Years and Authors of Summarized Original Work
2007; Halldórsson, Iwama, Miyazaki, Yanagisawa
2014; Huang, Iwama, Miyazaki, Yanagisawa
Problem Definition
Over the last 50 years, the stable marriage problem has been extensively studied for many problem settings (see, e.g., [11]), and one of the most intensively studied problem settings is MAX SMTI (MAXimum Stable Marriage with Ties and Incomplete lists). An input for the stable marriage problem consists of n men, n women, and each person’s preference list for the people of the opposite sex. In MAX SMTI, the preference list of each person can be incomplete, which means that each person is allowed to exclude unacceptable people from the preference list, and the preference list of each person is allowed to include ties to show indifference between two or more people.
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Recommended Reading
Dean BC, Jalasutram R (2015) Factor revealing LPs and stable matching with ties and incomplete lists. In Proceedings of the 3rd international workshop on matching under preferences, 2015 (to appear)
Halldórsson MM, Iwama K, Miyazaki S, Yanagisawa H (2004) Randomized approximation of the stable marriage problem. Theor Comput Sci 325(3):439–465
Halldórsson MM, Iwama K, Miyazaki S, Yanagisawa H (2007) Improved approximation results for the stable marriage problem. ACM Trans Algorithms 3(3):Article No. 30
Huang CC, Kavitha T (2014) An improved approximation algorithm for the stable marriage problem with one-sided ties. In: Proceedings of IPCO 2014, Bonn, pp 297–308
Huang CC, Iwama K, Miyazaki S, Yanagisawa H (2015) Approximability of finding largest stable matchings. Manuscript under submission
Irving RW, Manlove DF (2008) Approximation algorithms for hard variants of the stable marriage and hospital/residents problems. J Comb Optim 16(3):279–292
Irving RW, Manlove DF (2009) Finding large stable matchings. J Exp Algorithmics 14:Article No. 2
Iwama K, Miyazaki S, Yamauchi N (2007) A 1.875: approximation algorithm for the stable marriage problem. In: Proceedings of SODA 2007, New Orleans, pp 288–297
Iwama K, Miyazaki S, Yanagisawa H (2014) A 25/17-approximation algorithm for the stable marriage problem with one-sided ties. Algorithmica 68(3):758–775
Király Z (2011) Better and simpler approximation algorithms for the stable marriage problem. Algorithmica 60(1):3–20
Manlove DF (2013) Algorithmics of matching under preferences. World Scientific, Hackensack
Manlove DF, Irving RW, Iwama K, Miyazaki S, Morita Y (2002) Hard variants of stable marriage. Theor Comput Sci 276(1–2):261–279
Podhradský A (2010) Stable marriage problem algorithms. Master’s thesis, Faculty of Informatics, Masaryk University
Radnai A (2014) Approximation algorithms for the stable matching problem. Master’s thesis, Eötvös Loránd University
Yanagisawa H (2007) Approximation algorithms for stable marriage problems. Ph.D. thesis, Kyoto University
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Yanagisawa, H. (2016). Stable Marriage with One-Sided Ties. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_801
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