Stable Matching Research Articles

An Efficient Matching Game Approach to Association Formation in UAV-Enabled Hierarchical Distributed Learning.

Distributed machine learning has emerged as a promising data processing technology for next-generation communication systems. It leverages the computational capabilities of local nodes to efficiently handle large datasets, creating highly accurate data-driven models for analysis and prediction purposes. However, the performance of distributed machine learning can be significantly hampered by communication bottlenecks and node dropouts. In this article, a novel unmanned aerial vehicle (UAV)-enabled hierarchical distributed learning architecture is proposed to support machine learning applications, e.g., regional monitoring. Multiple UAV receivers (URs) are introduced as wireless relays to improve the communication between the UAV transmitters (UTs) and the cloud server. Our objective is to identify the optimal UT-UR association to maximize the social welfare of the network, which is distinctly different from the existing works that focus on the unilateral profit-maximizing problem. We formulate a two-side many-to-one matching game to model the UT-UR association problem, and a two-phase many-to-one matching algorithm is designed to identify the stable matching. The validity of our proposed scheme is verified through in-depth numerical simulations.

TRIMP: Three-Sided Stable Matching for Distributed Vehicle Sharing System using Stackelberg Game

TRIMP: Three-Sided Stable Matching for Distributed Vehicle Sharing System using Stackelberg Game

On a many-sided matching problem with mixed preferences

Motivated by recent results on lexicographic and cyclic preferences, we present new sufficient conditions for the existence of stable matching in many-sided matching problems. Here, our focus shifted towards integrating the two-sided matching problem, characterized by reciprocal preferences, with the many-sided matching problem, which involves cyclic preferences. In particular, we show that one of the configurations presented recently by Zhang and Zhong for three-sided matching problems can be generalized to more dimensions. In our setting, the preferences are cyclic and, in the case of all but two pairs of consecutive sets of agents, also reciprocal, which generalizes the three-set setting of Zhang and Zhong. Our approach can be also applied to generalize the problems with any system of cyclic preferences for which the existence of a stable matching is guaranteed.

Improvement of Energy Consumption in Fog Computing Via Task Offloading

The role of fog computing is to lessen the burden of Cloud and device computing. The purpose of this project is to solve the energy consumption and latency issues in the IoT 6G device as well as propose an approach to match the fog nodes with the IoT devices in task-offloading. This project implemented the Gale Shapley Stable Marriage Matching Game with a task-offloading energy efficiency technique. One-to-one matching is applied, in four fog nodes and four IoT devices according to the size of the task in IoT devices and energy in fog nodes. Simulation results prove that the proposed approach improves energy consumption and latency by 36.15% and 37.5% respectively.

Project on salary classification

In this project, The results use three different machine learning algorithms to approach salary classification. The analyzed data used many different variables such as education level, age, and work-class to label each person into two categories, one with a salary greater than 50k and the other with a salary less than or equal to 50k. First of all, this work uses a single decision tree model to visualize data because it is more concise and understandable, and then by using the support vector machine method, the result becomes more accurate. After building two different models, The accuracy was found to be about 86.32%, which is relatively high and reliable. However, higher accuracy may be more persuasive. So, this project uses another model which is the random forest model. This algorithm is considered a highly accurate method because of the number of decision trees that participated. This model explained 87.03% of the accuracy of my result. According to my models, if a person desires a wage increase, that person should do his best to improve his education level, and he needs to have a stable marriage situation and be able to start his own business as much as possible between the ages of 20 to 60.

Airborne Internet: An Ultradense LEO Networks Empowered Satellite-to-Aircraft Access and Resource Management Approach

With the rapid development of low earth orbit (LEO) satellite technologies and constellation projects (like Starlink, OneWeb), the ongoing ultra-dense LEO satellite networks can provide an efficient solution to ubiquitous connection of aircraft. It is urgent to design the ultra-dense LEO network enabled satellite-to-aircraft communication for in-cabin users with high-speed Internet connectivity requirements. In this paper, we investigate the resource scheduling of ultra-dense LEO network enabled satellite-to-aircraft communication and the in-cabin communication inside aircraft in civil aviation. First, we adopt the Lyapunov optimization framework to tackle the high dynamic and fast mobility of satellites and aircraft. For the satellite-to-aircraft access and subchannel assignment, we propose a dynamic access and subchannel allocation algorithm based on matching theory, which can converge to a stable matching within a finite iterations. To guarantee customized needs of in-cabin users, we propose a power control algorithm based on the successive convex approximation technology to optimize the power allocation of satellites on each subchannel and the transmit power of aircraft for each in-cabin user, which is proven to obtain a saddle point or a local minimum with low complexity. Extensive simulations have been carried out to validate the effectiveness of the proposed resource allocation method.

Z-mixture three-sided stable matching in seaborne coal exchange with cooperative partners and heterogeneous relationships among attributes

Three-sided matching decision-making (TSMDM) problems are widespread in the real world. In practical TSMDM scenarios, two of the three sides collaborate, and matching objects on each side give their assessments about matching objects on another side according to multi-attributes with heterogeneous relationships. Given its advantages in describing uncertain information and its credibility, Z-mixture number is utilized to represent assessment from matching object, which offers continuous variable or discrete variable leaves matching objects free to choose. Based on this, this paper constructs a multiple attribute TSMDM model with Z-mixture numbers to deal with such situations. First, the prioritized interactive aggregation operator is proposed to aggregate Z-mixture numbers, which takes the prioritization and various interrelationships among the input arguments into account. Second, a weight determination model based on maximal deviation and fuzzy measure is proposed to determine the importance of attribute coalitions. Furthermore, a three-sided stable matching model with cooperation which pursues the maximization of overall satisfaction of matching objects by considering the stable matching conditions is constructed to obtain the stable matching among matching objects. Lastly, a case for the matching of supply, transportation and demand in seaborne coal exchange is presented to validate the rationality and practicability of the proposed method. Compared with the existing studies, the advantages and effectiveness of the proposed method are demonstrated.

Green technology investment selection with carbon price and competition: One-to-many matching structure

With the deterioration of natural resources and the aggravation of environmental pollution, there is a growing imperative to implement industrial green reform through green technology investment (GTI). This paper constructs a nonlinear dual-objective function by drawing on the theory of two-sided matching under the carbon trading regulation, aiming to examine GTI selection decisions made by two oligarchic manufacturers (i.e., oligarchs) and a monopoly supplier (i.e., supplier). The supplier offers multiple green technologies, while oligarchs rack their brains to buy green technologies in an attempt to exploit their social, economic and environmental potentials. Available technologies vary in terms of their environmental efficiency and cost. Then, a two-sided matching mechanism is constructed to explore the availability of stable matchings and examine the impacts of the carbon price and green improvement coefficient on GTI, product pricing decisions and profits within a competitive environment. Finally, a Monte-Carlo experiment is designed to analyze the impact of uncertain market risks on supplier's decisions. The results show that there is a two-sided matching mechanism that enables oligarchs and suppliers to obtain stable matching solution sets. Higher carbon prices lead to higher product prices, lower market demand, and improved environmental performance. Product price and market demand are positively correlated with investment volumes of oligarchs themselves and negatively correlated with those of their competitors. Investment risk has a certain negative impact on suppliers' profitability.

A stakeholder decision and road-network-based deterministic model to simulate material flows in regional scale industrial symbioses

Industrial Symbiosis (IS) projects are today well known for their contribution to sustainable development. Designing IS projects implies modelling the quantity of material flows between economic components (ECs), in particular to evaluate the environmental and economic gains obtained through more material circularity and use efficiency. The Industrial Symbiosis concept is now being applied to activities distributed over territories much wider than industrial parks. For such setups, existing modelling methods are becoming strained by the number of economic components involved, their dissemination within heterogeneous landscapes and the resulting complexity of the exchanges. In this paper, we propose a generic, spatially explicit simulation model based on stakeholder decision rules to study regional scale flows quantification between ECs in n-n IS networks. Our approach introduces the use of the Gale-Shapley stable matching algorithm for addressing the many-to-many supply-demand matching problem. The method is deterministic and provides stable solutions that optimise the individual objectives of the ECs. A second introduction considers using transport cost along the road network among the decision rules when ECs preferences are ordered. This solves the issue of correctly estimating travel distance in heterogeneous landscapes where it can be significantly different to the distance as the crow flies. We tested the model with the implementation of two real and concrete case studies related to the bioeconomy of a tropical island: (i) collective storage of fodder and (ii) co-composting platforms. The outputs of the model make it possible to compare scenarios based on EC satisfaction relative to supply and demand as well as the total distance travelled along the road network. Finally, we discuss the limitations and genericity of the model to explore diverse industrial symbiosis projects.

Energy supply-demand interaction model integrating uncertainty forecasting and peer-to-peer energy trading

With the penetration of large amounts of renewable energy resources into energy system, the interaction between energy supply and demand has become more complex and diverse. The complexity and diversity make it more difficult to achieve real-time, efficient, accurate and dynamic matching of energy supply and demand. Therefore, the study proposes an efficient energy supply-demand interaction model integrating uncertainty forecasting and peer-to-peer energy trading. First, to reduce the impact of supply and demand uncertainty on the energy supply and demand matching, gate recurrent unit and long short-term memory models are used to forecast power generation and consumption. Then, based on the results of forecasting, an energy supply-demand interaction model is proposed to assist the energy system in achieving dynamic energy supply-demand matching. Finally, the effectiveness of the proposed energy supply-demand interaction model has been verified through experiments. The proposed energy supply-demand interaction model that considers supply and demand uncertainty and economic benefits helps to better achieve transparent, efficient, stable, and sustainable matching of supply and demand. This study can reduce the impact of supply and demand uncertainty by forecasting power generation and consumption. In addition, this study considers the preferences of prosumers in their trading, reduces the cost of electricity for prosumers, and realizes the profitability of multiple subjects involved in the trading.

An Optimal Solution for the Stable Marriage Problem using Particle Swarm Optimization and Firefly Algorithms

This paper proposes a hybrid approach to solving the Stable Marriage Problem (SM) by fusing ideas from the firefly optimization (FA) and particle swarm optimization (PSO) methods. It is commonly known that there is always at least one stable matching exists for each instance. The conventional Gale-Shapley formula, on the other hand, produces a partnership that either strongly favours men over women or vice versa. Our proposed approach uses a hybrid optimization technique to solve the problem of stable marriage by providing the best possible pairs. The fitness function is defined here on the basis of the type of optimal solution. To categorize the kind of optimal solution two score functions are defined in this work.The proposed research uses FA to explore the undiscovered solution space, in contrast to our suggested technique which is based on PSO. The particles are then subjected to a dynamic adaptation mechanism for certain parameters, which gradually raises their values as part of the process of determining the velocities. The generation number of the swarm is the dynamic value for these parameters. These two parameters will use their predetermined values for the remaining particles in the swarm. It's worth noting that the dynamic values will be used by different particles in each generation. The proposed method is found to be superior than the conventionaltechniques in terms of the performance scores representing the quality of matching for different types of optimal solutions.

The Stable Marriage Problem and Sudoku

Summary Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That’s right—your path to coupled life isn’t through Tinder; it’s through Sudoku! Read our fabulous paper, where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor.

Power Allocation Stable Matching User Pairing (SMUP) in NOMA with SWIPT

Power Allocation Stable Matching User Pairing (SMUP) in NOMA with SWIPT

Online 2-stage stable matching

We focus on an online 2-stage problem, motivated by the following situation: consider a system where students shall be assigned to universities. There is a first round where some students apply, and a first (stable) matching M1 has to be computed. However, some students may decide to leave the system (change their plan, go to a foreign university, or to some institution not in the system). Then, in a second round (after these deletions), we shall compute a second (final) stable matching M2. As it is undesirable to change assignments, the goal is to minimize the number of divorces/modifications between the two stable matchings M1 and M2. Then, how should we choose M1 and M2? We show that there is an optimal online algorithm to solve this problem. In particular, thanks to a dominance property, we show that we can optimally compute M1 without knowing the students that will leave the system. We generalize the result to some other possible modifications in the input (i.e., in the sets of students and/or open positions in universities). We also tackle the case of more stages, showing that no competitive (online) algorithm can be achieved for the considered problem as soon as there are 3 stages.

The online dating effect: Where a couple meets predicts the quality of their marriage

Drawing on social ecology theory, this study compares the marriages of people who met in online dating to those who were introduced offline. A survey was administered to a sample of 923 married U.S. adults, roughly half of whom met their spouse in online dating. The results provided evidence of an online dating effect, with online daters reporting less satisfying and stable marriages than offline daters. Importantly, effect sizes were modest, and means showed marital quality was still relatively high in both groups. Effects did not vary based on individual differences, but they could be explained by external pressures (i.e., societal marginalization and geographic distance) on participants’ relationships. Participants who used online dating confronted greater societal marginalization and geographic distance, which affected their disclosure and perceptions of network approval and, in turn, the satisfaction and stability of their marriages. Implications for research on online dating and marriage are discussed.

Stable matching with multilayer approval preferences: Approvals can be harder than strict preferences

We study stable matching problems where agents have multilayer preferences: There are ℓ layers each consisting of one preference order for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences, establishing four multilayer adaptations of classical notions of stability. We follow up on their work by analyzing the computational complexity of stable matching problems with multilayer approval preferences, which leads to problems that are incomparable to the previously studied ones. We consider eleven stability notions derived from three well-established stability notions for stable matchings with ties and the four adaptations proposed by Chen et al. For each stability notion, we show that the problem of finding a stable matching is either polynomial-time solvable or NP-hard. Furthermore, we examine the influence of the number of layers and the desired “degree of stability” on the problems' complexity.

Moscow-Havana Relations. Continuities of the Past in an Asymmetric Triangle

This article examines Moscow-Havana relations from the Russian Revolution in November 1917 to the present to inform debates on (1) continuities from history impacting contemporary Russian foreign policy; (2) the assumption that before the Cuban Revolution of 1959 Moscow suffered from ‘geographical fatalism’ concerning Latin America; (3) contemporary Moscow-Havana relations; and (4) asymmetrical triangles in international relations. A rigorous historical qualitative analysis of primary and secondary sources is used to examine the periods November 1917–January 1959, 1959–1991, and 1992 onwards. Both realism and constructivism are utilised throughout. Acting as a bridge between historical research and the study of international relations this article posits that in each period Moscow and Havana’s individual relationships with Washington were key to Moscow-Havana relations. Continuities from history for the contemporary relationship are to both the November 1917–January 1959 era and the 1959–1991 period. Consequently, since 1917 an asymmetrical triangle comprising Moscow, Havana, and Washington has principally existed. Aiding its originality this article postulates that a ‘stable marriage’ with the most powerful member of an asymmetrical triangle (Washington) being the ‘pariah’ can become the norm. This finding has resonance for global politics and the behaviour of regional superpowers within their respective region.

Application of Two-sided Matching Theory in Financing of Small and Medium-sized Enterprises

The nation's small and medium-sized businesses (also known as SMEs) constitute an essential component of the economy as a whole; yet, many companies are right now struggling to obtain adequate funding. On the one hand, increasing the amount of capital invested in venture firms by venture capitalists can considerably promote the development of venture enterprises. On the other hand, venture capitalists look for businesses in which they may invest, with the goal of achieving high levels of success and gaining substantial profits. Therefore, in order to make a reasonable and stable match between venture capitalists and SMEs according to their respective preference lists, this paper makes use of the Gale-Shapley algorithm, which is part of the two-sided matching theory. This helps improve cooperation efficiency and maximizes the benefits for both parties. In addition to that, based on the algorithm, this article offers some policy recommendations for the venture capital market in China.

Digital Twin-Enabled Computation Offloading in UAV-Assisted MEC Emergency Networks

With the advantage of flexible deployment in all terrains, unmanned aerial vehicles (UAV) equipped with lightweight computing module can bring mobile edge computing (MEC) service closer to both survivors and rescuers in disaster scenarios. However, the mismatch between the sudden computing demands of mobile users (MUs) and limited computation resources of UAVs cannot meet the high delay sensitivity requirements for computation offloading. In this letter, we aim to exploit the real-time prediction capability of digital twin (DT) to optimize the offloading decision under uncertainty. Considering the mapping deviations between the DT and the real network status, we formulate the computation offloading problem as an online matching problem in uncertain bipartite graph. Furthermore, we transform this matching problem into a multi-armed bandits (MAB) problem and finally solve it through an upper confidence bound (UCB)-based stable matching algorithm. The simulation results prove the superiority of our proposed method.

The Neuromuscular Portal and Match: Working Toward a More Fair, Equitable, and Transparent Process.

Prior to 2021, the neuromuscular medicine fellowship application process suffered from non-standardized timelines and substantial variability. To rectify this, the American Association of Neuromuscular & Electrodiagnostic Medicine (AANEM) established a standardized application timeline and an online application portal in 2020-2021, followed by the introduction of a partial match process. In 2021-2022, AANEM launched a traditional, binding, two-way match system for fellowship positions allocation based on the Gale-Shapley stable matching algorithm. Surveys assessing perceptions of fairness in the application portal and match process were dispatched to applicants and program directors following the 2021 and 2022 recruitment cycles. In the 2020-21 cycle, 90% of program directors and 95% of applicants affirmed the standardized timeline benefited applicants. However, 57% of applicants deemed the process as unfair. All programs and most applicants (58%) favored a transition to a two-way match. The implementation of the two-way match in 2021-22 attracted participation from 97% of programs, with 80% of applicants and 95% of programs viewing the process as fair to applicants. A significant majority of both applicants (86%) and programs (94%) supported maintaining the standardized timeline and two-way match. We advocate for the universal adoption of the AANEM Match for neuromuscular fellowship recruitment and a standardized fellowship application timeline across all neurologic specialties to promote transparency, fairness, and equity for applicants.