Complexity Study for the Robust Stable Marriage Problem

Genç, Begüm; Siala, Mohamed; Simonin, Gilles; O’Sullivan, Barry

doi:10.1016/j.tcs.2018.12.017

Cited by 7 publications

(8 citation statements)

References 18 publications

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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%

Adapting Stable Matchings to Evolving Preferences

Bredereck

Knop

Luo

et al. 2020

AAAI

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Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing “incrementalized versions” of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters “degree of change” both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter “distance between old and new stable matching”.

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Section: Related Workmentioning

confidence: 99%

Adapting Stable Matchings to Evolving Preferences

Bredereck

Knop

Luo

et al. 2020

AAAI

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“…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%

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An Approach to Robustness in the Stable Roommates Problem and Its Comparison with the Stable Marriage Problem

Genç

Siala

Simonin

et al. 2019

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Recently a robustness notion for matching problems based on the concept of a (a, b)-supermatch is proposed for the Stable Marriage problem (SM). In this paper we extend this notion to another matching problem, namely the Stable Roommates problem (SR). We define a polynomial-time procedure based on the concept of reduced rotation poset to verify if a stable matching is a (1, b)supermatch. Then, we adapt a local search and a genetic local search procedure to find the (1, b)-supermatch that minimises b in a given SR instance. Finally, we compare the two models and also create different SM and SR instances to present empirical results on the robustness of these instances.

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“…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%

Adapting Stable Matchings to Evolving Preferences

Bredereck¹,

Knop²,

Luo³

et al. 2019

Preprint

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Adaptivity to changing environments and constraints is key to success in modern society. We address this view by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be close to the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters "degree of change" both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, among the latter being one of the few fixed-parameter tractability results (exploiting the parameter "distance between old and new stable matching") in the context of computationally hard stable matching problems. * Supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement numbers 677651. † Supported by the DFG, project MaMu (NI 369/19). ‡ Supported by CAS-DAAD Joint Fellowship Program for Doctoral Students of UCAS. Work done while with TU Berlin. 1 The naming "Incremental" is inspired by work in the context of clustering and information retrieval [6].

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Complexity Study for the Robust Stable Marriage Problem

Cited by 7 publications

References 18 publications

Adapting Stable Matchings to Evolving Preferences

Adapting Stable Matchings to Evolving Preferences

An Approach to Robustness in the Stable Roommates Problem and Its Comparison with the Stable Marriage Problem

Adapting Stable Matchings to Evolving Preferences

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