On the Complexity of Robust Stable Marriage

Begum Genc; Mohamed Siala; Gilles Simonin; Barry O'Sullivan

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arXiv · 1709.06172

On the Complexity of Robust Stable Marriage

Begum Genc·Mohamed Siala·Gilles Simonin·Barry O'Sullivan

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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.

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BibTeX RIS

Begum Genc, Mohamed Siala, Gilles Simonin, Barry O'Sullivan. 2017-09-18. On the Complexity of Robust Stable Marriage. https://arxiv.org/abs/1709.06172

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