Strategyproof Mechanism for Two Heterogeneous Facilities with Constant Approximation Ratio

Li, Minming; Lu, Pinyan; Yao, Yuhao; Zhang, Jialin

doi:10.24963/ijcai.2020/34

Cited by 20 publications

(9 citation statements)

References 6 publications

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“…The aforementioned works address linear (sum) welfare function. Yuan et al studied non-linear welfare functions (max and min) for building two nonobnoxious facilities [26]; their results have subsequently been strengthened [4,18]. In the present paper, we initiate the study of a non-linear welfare function (min) for building multiple obnoxious facilities.…”

Section: Related Workmentioning

confidence: 86%

The Obnoxious Facility Location Game with Dichotomous Preferences

Li,

Plaxton,

Sinha

2021

Preprint

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We consider a facility location game in which n agents reside at known locations on a path, and k heterogeneous facilities are to be constructed on the path. Each agent is adversely affected by some subset of the facilities, and is unaffected by the others. We design two classes of mechanisms for choosing the facility locations given the reported agent preferences: utilitarian mechanisms that strive to maximize social welfare (i.e., to be efficient), and egalitarian mechanisms that strive to maximize the minimum welfare. For the utilitarian objective, we present a weakly group-strategyproof efficient mechanism for up to three facilities, we give a strongly group-strategyproof mechanism that guarantees at least half of the optimal social welfare for arbitrary k, and we prove that no strongly group-strategyproof mechanism achieves an approximation ratio of 5/4 for one facility. For the egalitarian objective, we present a strategyproof egalitarian mechanism for arbitrary k, and we prove that no weakly groupstrategyproof mechanism achieves a o( √ n) approximation ratio for two facilities. We extend our egalitarian results to the case where the agents are located on a cycle, and we extend our first egalitarian result to the case where the agents are located in the unit square.

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Section: Related Workmentioning

confidence: 86%

The Obnoxious Facility Location Game with Dichotomous Preferences

Li,

Plaxton,

Sinha

2021

Preprint

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“…The setting was later extended by Yuan et al [2016] who considered the min and max functions instead, and they proved upper and lower bounds on the approximation ratio of deterministic strategyproof mechanisms for different objective functions. The upper bound for the min function was later improved [Li et al, 2019a]. Recently, Deligkas et al…”

Section: Heterogeneous Facility Locationmentioning

confidence: 99%

Mechanism Design for Facility Location Problems: A Survey

Chan

Filos-Ratsikas

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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The study of approximate mechanism design for facility location has been in the center of research at the intersection of artificial intelligence and economics for the last decade, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to select a number of locations on which to build a set of facilities, aiming to optimize some social objective based on the preferences of strategic agents, who might have incentives to misreport their private information. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting all the different variants and methodologies, as well as the most interesting directions for future research.

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“…In particular, Chen et al [2020] consider a se ing in which agents have approval preferences over the facilities, similarly to what we do here, and for which the positions of the agents are known. Li et al [2020a] consider a more general metric se ing along the lines of Chen et al [2020], and design a deterministic mechanism which improves upon the result of Chen et al [2020] when the metric is a line. Fong et al [2018] consider a se ing in which the agents have fractional preferences in (0, 1); similarly to us, besides studying the general se ing, they also consider restricted se ings with known preferences or known positions.…”

Section: Related Workmentioning

confidence: 99%

“…Since then, the problem has been extensively studied in the literature of theoretical computer science and arti cial intelligence, with a plethora of interesting variants emerging over the years. Among those, one particularly meaningful variant, which captures several important scenarios, is that of heterogeneous facility location, introduced by Feigenbaum and Sethuraman [2015] and studied notably by Sera no and Ventre [2015,2016], Anastasiadis and Deligkas [2018], Fong et al [2018], Chen et al [2020] and Li et al [2020a]. In this se ing, there are multiple facilities, and each of them plays a di erent role -for example, a library and a basketball court.…”

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confidence: 99%

Heterogeneous Facility Location with Limited Resources

Deligkas¹,

Filos-Ratsikas²,

Voudouris³

2021

Preprint

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We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0, 1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three di erent se ings depending on the level of agent-related information that is public or private. For each se ing, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results.

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Strategyproof Mechanism for Two Heterogeneous Facilities with Constant Approximation Ratio

Cited by 20 publications

References 6 publications

The Obnoxious Facility Location Game with Dichotomous Preferences

The Obnoxious Facility Location Game with Dichotomous Preferences

Mechanism Design for Facility Location Problems: A Survey

Heterogeneous Facility Location with Limited Resources

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