Stable Matching with Uncertain Linear Preferences

Aziz, Haris; Bíró, Péter; Gaspers, Serge; Haan, Ronald de; Mattei, Nicholas; Rastegari, Baharak

doi:10.1007/978-3-662-53354-3_16

Cited by 33 publications

(65 citation statements)

References 14 publications

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“…It would be interesting to know whether it is also complete for LOGSNP. 2 However, LOGSNP-hardness for our problem would also imply LOGSNP-hardness for GRAPH ISOMORPHISM (see Theorem 6.5).…”

Section: Open Problems and Conclusionmentioning

confidence: 88%

“…Aziz et al [2] considered a variant of STABLE MARRIAGE, where each agent has a probability for each ordered pair of potential partners. Assigning a probability of 1 to either (x, y) or (y, x) for each x and y, their variant is closely related to the one of Farczadi et al [23] and is shown to be NP-hard.…”

Section: Related Workmentioning

confidence: 99%

“…The idea of introducing such dummy agents is to make sure that each α-layer globally stable matching must include all pairs {u j , w j }, j ∈ [ℓ − α + 1]. However, this is the case only when such matching is stable in the two layers constructed in the NP-hardness proof of Theorem 4.2; we denote these two layers as layers (1) and (2). In the following, we use "· · · " to denote an arbitrary order of the unmentioned agents.…”

Section: Np-hardness For α-Layer Global Stabilitymentioning

confidence: 99%

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Stable Marriage with Multi-Modal Preferences

Chen

Niedermeier

Skowron

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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We introduce a generalized version of the famous STABLE MARRIAGE problem, now based on multimodal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the GRAPH ISOMORPHISM problem.

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Section: Open Problems and Conclusionmentioning

confidence: 88%

Section: Related Workmentioning

confidence: 99%

Section: Np-hardness For α-Layer Global Stabilitymentioning

confidence: 99%

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Stable Marriage with Multi-Modal Preferences

Chen

Niedermeier

Skowron

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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“…Recent work by Aziz et al [Azi+16] looked at the stable matching problem in settings where there is uncertainty about the preferences of the agents. They considered three different models of uncertainty and primarily studied the complexity of computing the stability probability of a given matching and the question of finding a matching that will have the highest probability of being stable.…”

Section: Related Workmentioning

confidence: 99%

Robust and Approximately Stable Marriages Under Partial Information

Menon

Larson

2018

Web and Internet Economics

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We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders either because their true orders are unknown to them or they are unwilling to completely disclose the same. Specifically, we focus on the case where the agents are allowed to submit strict weak orders and we try to address the following questions from the perspective of a market-designer: i) How can a designer generate matchings that are robust-in the sense that they are "good" with respect to the underlying unknown true orders? ii) What is the trade-off between the amount of missing information and the "quality" of solution one can get? With the goal of resolving these questions through a simple and prior-free approach, we suggest looking at matchings that minimize the maximum number of blocking pairs with respect to all the possible underlying true orders as a measure of "goodness" or "quality", and subsequently provide results on finding such matchings.In particular, we first restrict our attention to matchings that have to be stable with respect to at least one of the completions (i.e., weakly-stable matchings) and show that in this case arbitrarily filling-in the missing information and computing the resulting stable matching can give a non-trivial approximation factor (i.e., o(n 2 )) for our problem in certain cases. We complement this result by showing that, even under severe restrictions on the preferences of the agents, the factor obtained is asymptotically tight in many cases. We then investigate a special case, where only agents on one side provide strict weak orders and all the missing information is at the bottom of their preference orders, and show that in this special case the negative result mentioned above can be circumvented in order to get a much better approximation factor; this result, too, is tight in many cases. Finally, we move away from the restriction on weakly-stable matchings and show a general hardness of approximation result and also discuss one possible approach that can lead us to a near-tight approximation bound.

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“…They mostly focus on providing algorithms to find such matchings. Aziz et al considered different models to study this problem and mostly focused on the complexity part of the problem [2]. They define stability probability as the probability of a matching being stable.…”

Section: Introductionmentioning

confidence: 99%

Complexity Study for the Robust Stable Marriage Problem

Genç

Siala

Simonin

et al. 2019

Theoretical Computer Science

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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 partners of those a men/women and the partners of at most b others. We first discuss a model based on independent sets for finding (1, 1)-supermatches. Secondly, in order to show that deciding whether or not there exists a (1, b)-supermatch is N P-complete, we first introduce a SAT formulation for which the decision problem is N P-complete by using Schaefer's Dichotomy Theorem. We then show the equivalence between this SAT formulation and finding a (1, 1)supermatch on a specific family of instances. We also focus on studying the threshold between the cases in P and N P-complete for this problem.

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Stable Matching with Uncertain Linear Preferences

Cited by 33 publications

References 14 publications

Stable Marriage with Multi-Modal Preferences

Stable Marriage with Multi-Modal Preferences

Robust and Approximately Stable Marriages Under Partial Information

Complexity Study for the Robust Stable Marriage Problem

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