Near-Feasible Stable Matchings with Budget Constraints

Kawase, Yasushi; Iwasaki, Atsushi

doi:10.24963/ijcai.2017/35

Cited by 13 publications

(16 citation statements)

References 36 publications

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“…Kell and Panigrahi (2016) considered Online Budgeted Allocation with General Budgets, where offline agents have multiple tiers of budget constraints forming a laminar structure. There are several interesting matching problems with constraints with applications in the AI and game theory community, which studied the stability and strategic issues, see, e.g., (Kawase and Iwasaki 2018;Goto et al 2016;Kurata et al 2017;Aziz et al 2018).…”

Section: Additional Related Workmentioning

confidence: 99%

A Unified Approach to Online Matching with Conflict-Aware Constraints

Shi

Cheng

et al. 2019

AAAI

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Online bipartite matching and allocation models are widely used to analyze and design markets such as Internet advertising, online labor, and crowdsourcing. Traditionally, vertices on one side of the market are fixed and known a priori, while vertices on the other side arrive online and are matched by a central agent to the offline side. The issue of possible conflicts among offline agents emerges in various real scenarios when we need to match each online agent with a set of offline agents.For example, in event-based social networks (e.g., Meetup), offline events conflict for some users since they will be unable to attend mutually-distant events at proximate times; in advertising markets, two competing firms may prefer not to be shown to one user simultaneously; and in online recommendation systems (e.g., Amazon Books), books of the same type “conflict” with each other in some sense due to the diversity requirement for each online buyer.The conflict nature inherent among certain offline agents raises significant challenges in both modeling and online algorithm design. In this paper, we propose a unifying model, generalizing the conflict models proposed in (She et al., TKDE 2016) and (Chen et al., TKDE 16). Our model can capture not only a broad class of conflict constraints on the offline side (which is even allowed to be sensitive to each online agent), but also allows a general arrival pattern for the online side (which is allowed to change over the online phase). We propose an efficient linear programming (LP) based online algorithm and prove theoretically that it has nearly-optimal online performance. Additionally, we propose two LP-based heuristics and test them against two natural baselines on both real and synthetic datasets. Our LP-based heuristics experimentally dominate the baseline algorithms, aligning with our theoretical predictions and supporting our unified approach.

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Section: Additional Related Workmentioning

confidence: 99%

A Unified Approach to Online Matching with Conflict-Aware Constraints

Shi

Cheng

et al. 2019

AAAI

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“…The environment that groups students into types has also been studied in the literature of school choice problems (Abdulkadiroglu, 2005;Abdulkadiroglu & Sönmez, 2003;Ehlers, Hafalir, Yenmez, & Yildirim, 2014;Kojima, 2012;Yenmez, Yildirim, & Hafalir, 2013). Recently, a similar model was considered (Kawase & Iwasaki, 2017. The goals of their works (approximate matching) are different from ours.…”

Section: Introductionmentioning

confidence: 96%

“…While our model is more general, they concentrate on additive utilities of colleges. First, they relax feasibility such that a college is allowed to exceed its budget limit to some extent (Kawase & Iwasaki, 2017). Second, they relax pairwise stability such that a college does not form a blocking pair unless its utility increases more than a certain factor α (Kawase & Iwasaki, 2018).…”

Section: Introductionmentioning

confidence: 99%

Weighted Matching Markets with Budget Constraints

Ismaili¹,

Hamada²,

Zhang³

et al. 2019

jair

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We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is SigmaP2-complete: NPNP-complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets.

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“…Matching with constraints has been prominent across computer science and economics since the seminal work by [19]. In many applications, various constraints are often imposed on an outcome, e.g., type-specific quotas on hospitals to assign several different types (skills) of doctors [1], budget constraints on hospitals to limit the total amount of wages [2,20,21]. The current paper exactly covers these complicated constraints and further generalizes them.…”

Section: Introductionmentioning

confidence: 99%

Approximately Stable Matchings with General Constraints

Kawase,

Iwasaki

2019

Preprint

Self Cite

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This paper focuses on two-sided matching where one side (a hospital or firm) is matched to the other side (a doctor or worker) so as to maximize a cardinal objective under general feasibility constraints. In a standard model, even though multiple doctors can be matched to a single hospital, a hospital has a responsive preference and a maximum quota. However, in practical applications, a hospital has some complicated cardinal preference and constraints. With such preferences (e.g., submodular) and constraints (e.g., knapsack or matroid intersection), stable matchings may fail to exist. This paper first determines the complexity of checking and computing stable matchings based on preference class and constraint class. Second, we establish a framework to analyze this problem on packing problems and the framework enables us to access the wealth of online packing algorithms so that we construct approximately stable algorithms as a variant of generalized deferred acceptance algorithm. We further provide some inapproximability results.

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Near-Feasible Stable Matchings with Budget Constraints

Cited by 13 publications

References 36 publications

A Unified Approach to Online Matching with Conflict-Aware Constraints

A Unified Approach to Online Matching with Conflict-Aware Constraints

Weighted Matching Markets with Budget Constraints

Approximately Stable Matchings with General Constraints

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