Stable matching problem: Difference between revisions

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Revert: those are not quotes, they are primes. An ASCII apostrophe at least might show up primelike for some readers; quotes never should.
Similar problems: Added stable roommates problem and hospitals/residents problem (with or without couples)
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== Similar problems ==
The '''[[weighted matching problem]]''' isseeks 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 '''[[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 '''[[hospitals/residents problem]]''' — also known as the '''college admissions problem''' — differs from the stable marriage problem in that the "women" can accept "proposals" from more than one "man" (e.g., 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'' (female-optimal) or ''resident-oriented'' (male-optimal).
 
The '''[[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>Gusfield and Irving, ''The Stable Marriage Problem: Structure and Algorithms,'' p. 54; MIT Press, 1989.</ref>
 
==References==