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Citation bot (talk | contribs) Add: isbn, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Combinatorics | #UCB_Category 165/188 |
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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 />
The [[Gale-Shapley algorithm]] for stable matching is used to assign rabbis who graduate from [[Hebrew Union College – Jewish Institute of Religion|Hebrew Union College]] to Jewish congregations.<ref>{{Cite journal |
==Different stable matchings==
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| title = Proceedings of the 50th Symposium on Theory of Computing (STOC 2018)
| year = 2018| arxiv = 1711.01032
| isbn = 978-1-4503-5559-9 }}</ref>
Counting the number of stable matchings in a given instance is [[♯P-complete|#P-complete]].<ref>{{cite journal
| last1 = Irving | first1 = Robert W.
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| title = Algorithms - ESA 2006, 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006, Proceedings
| volume = 4168
| year = 2006
}}</ref>
The GS algorithm is non-truthful for the women (the reviewing side): each woman may be able to misrepresent her preferences and get a better match.
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