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The Stable marriage problem - structure and algorithms
TLDR
The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a moregeneral set of problems.
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An Efficient Algorithm for the "Stable Roommates" Problem
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The b-chromatic Number of a Graph
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Hard variants of stable marriage
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Stable Marriage and Indifference
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An efficient algorithm for the “optimal” stable marriage
TLDR
By exploiting the structure of the set of all stable matchings, and using graph-theoretic methods, an O(n4) algorithm for this problem is derived and achieves the objective of maximizing the average “satisfaction” of all people.
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The Complexity of Counting Stable Marriages
TLDR
It is proved that the enumeration version of the problem—determining the number of stable matchings—is P-complete, and therefore cannot be solved in polynomial time if the search version ofThe problem is polynomially solvable.
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The College Admissions problem with lower and common quotas
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A Database Index to Large Biological Sequences
TLDR
This work presents an approach to searching genetic DNA sequences using an adaptation of the sufx tree data structure deployed on the general purpose persistent Java platform, PJama, and proposes to use such indexes as an alternative to the current practice of serial scanning.
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Popular matchings
TLDR
The first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists are given.
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