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On the Complexity of Robust Stable Marriage


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 others. In order to show deciding if there exists an (a, b)-supermatch is N P-complete, we first introduce a SAT formulation that is N P-complete by using Schae-fer'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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hal-01689884 , version 1 (22-01-2018)


  • HAL Id : hal-01689884 , version 1


Begum Genc, Mohamed Siala, Gilles Simonin, Barry O ' Sullivan. On the Complexity of Robust Stable Marriage. COCOA 2017 11th Annual International Conference on Combinatorial Optimization and Applications , Dec 2017, Shanghai, China. ⟨hal-01689884⟩
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