Adapting Stable Matchings to Evolving Preferences

TL;DR

This paper explores the computational complexity of updating stable matchings in response to changing preferences, proposing incremental algorithms that balance stability and similarity to previous matchings.

Contribution

It formalizes incremental versions of Stable Marriage and Stable Roommates, analyzing their complexity and introducing fixed-parameter tractability results based on preference changes.

Findings

Identifies hardness and tractability in incremental stable matching problems.

Provides fixed-parameter algorithms based on the difference between old and new matchings.

Models the impact of preference changes on computational complexity.

Abstract

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters "degree of change" both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter "distance between old and new stable matching".