Marriage Matching: A Conjecture of Donald Knuth
Variations of the Gale-Shapley algorithm have been used and studied extensively in real world markets. Examples include matching medical residents with residency programs, the kidney exchange program and matching college students with on-campus housing. The performance of the Gale-Shapley marriage matching algorithm (1962) has been studied extensively in the special case of men's and women's preferences random. We drop the assumption that women's preferences are random and show that En /n ln n -> 1, where En is the expected number of proposals made when the men-propose Gale-Shapley algorithm is used to match n men with n women. This establishes in spirit a conjecture of Donald Knuth (1976, 1997) of thirty years standing. Under the same assumptions, we also establish bounds on the expected ranking by a woman of her assigned mate. Bounds on men's rankings of their assigned mates follow directly from the conjecture.
|Date of creation:||May 2007|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (860) 486-4889
Fax: (860) 486-4463
Web page: http://www.econ.uconn.edu/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003.
Game Theory and Information
- Yan Chen & Tayfun S�nmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, vol. 92(5), pages 1669-1686, December.
When requesting a correction, please mention this item's handle: RePEc:uct:uconnp:2007-15. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Francis Ahking)
If references are entirely missing, you can add them using this form.