# Adapting Stable Matchings to Evolving Preferences

arXiv: https://arxiv.org/abs/1907.01375 · HTML: https://mlsanity.com/paper/1907.01375/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2019.

## Built on by (most cited first, 4 of 4)

- [Multiwinner Temporal Voting with Aversion to Change](https://mlsanity.com/paper/2408.11017/) (2024)
- [Online 2-stage Stable Matching](https://mlsanity.com/paper/2207.02057/) (2022)
- [When Agents Break Down in Multiagent Path Finding](https://mlsanity.com/paper/2508.03777/) (2025)
- [DataCupid: Stable Matching Repair for Training Data Acquisition with Delayed Feedback](https://mlsanity.com/paper/2610.12960/) (2026)

## Abstract (arXiv)

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".