Theory of and Experiments on Minimally Invasive Stability Preservation in Changing Two-Sided Matching Markets

TL;DR

This paper extends theoretical understanding and provides empirical evidence on efficiently maintaining stable matchings in dynamic two-sided markets, highlighting practical properties and computational complexities.

Contribution

It introduces new problems related to incremental stable matchings, analyzes their complexity, and simplifies change scenarios, complemented by extensive empirical studies.

Findings

Allowing a few blocking pairs reduces the difference between old and new matchings.

New problem variants are computationally complex, but some equivalences simplify analysis.

Empirical results suggest practical benefits of minimal changes in dynamic settings.

Abstract

Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous practically useful properties. Our theoretical extensions include the study of new problems (that is, incremental variants of Almost Stable Marriage and Hospital Residents), focusing on their (parameterized) computational complexity and the equivalence of various change types (thus simplifying algorithmic and complexity-theoretic studies for various natural change scenarios). Our experimental findings reveal, for instance, that allowing the new matching to be blocked by a few pairs significantly decreases the necessary differences between the old and the new stable matching.