Book Chapter Details
Mandatory Fields
Genc, Begum; Siala, Mohamed; Simonin, Gilles; O’Sullivan, Barry; Gao, Xiaofeng; Du, Hongwei; Han, Meng
2017 November
Combinatorial Optimization and Applications: 11th International Conference, COCOA 2017, Shanghai, China, December 16-18, 2017, Proceedings, Part II. Lecture Notes in Computer Science, vol 10628
On the Complexity of Robust Stable Marriage
Springer International Publishing
Optional Fields
Robust Stable Marriage (RSM) Schaefer’s Dichotomy Theorem Stable Marriage problem
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 $$\mathcal {NP}$$ NP -complete, we first introduce a SAT formulation that is $$\mathcal {NP}$$ 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.
Gao, X.; Du, H.; Ha, M.
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