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 \(\mathcal {NP}\)-complete, we first introduce a SAT formulation that is \(\mathcal {NP}\)-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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Acknowledgements
This research has been funded by Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.
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Genc, B., Siala, M., Simonin, G., O’Sullivan, B. (2017). On the Complexity of Robust Stable Marriage. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_30
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DOI: https://doi.org/10.1007/978-3-319-71147-8_30
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