Hard variants of stable marriage
Theoretical Computer Science
Stable Marriage with Incomplete Lists and Ties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximability results for stable marriage problems with ties
Theoretical Computer Science
Randomized approximation of the stable marriage problem
Theoretical Computer Science - Special papers from: COCOON 2003
Improved approximation results for the stable marriage problem
ACM Transactions on Algorithms (TALG)
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding large stable matchings
Journal of Experimental Algorithmics (JEA)
A 3/2-Approximation Algorithm for General Stable Marriage
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Communication requirements for stable marriages
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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We first consider the problem of finding a maximum stable matching if incomplete lists and ties are both allowed, but ties only for one gender. For this problem we give a simple, linear time 3/2-approximation algorithm, improving on the best known approximation factor 5/3 of Irving and Manlove [5]. Next, we show how this extends to the Hospitals/Residents problem with the same ratio if the residents have strict orders. We also give a simple linear time algorithm for the general problem with approximation factor 5/3, improving the best known 15/8-approximation algorithm of Iwama, Miyazaki and Yamauchi [7]. For the cases considered in this paper it is NP-hard to approximate within a factor of 21/19 by the result of Halldórsson et al. [3].Our algorithms not only give better approximation ratios than the cited ones, but are much simpler and run significantly faster. Also we may drop a restriction used in [5] and the analysis is substantially more moderate.