Stable matching with preferences derived from a psychological model

Bartholdi, John J.; Trick, Michael A.

doi:10.1016/0167-6377(86)90072-6

Cited by 104 publications

(152 citation statements)

References 7 publications

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“…We have already mentioned their use in [38] for the problem of controlling elections; one could think of other uses in computational aspects of social choice, an important subfield of artificial intelligence. For example, one could ask the questions of whether efficient algorithms for deciding whether a given incomplete preference structure can be extended to a double-peaked profile, similarly to the corresponding questions for single-peaked preferences [3,15]. Another question is whether it is possible to efficiently elicit double-peaked preference orderings using some kind of query operation, e.g.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Therefore, the approximation ratio is at least c+3λ/2 c+λ . As λ grows to infinity, the approximation ratio approaches 3 2 . To generalize the proof to more than two agents, place every other agent on f opt (x) + b on instance x.…”

Section: Lemma 2 On Instance X At Least One Ofmentioning

confidence: 99%

“…For any values of c and b, no truthful-in-expectation mechanism can achieve an approximation lower than 3 2 for the maximum cost.…”

Section: Theoremmentioning

confidence: 99%

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Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

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We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture reallife scenarios and thus complement the well-studied notion of single-peaked preferences. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent's two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, we mainly focus on the case where peaks are equidistant from the agents' locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting, which makes the problem more challenging. As our main contribution, we present a simple truthfulin-expectation mechanism that achieves an approximation ratio of 1 + b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be groupstrategyproof.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Lemma 2 On Instance X At Least One Ofmentioning

confidence: 99%

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Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

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“…The algorithm in [7] relies on the observation that there will always be a pair or participants who are each other's first choice with narcissistic single-peaked preferences. Thus a greedy approach where one such pair is selected and then removed works well.…”

Section: Remarks On Finding a Stable Matching For Single-peaked Prefementioning

confidence: 99%

“…As explained below, these preferences can be succinctly represented. Bartholdi and Trick [7] present a subquadratic time algorithm for stable roommates (and stable matching) with narcissistic, single-peaked preferences. In the narcissistic case, the participants are located at their own ideals.…”

Section: Introductionmentioning

confidence: 99%

Subquadratic Algorithms for Succinct Stable Matching

Künnemann

Moeller

Paturi

et al. 2016

Computer Science – Theory and Applications

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We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give subquadratic algorithms for finding a stable matching in special cases of natural succinct representations of the problem, the d-attribute, d-list, geometric, and single-peaked models. We also present algorithms for verifying a stable matching in the same models. We further show that for d = ω(log n) both finding and verifying a stable matching in the d-attribute and d-dimensional geometric models requires quadratic time assuming the Strong Exponential Time Hypothesis. This suggests that these succinct models are not significantly simpler computationally than the general case for sufficiently large d.

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On the Existence of Stable Roommate Matchings

Chung

2000

Games and Economic Behavior

141

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Stable matching with preferences derived from a psychological model

Cited by 104 publications

References 7 publications

Facility location with double-peaked preferences

Facility location with double-peaked preferences

Subquadratic Algorithms for Succinct Stable Matching

On the Existence of Stable Roommate Matchings

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