Matching With Couples: A Multidisciplinary Survey

Bíró, Péter; Klijn, Flip

doi:10.1142/s0219198913400082

Cited by 33 publications

(34 citation statements)

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“…One of the special features of this program (and its counterparts in other countries, such as Scotland [34]) is that couples may submit joint applications for pair of positions. This feature makes the problem challenging to solve both in theory and practice (see more in a recent survey on this problem [10]). At the end of our paper we illustrate how the Scarf algorithm can be used as a heuristic for solving this problem.…”

Section: Related Literaturementioning

confidence: 99%

“…In most papers on the hospitals residents problem with couples, the possibility of a couple applying to a pair of positions to the same hospital is neglected (see more details on this issue in [10]). However, this possibility is open in many current applications, such as the NRMP [27] or the Scottish resident allocation scheme (SFAS) [9].…”

Section: Paired Applications To the Same Hospitalmentioning

confidence: 99%

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Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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Abstract. In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf's Lemma. Then we describe the interpretation of these results for matching games. Finally we consider an even more general setting where players' contributions in a joint activity may be different. We show that a stable allocation can be found by the Scarf algorithm in this case as well, and we demonstrate the usage of this method for the hospitals resident problem with couples. This problem is relevant in many practical applications, such as NRMP (National Resident Matching Program).

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Section: Related Literaturementioning

confidence: 99%

Section: Paired Applications To the Same Hospitalmentioning

confidence: 99%

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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“…When considering matching problems involving ordinal preferences, the model that most closely resembles our problem is the Hospitals / Residents problem with Couples [6]. This underpins the problem of assigning medical graduates to their first hospital posts on the basis of two-sided preferences, when couples (i.e., pairs of applicants) are able to submit joint preferences over pairs of hospitals, typically in order to be matched to geographically close positions.…”

Section: Related Workmentioning

confidence: 99%

Modelling practical placement of trainee teachers to schools

Cechlárová

Fleiner

Manlove

et al. 2014

Cent Eur J Oper Res

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Several countries successfully use centralized matching schemes for assigning students to study places or fresh graduates to their first positions. In this paper we explore the computational aspects of a possible similar scheme for assigning trainee teachers to schools. Our model is motivated by the situation characteristic for Slovak and Czech education system where each pre-service teacher specializes in two subjects. We show that if the two subjects can be performed independently, then a feasible assignment can be found efficiently by employing network flow techniques, while the requirement to perform both subjects at the same school leads to intractable problems even under several strict restrictions concerning the total number of subjects, partial capacities of schools and the number of acceptable schools each teacher is allowed to list. Finally, we report on an integer programming model for solving the teachers assignment problem and the results of its application to real data.

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“…Several attempts have been made to obtain positive results, such as determining a preference domain for existence (Klaus and Klijn [33]) and considering a large market (Kojima et al [36]). We refer the reader to Biró and Klijn [9] for a comprehensive survey on this topic. We remark here that since the model of matching with couples treats a couple as a single agent instead of two separate agents, there are subtle differences in the stability concepts of the model with couples with those in the model with externalities.…”

Section: Introductionmentioning

confidence: 99%

“…Currently, there are many surveys and books on matching problems. To our knowledge, the list includes books by Roth and Sotomayor [59] and Gusfield and Irving [26] and surveys by Roth [56] and Roth [54] for general two-sided matching problems; Biró and Klijn [9] for matching problems with couples; and in relation to market design, which uses among many theories the theory of two-sided matching to solve real-life problems involving markets, there are Roth [55] and Roth [57]. In contrast, while the literature on matching with externalities has grown recently, to our knowledge, there is no survey that provides an overall perspective on the topic.…”

Section: Introductionmentioning

confidence: 99%

Two-Sided Matching With Externalities: A Survey

Bando

Kawasaki

Muto

2016

JORSJ

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The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.

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Matching With Couples: A Multidisciplinary Survey

Cited by 33 publications

References 50 publications

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Modelling practical placement of trainee teachers to schools

Two-Sided Matching With Externalities: A Survey

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