Editing Stable matching problem (section)

==Related problems==
In '''[[stable matching with indifference]]''', some men might be indifferent between two or more women and vice versa.

The '''[[stable roommates problem]]''' is similar to the stable marriage problem, but differs in that all participants belong to a single pool (instead of being divided into equal numbers of "men" and "women").

The '''[[Hospital resident|hospitals/residents problem]]''' – also known as the '''college admissions problem''' – differs from the stable marriage problem in that a hospital can take multiple residents, or a college can take an incoming class of more than one student.  Algorithms to solve the hospitals/residents problem can be ''hospital-oriented'' (as the [[National Resident Matching Program|NRMP]] was before 1995)<ref name="Robinson">{{cite journal|last=Robinson|first=Sara|date=April 2003|title=Are Medical Students Meeting Their (Best Possible) Match?|url=http://www.siam.org/pdf/news/305.pdf|journal=SIAM News|issue=3|page=36|access-date=2 January 2018}}</ref> or ''resident-oriented''. This problem was solved, with an algorithm, in the same original paper by Gale and Shapley, in which the stable marriage problem was solved.<ref name=gs62/>

The '''[[Hospital resident|hospitals/residents problem with couples]]''' allows the set of residents to include couples who must be assigned together, either to the same hospital or to a specific pair of hospitals chosen by the couple (e.g., a married couple want to ensure that they will stay together and not be stuck in programs that are far away from each other).  The addition of couples to the hospitals/residents problem renders the problem [[NP-complete]].<ref>{{cite book|title=The Stable Marriage Problem: Structure and Algorithms|last1=Gusfield|first1=D.|last2=Irving|first2=R. W.|publisher=MIT Press|year=1989|isbn=0-262-07118-5|page=54}}</ref>

The '''[[assignment problem]]''' seeks to find a matching in a weighted [[bipartite graph]] that has maximum weight. Maximum weighted matchings do not have to be stable, but in some applications a maximum weighted matching is better than a stable one.

The '''matching with contracts''' problem is a generalization of matching problem, in which participants can be matched with different terms of contracts.<ref>{{cite journal |first1=John William |last1=Hatfield |first2=Paul |last2=Milgrom |title=Matching with Contracts |journal=[[American Economic Review]] |volume=95 |issue=4 |year=2005 |pages=913–935 |jstor=4132699 |doi=10.1257/0002828054825466}}</ref> An important special case of contracts is matching with flexible wages.<ref>{{cite journal |first1=Vincent |last1=Crawford |first2=Elsie Marie |last2=Knoer |title=Job Matching with Heterogeneous Firms and Workers |year=1981 |journal=[[Econometrica]] |volume=49 |issue=2 |pages=437–450 |jstor=1913320 |doi=10.2307/1913320}}</ref>