Stable matching problem: Difference between revisions

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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.<ref>[http://www.dcs.gla.ac.uk/research/algorithms/stable/ Stable Matching Algorithms]</ref> In 2012, [[Nobel Memorial Prize in Economic Sciences]] was awarded to [[Lloyd S. Shapley]] and [[Alvin E. Roth]] "for the theory of stable allocations and the practice of market design."<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economics/laureates/2012/ |title=The Prize in Economic Sciences 2012 |publisher=Nobelprize.org |access-date=2013-09-09}}</ref>

An important and large-scale application of stable marriage is in assigning users to servers in a large distributed Internet service.<ref name=nuggets>{{cite journal | author= Bruce Maggs and [[Ramesh Sitaraman]] | title = Algorithmic nuggets in content delivery | journal= ACM SIGCOMM Computer Communication Review |year=2015|volume=45|issue=3|url = http://www.sigcomm.org/sites/default/files/ccr/papers/2015/July/0000000-0000009.pdf}}</ref> Billions of users access web pages, videos, and other services on the Internet, requiring each user to be matched to one of (potentially) hundreds of thousands of servers around the world that offer that service. A user prefers servers that are proximal enough to provide a faster response time for the requested service, resulting in a (partial) preferential ordering of the servers for each user. Each server prefers to serve users that it can with a lower cost, resulting in a (partial) preferential ordering of users for each server. [[Content delivery network]]s that distribute much of the world's content and services solve this large and complex stable marriage problem between users and servers every tens of seconds to enable billions of users to be matched up with their respective servers that can provide the requested web pages, videos, ,or other services.<ref name=nuggets />

==Different stable matchings==