Faster and simpler approximation of stable matchings

TL;DR

This paper introduces a faster, simpler 3/2-approximation algorithm for stable matchings that operates in linear time and extends to many-to-many scenarios, improving efficiency over previous methods.

Contribution

It presents a new linear-time approximation algorithm for stable matchings with a simpler design and analysis, extending to many-to-many matchings.

Findings

Runs in O(m) time, faster than previous algorithms.

Achieves a 3/2 approximation ratio.

Extends to many-to-many matching scenarios.

Abstract

We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and $m$ is the total length of the preference lists in a given instance. Also the algorithm and the analysis are much simpler. We also give the extension of the algorithm for the many-to-many setting. (This is the version of the paper from March 2011)