On the Multidimensional Stable Marriage Problem

TL;DR

This paper generalizes the stable marriage problem to multiple parties, introduces algorithms to find stable matchings, and analyzes their stability and computational complexity.

Contribution

It extends the stable marriage problem to multiple parties and proposes algorithms with proven stability and polynomial runtime.

Findings

Algorithms generate stable matchings for the multidimensional problem.

The elemental algorithm runs in O(pn^2) time.

Matchings produced are proven to be stable.

Abstract

We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural way and present so called elemental and compound algorithms to generate matchings for a problem instance. We demonstrate the stability of matchings generated by both algorithms, as well as show that the former runs in $O(pn^2)$ time.