Stable Marriage with Multi-Modal Preferences

TL;DR

This paper extends the Stable Marriage problem to multi-modal preferences, allowing agents to rank matches based on multiple criteria, and explores the complexity and stability concepts in this generalized setting.

Contribution

It introduces a multi-modal preference framework for stable marriage, analyzes stability notions, and investigates computational complexity, revealing NP-hardness and connections to Graph Isomorphism.

Findings

Most problems are NP-hard to solve.

Certain cases are computationally tractable.

A surprising link to Graph Isomorphism was found.

Abstract

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the \textsc{Graph Isomorphism} problem.