Corpus ID: 155099964

Two-sided profile-based optimality in the stable marriage problem

  title={Two-sided profile-based optimality in the stable marriage problem},
  author={Frances Cooper and D. Manlove},
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the number of agents who have their first-, second-, third-choice partner, etc. In a rank maximal stable matching, the maximum number of agents have their first-choice partner, and subject to this, the maximum number of agents have their second-choice partner, etc… Expand


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An O(n2) algorithm is described that will determine, for any instance of the stable marriage problem, whether a stable matching exists, and if so, will find such a matching. Expand
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  • C. Lennon, B. Pittel
  • Computer Science, Mathematics
  • Combinatorics, Probability and Computing
  • 2009
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Three Fast Algorithms for Four Problems in Stable Marriage
  • D. Gusfield
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1987
An $O(n^2 )$ time algorithm is given which, for any problem instance of n men and n women, finds every man–woman pair that is contained in at least one stable marriage. Expand
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Efficient algorithms for bipartite matching problems with preferences
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The Generalized Median Stable Matchings: Finding Them Is Not That Easy
A new characterization of these stable matchings that is solely based on I's rotation poset is presented, and it is proved that when i = O(log n), where n is the number of men, αi can be found efficiently; but when i is a constant fraction of N, finding αi is NP-hard. Expand