Matching couples with Scarf’s algorithm

Scarf's algorithm [20] provides fractional core elements for NTU-games. Bir�o and Fleiner [3] showed that Scarf's algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with di�erent intensities up to some limits, and the contribution of the agents can also di�er in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called stable allocations. In this paper we apply this solution concept for the Hospitals / Residents problem with Couples (HRC). This is one of the most important general stable matching problems due to its relevant applications, also well-known to be NP-hard. We show that if a stable allocation yielded by the Scarf algorithm turns out to be integral then it provides a stable matching for an instance of HRC, so this method can be used as a heuristic. In an experimental study, we compare this method with other heuristics constructed for HRC that are applied in practice in the American and Scottish resident allocation programs, respectively. Our main �nding is that the Scarf algorithm outperforms all the other known heuristics when the proportion of couples is high

Integer programming methods for special college admissions problems

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones

New and simple algorithms for stable flow problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting-path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocation as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kir\'{a}ly and Pap. The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists

Stable and crossing structures

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Trading networks with frictions

We show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Our model incorporates distortionary frictions such as transaction taxes and commissions. When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative solution concept called trail stability. However, competitive equilibria are generally neither stable nor Pareto-efficient

Rotation-based formulation for stable matching

We introduce new CP models for the many-to-many stable matching problem. We use the notion of rotation to give a novel encoding that is linear in the input size of the problem. We give extra filtering rules to maintain arc consistency in quadratic time. Our experimental study on hard instances of sex-equal and balanced stable matching shows the efficiency of one of our propositions as compared with the state-of-the-art constraint programming approach

Barriers and facilitators to adherence to group exercise in institutionalized older people living with dementia: a systematic review

Objectives Research suggests targeted exercise is important for people living with dementia, especially those living in residential care. The aim of this review was to collect and synthesize evidence on the known barriers and facilitators to adherence to group exercise of institutionalized older people living with dementia. Methods We searched all available electronic databases. Additionally, we searched trial registries (clinicaltrial.gov, and WHO ICTRP) for ongoing studies. We searched for and included papers from January 1990 until September 2017 in any language. We included randomized, non-randomized trials. Studies were not eligible if participants were either healthy older people or people suffering from dementia but not living in an institution. Studies were also excluded if they were not focused on barriers and facilitators to adherence to group exercise. Results Using narrative analysis, we identified the following themes for barriers: bio-medical reasons and mental wellbeing and physical ability, relationships dynamics, and socioeconomic reasons. The facilitators were grouped under the following thematic frames: bio-medical benefits and benefits related to physical ability, feelings and emotions and confidence improvements, therapist and group relationships dynamics and activity related reasons. Conclusions We conclude that institutionalized older people living with dementia, even those who are physically frail, incontinent and/or have mild dementia can demonstrate certain level of exercise adherence, and therefore can respond positively to exercise programs. Tailored, individually-adjusted and supported physical activity, led by a knowledgeable, engaging and well communicating therapist/facilitator improves the adherence to group exercise interventions of institutionalized older people living with dementia