Scaling Behavior in the Stable Marriage Problem

TL;DR

This paper investigates the scaling properties of stable solutions in the stable marriage problem, revealing that they are near-optimal and follow specific scaling laws through numerical and analytical analysis.

Contribution

It introduces the analysis of scaling laws in stable marriage solutions and compares their quality to global optima using combined numerical and analytical methods.

Findings

Stable solutions are close to the global optimum.

Stable solutions form a subset obeying scaling laws.

Numerical and analytical methods support the findings.

Abstract

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.