scholarly journals Stable Marriage Problem Mapped to Lotka-volterra Model: Stable Equilibria Mapped from Stable Matchings

2014 ◽  
Vol 35 ◽  
pp. 1398-1406 ◽  
Author(s):  
Yoshikazu Hata ◽  
Yoshiteru Ishida
Keyword(s):  
Volterra Model ◽  
Stable Marriage ◽  
Stable Marriage Problem ◽  
Stable Matchings ◽  
Marriage Problem ◽  
Stable Equilibria

scholarly journals Solving stable matching problems using answer set programming

2016 ◽  
Vol 16 (3) ◽  
pp. 247-268
Author(s):  
SOFIE DE CLERCQ ◽  
STEVEN SCHOCKAERT ◽  
MARTINE DE COCK ◽  
ANN NOWE
Keyword(s):  
Answer Set Programming ◽  
Stable Marriage ◽  
Maximum Cardinality ◽  
Stable Marriage Problem ◽  
Stable Matchings ◽  
Marriage Problem ◽  
Matching Problems ◽  
The Stable Marriage Problem ◽  
Application Potential ◽  
Answer Set

AbstractSince the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed.

scholarly journals EMPLOYMENT BY LOTTO REVISITED

2009 ◽  
Vol 11 (02) ◽  
pp. 181-198
Author(s):  
BETTINA KLAUS ◽  
FLIP KLIJN
Keyword(s):  
Stable Marriage ◽  
Matching Markets ◽  
Stable Marriage Problem ◽  
Stable Matchings ◽  
Marriage Problem ◽  
Matching Algorithm ◽  
Serial Dictatorship

We study employment by lotto (Aldershof et al., 1999), a procedurally fair matching algorithm for the so-called stable marriage problem. We complement Aldershof et al.'s (1999) analysis in two ways. First, we give an alternative and intuitive description of employment by lotto in terms of a probabilistic serial dictatorship on the set of stable matchings. Second, we show that Aldershof et al.'s (1999) conjectures are correct for small matching markets but not necessarily correct for large matching markets.

scholarly journals Approximation algorithms for the sex-equal stable marriage problem

2010 ◽  
Vol 7 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Kazuo Iwama ◽  
Shuichi Miyazaki ◽  
Hiroki Yanagisawa
Keyword(s):  
Approximation Algorithms ◽  
Stable Marriage ◽  
Stable Marriage Problem ◽  
Marriage Problem

Improved approximation results for the stable marriage problem

2007 ◽  
Vol 3 (3) ◽  
pp. 30 ◽  
Author(s):  
Magnús M. Halldórsson ◽  
Kazuo Iwama ◽  
Shuichi Miyazaki ◽  
Hiroki Yanagisawa
Keyword(s):  
Stable Marriage ◽  
Stable Marriage Problem ◽  
Marriage Problem ◽  
The Stable Marriage Problem
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