley, L. S. (1962).

Consider the possibility of n=/m.

<<Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical students to their first hospital appointments>>

Is a case of many to one matching problem different from the one to one case of the marriage problem.

<<This algorithm guarantees that:

Everyone gets married

At the end, there cannot be a man and a woman both unengaged>>

This is under the assumption the every one is admissible to all the agents on the other side of the market.

}}

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Romero Medina has expertise on the topic of this article, since he has published relevant scholarly research:

*'''Reference ''': Antonio Romero-Medina & Matteo Triossi, 2011. "Games with capacity manipulation : incentives and Nash equilibria," Economics Working Papers we1125, Universidad Carlos III, Departamento de Economia.

[[User:ExpertIdeasBot|ExpertIdeasBot]] ([[User talk:ExpertIdeasBot|talk]]) 15:46, 24 August 2016 (UTC)

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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-->

:Whatever do you mean by a stable pair? A specific matching can have an UNstable pair, but being stable is a property of a whole matching, not a pair. In any case, this talk page is for improvements to our article based on published sources (and since there are so many publications on this topic, the bar to inclusion is pretty high). It is not for speculation on what directions research on this problem should take. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 05:19, 6 May 2022 (UTC)