2019
DOI: 10.1016/j.tcs.2018.12.017
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Complexity Study for the Robust Stable Marriage Problem

Abstract: The Robust Stable Marriage problem (RSM) is a variant of the classic Stable Marriage problem in which the robustness of a given stable matching is measured by the number of modifications required to find an alternative stable matching should some pairings break due to an unforeseen event. 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 … Show more

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Cited by 7 publications
(8 citation statements)
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“…They define an (x, y)-supermatch as a stable matching that satisfies the following: If any x agents break up, then it is possible to rematch these x agents so that the new matching is again stable; further, this re-matching must not break up more than y other pairs. Genc et al (2019) showed that deciding whether a (1, 1)-supermatch exists is NP-complete. The main distinguishing features compared to our model are that, using our two regulating screws mentioned above, we can model both moderate changes in the preferences (that is, the input) and moderate differences between the old and the new stable matching (that is, the output).…”
Section: Related Workmentioning
confidence: 99%
“…They define an (x, y)-supermatch as a stable matching that satisfies the following: If any x agents break up, then it is possible to rematch these x agents so that the new matching is again stable; further, this re-matching must not break up more than y other pairs. Genc et al (2019) showed that deciding whether a (1, 1)-supermatch exists is NP-complete. The main distinguishing features compared to our model are that, using our two regulating screws mentioned above, we can model both moderate changes in the preferences (that is, the input) and moderate differences between the old and the new stable matching (that is, the output).…”
Section: Related Workmentioning
confidence: 99%
“…Every (a, b)-supermatch in the I SM is also an (a, b)-supermatch in the I SR and vice versa. Hence, RSR is N P-hard because RSM is N P-hard [6].…”
Section: Robust Stable Roommatesmentioning
confidence: 99%
“…An (a, b)-supermatch is a stable matching such that if any a non-fixed agents (men/women) break-up, it is possible to find another stable matching by changing the partners of those a agents and also changing the partners of at most b others. The previous work on the RSM includes the proposal of the problem, a complexity study, a polynomial-time verification procedure for a given (1, b)-supermatch, and three different models (constraint programming, genetic algorithm, local search) to find the (1, b)-supermatch that minimises b for a given SM instance [6,4]. We investigate in this paper this robustness concept further on a generalised version of the SM, namely the Stable Roommates problem (SR).…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Genc et al [12,13,14] studied robustness of a matching in Stable Marriage. Herein, the robustness of a given stable matching is measured by the number of modifications needed to find an alternative stable matching if some currently matched agent pairs break up.…”
Section: Related Workmentioning
confidence: 99%