Years and Authors of Summarized Original Work
2013; Király
Introduction
We have a two-sided market, one side is a set U of men, the other side is a set V of women. The first part of the input also contains the mutually acceptable man-woman pairs E. This makes up a bipartite graph \(G(U \cup V\), E). The second part of the input contains the preference lists of each person, that is a weak order (may contain ties) on his/her acceptable pairs.
A matching is a set of mutually disjoint acceptable man-woman pairs. Given a matching M, a man m and a woman w form a blocking pair, if they are an acceptable pair but are not partners in M, and they both prefer each other to their partner, or have no partner in M. That is either w is unmatched in M or w prefers m to her M-partner, and either m is unmatched in M or m prefers w to his M-partner. A matching M is stable if there are no blocking pairs.
We consider a two-sided market under incomplete preference lists with ties (SMTI), where the goal is...
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsRecommended Reading
Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15
Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithms. MIT, Boston
Halldórsson MM, Irving RW, Iwama K, Manlove DF, Miyazaki S, Morita Y, Scott S (2003) Approximability results for stable marriage problems with ties. Theor Comput Sci 306:431–447
Iwama K, Manlove DF, Miyazaki S, Morita Y (1999) Stable marriage with incomplete lists and ties. In: Proceedings of the 26th international colloquium on automata, languages and programming (ICALP 1999), Prague. LNCS, vol 1644, pp 443–452
Iwama K, Miyazaki S, Yamauchi N (2007) A 1.875-approximation algorithm for the stable marriage problem. In: SODA ’07: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, pp 288–297
Király Z (2009(online), 2011) Better and simpler approximation algorithms for the stable marriage problem. Algorithmica 60(1):3–20
Király Z (2013) Linear time local approximation algorithm for maximum stable marriage. Algorithms 6(3):471–484
Manlove D (2013) Algorithmics of matching under preferences. World Scientific Publishing, Singapore
McDermid EJ (2009) A \(\frac{3} {2}\)-approximation algorithm for general stable marriage. In: Proceedings of the 36th international colloquium automata, languages and programming (ICALP 2009), Rhodes, pp 689–700
Paluch K (2014) Faster and simpler approximation of stable matchings. Algorithms 7(2):189–202
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
Király, Z. (2016). Simpler Approximation for Stable Marriage. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_676
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2864-4_676
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2863-7
Online ISBN: 978-1-4939-2864-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering