J. Phys. I France
Volume 7, Numéro 12, December 1997
Page(s) 1723 - 1732
DOI: 10.1051/jp1:1997166
J. Phys. I France 7 (1997) 1723-1732

Scaling Behavior in the Stable Marriage Problem

Marie-José Oméro, Michael Dzierzawa, Matteo Marsili and Yi-Cheng Zhang

Institut de Physique Théorique, Université de Fribourg, 1700 Fribourg, Switzerland

(Received 15 July 1997, accepted 18 August 1997)

We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best solution, but reasonably close to it. All the stable solutions form a special sub-set of the meta-stable states, obeying interesting scaling laws. Both numerical and analytical tools are used to derive our results.

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