A Map of Diverse Synthetic Stable Roommates Instances

TL;DR

This paper introduces a visual map of synthetic Stable Roommates instances using a new similarity measure, enabling better understanding of instance diversity and aiding experimental analysis in stable matching problems.

Contribution

It presents a polynomial-time pseudometric for measuring SR instance similarity and creates a visual map of 460 synthetic instances from diverse statistical cultures.

Findings

The map visualizes the diversity of synthetic SR instances.

Experiments demonstrate the map's usefulness for analysis.

The framework extends to Stable Marriage instances.

Abstract

Focusing on Stable Roommates (SR) instances, we contribute to the toolbox for conducting experiments for stable matching problems. We introduce a polynomial-time computable pseudometric to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar to each other. Subsequently, we conduct several exemplary experiments and depict their results on the map, illustrating the map's usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures. Lastly, to demonstrate that our framework can also be used for other matching problems under preference, we create and analyze a map of Stable Marriage instances.