On the Complexity of Robust Stable Marriage
Abstract
Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We focus on the complexity of finding an (a,b)-supermatch. An (a,b)-supermatch is defined as a stable matching in which if any 'a' (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those 'a' men/women and also the partners of at most 'b' other couples. In order to show deciding if there exists an (a,b)-supermatch is NP-Complete, we first introduce a SAT formulation that is NP-Complete by using Schaefer's Dichotomy Theorem. Then, we show the equivalence between the SAT formulation and finding a (1,1)-supermatch on a specific family of instances.
Keywords
Cite
@article{arxiv.1709.06172,
title = {On the Complexity of Robust Stable Marriage},
author = {Begum Genc and Mohamed Siala and Gilles Simonin and Barry O'Sullivan},
journal= {arXiv preprint arXiv:1709.06172},
year = {2022}
}
Comments
Accepted for publication in COCOA'17