From: scerir (scerir@libero.it)
Date: Sat Sep 09 2000 - 12:37:14 MDT
THE STABLE MARRIAGE PROBLEM (*)
beauty, ugliness, distance, fate
(and many more human afflictions)
http://xxx.lanl.gov/abs/cond-mat?0008337
The *stable marriage* problem has been introduced
in order to describe a complex system where individuals
attempt to optimise their own satisfaction, subject to
mutually conflicting constraints. Due to the potential
large applicability of such model to describe all
the situation where different objects has to be matched
pairwise, the statistical properties of this model
have been extensively studied. In this paper we
present a generalization of this model,
introduced in order to take into account the presence
of correlations in the lists and the effects of distance
when the *player* are supposed to be represented by a
position in space.
http://xxx.lanl.gov/abs/cond-mat?0007321
In the *stable marriage* problem N men and N women have
to be matched by pairs under the constraint that
the resulting matching is stable. We study the
statistical properties of stable matchings
in the large N limit using both numerical
and analytical methods. Generalizations of
the model including *singles* and unequal
numbers of men and women are also investigated.
http://xxx.lanl.gov/abs/cond-mat/9710077
In the *stable marriage* problem, a variant of the bi-parted
matching problem, each member has a *wish-list*
expressing his/her preference for all possible partners;
this list consists of random, positive real numbers
drawn from a certain distribution. One searches the lowest
cost for the society, at the risk of breaking up pairs
in the course of time. Minimization of a global cost function
(Hamiltonian) is performed with statistical mechanics
techniques at a finite fictitious *temperature*.
The problem is generalized to include *bachelors*,
needed in particular when the groups have different size,
and *polygamy*. Exact solutions are found for the optimal
solution (T=0). The entropy is found to vanish
quadratically in T. Whether bachelors occur or not,
depends not only on their intrinsic *qualities*,
or lack thereof, but also on global aspects of the chance
for pair formation in society.
(*) Sometimes called the stable employment problem
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