Ex-post Stability under Two-Sided Matching: Complexity and Characterization
Abstract
A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A prominent open problem is characterizing ex-post stability and establishing its computational complexity. We investigate the computational complexity of testing ex-post stability. Our central result is that when either side has ties in the preferences/priorities, testing ex-post stability is NP-complete. The result even holds if both sides have dichotomous preferences. On the positive side, we give an algorithm using an integer programming approach, that can determine a decomposition with a maximum probability of being weakly stable. We also consider stronger versions of ex-post stability (in particular robust ex-post stability and ex-post strong stability) and prove that they can be tested in polynomial time.
Cite
@article{arxiv.2411.14821,
title = {Ex-post Stability under Two-Sided Matching: Complexity and Characterization},
author = {Haris Aziz and Gergely Csáji and Péter Biró},
journal= {arXiv preprint arXiv:2411.14821},
year = {2026}
}