Two-sided Matching Problem Research Articles

Fair resource optimization for cooperative non-terrestrial vehicular networks

Non-terrestrial networks aim to extend wireless communications capabilities beyond traditional terrestrial infrastructure by utilizing various platforms such as satellites, high-altitude platform stations (HAPS), and unmanned aerial vehicles to provide global or localized coverage. However, improving data rates in non-terrestrial cooperative communications (NTCC) networks presents unique challenges, necessitating innovative solutions. This paper presents a novel approach to enhance the request–response ratio (RRR) of NTCC in time asynchrony. By leveraging the advantages of HAPS, such as wide coverage, high altitude, and flexible deployment, we aim to optimize the performance of NTCC networks. We formulate an optimization problem considering the simultaneous connection between the HAPS and ground users, power distribution, and decoding order. The joint optimization problem is formulated as non-convex-non-linear and is also NP-hard, making it very challenging to obtain a globally optimal solution. To reduce the complexity of the problem and make it more tractable, we decouple it into subproblems and achieve an efficient solution in two steps. In the first step, we use the Gale–Shapley algorithm to solve the many-to-many two-sided matching problem of HAPS user terminal association, given the fixed decoding and power allocation. Then, we solve the decoding order and power allocation problem using the Dinkeback-like algorithm, given the optimal association in the second step. Our proposed method iteratively updates the preference lists, mitigating interference among HAPS and enhancing overall system performance. Through extensive simulations, we demonstrate that implementing our proposed schemes achieves high RRR compared to benchmark schemes. Additionally, when temporal asynchrony is employed alongside our approach, there is an increase in the overall performance obtained from the process.

Stable Matchings in Practice: A Constraint Programming Approach

We study a practical two-sided matching problem of allocating children to daycare centers, which has significant social implications. We are cooperating with several municipalities in Japan and our goal is to devise a reliable and trustworthy clearing algorithm to deal with the problem. In this paper, we describe the design of our new algorithm that minimizes the number of unmatched children while ensuring stability. We evaluate our algorithm using real-life data sets, and experimental results demonstrate that our algorithm surpasses the commercial software that currently dominates the market in terms of both the number of matched children and the number of blocking coalitions (measuring stability). Our findings have been reported to local governments, and some are considering adopting our proposed algorithm in the near future, instead of the existing solution. Moreover, our model and algorithm have broader applicability to other important matching markets, such as hospital-doctor matching with couples and school choice with siblings.

Multi-stage probabilistic linguistic matching method with the screening mechanism and individual preference relationship fusion

Considering the diversification of transaction information and complexity of matching environment, the original information with the language tendency plays an important role. Thus, under this circumstance, this paper gives a matching decision-making system under the probabilistic linguistic environment so as to improve the matching efficiency and quality. First, this paper demonstrates the multi-stage two-sided matching problem and illustrates the system frame. Then, for the multiple indicators, a probabilistic linguistic integrated cloud Bayesian network is constructed to present the dependency relationship, and determine the corresponding probability. It is known that the accuracy of agents’ preference information acts on the stability of final matching results, which may involve the strong ranking, agents’ psychological preferences and personal interests, etc. Thus, the improved ORESTE (organísation, rangement et Synthèse de données relarionnelles, in French) method is introduced to derive strong ranking and determine preference, indifference, and incomparability relation (PIR). Furthermore, this paper constructs the dynamic two-sided matching model considering the screening effect. Finally, a case study in second-hand house transaction is used to demonstrate the matching process. Simulation and comparison analysis validate its feasibility and effectiveness.

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.

Two-sided Matching Theory and Its Application in E-commerce Environment

Since the turn of the 21st century, China's e-commerce has exhibited a rapid development trend of diversification and internationalization. The number of users on e-commerce platforms has increased significantly, the network infrastructure has continued to improve, the number of cross-border e-commerce transactions has risen steadily, and the two-sided matching problem inherent to it has become a topic of increasing interest. Each agent in the e-commerce market may have several attributes, and e-commerce market matches are sophisticated and multi-variant. Thus, the development of a suitable matching mechanism is crucial for the market's effective operation. This paper explores the prior literature on two-sided matching theory and its application in the e-commerce sector, combs its research progress, summarizes the advantages and disadvantages of present matching approaches, and anticipates the growth of application domains in the future.

Two-way referral cooperative hospital selection with uncertain information: A two-sided matching decision-making approach

To better rationalize the allocation of medical resources and improve the efficiency of medical resource utilization, researchers have focused on the problem of two-way referral cooperation among hospitals. The selection of an appropriate referral hospital constitutes a crucial aspect of a two-way referral system, which affects the quality of patient treatment and the financial outcome of hospital operations. Within this context, this study regards the collaborative referral hospital selection problem as a two-sided matching decision-making process. Given the hesitance and bounded rationality of decision-makers, a novel two-sided matching framework is developed that integrates hesitant fuzzy linguistic term sets and regret theory to more accurately reflect real-world conditions. Specifically, evaluation information is converted to hesitant fuzzy linguistic term sets via context-free grammar, and new utility functions are introduced to calculate the utility value, regret utility, and rejoice utility through the hesitant degree and score function. Furthermore, an optimization model for calculating the criteria weight is established based on the Euclidean distance and maximization deviation method. Ultimately, the matching satisfaction degree is determined, and a biobjective programming model that maximizes the overall matching satisfaction degree is formulated and solved. The results from experiments and analysis indicate that the proposed framework produces optimal and stable matching solutions, thereby providing a useful reference for hospitals seeking satisfactory referral partners. Moreover, this model could be extended to address large-scale two-sided matching problems or to refine the referral hospital selection problem by considering individual patient needs.

A two-sided matching decision method based on interval triangular fuzzy sets

The research work on two-sided matching decision problem considering interval triangular fuzzy information is very scarce, and it needs to be further studied. Based on this, this paper proposes a two-sided matching model based on interval triangular fuzzy sets, with the background of the two-sided matching problem in the interval triangular fuzzy set environment. Firstly, the theory of two-sided matching and interval triangular fuzzy sets is given; Secondly, the comprehensive mean value formula is defined, and the interval triangular fuzzy evaluation matrix is transformed into the comprehensive mean value matrix by using the comprehensive mean value formula; Thirdly, a two-sided matching model is built with the goal of maximizing the satisfaction of each subject; Finally, the feasibility and effectiveness of the proposed method are verified by examples of investment fund institutions and financing enterprises.

Centralized refugee matching mechanisms with hierarchical priority classes

This study examines the refugee reallocation problem by modeling it as a two-sided matching problem between countries and refugees. Based on forced hierarchical priority classes, I study two interesting refugee matching algorithms to match refugees with countries. Axioms for fairness measures in resource allocation are presented by considering the stability and fairness properties of the matching algorithms. Two profiles are explicitly modeled---country preferences and forced prioritization of refugee families by host countries. This approach shows that the difference between the profiles creates blocking pairs of countries and refugee families owing to the forced hierarchical priority classes. Since the forced priorities for countries can cause certain refugees to linger in a lower priority class in every country, this study highlights the importance of considering refugees' preferences. It also suggests that a hierarchical priority class-based approach without category-specific quotas can increase countries' willingness to solve the refugee reallocation problem.

A Dynamic Social Network Matching Model for Virtual Power Plants and Distributed Energy Resources with Probabilistic Linguistic Information

Virtual power plants (VPPs) offer an effective means to address the imbalance issue between electricity supply and demand to advance the world’s low-carbon development. To fully utilize the limited resources in the virtual power plant planning stage, a two-sided match between VPPs and distributed energy companies is needed to better implement resource aggregation management. Because of the vagueness in this matching environment, the probabilistic linguistic term set (PLTS) is necessary to apply to express the decision makers’ preference. Considering the complex social relationships and intense competition among companies, a dynamic social network two-sided matching model is proposed for solving the multi-attribute two-sided matching decision-making problem. Firstly, we present a matching satisfaction degree described by PLTS. A dynamic social trust degree based on the sliding time concept is proposed. Secondly, the social trust network relationships are built based on the direct and indirect dynamic trust degree among companies. This relationship is then combined with an improved trust rank algorithm to identify the most authoritative and the most trusted company to provide the target company with a recommendation for the next moment. Besides, given that companies compete for limited resources, we further define the competitive satisfaction degree and apply the two-sided matching model. Additionally, then a two-sided matching model is developed. Finally, our model is tested numerically to ensure its accuracy and reliability.

A new theory of triangular intuitionistic fuzzy sets to solve the two-sided matching problem

In view of the limitations of triangular intuitionistic fuzzy numbers (TIFNs) in value selection and application, the purpose of this paper is to redefine and demonstrate the algorithm, expectation function and distance measure of TIFNs, and to put forward a new theory of triangular intuitionistic fuzzy sets (TIFSs). The new theory of TIFSs is then applied to the field of two-sided matching decision-making. To solve the two-sided matching problem based on TIFSs, the agent behavior factors of both sides are calculated by this theory. On this basis, a multi-objective matching model under TIFS preference is constructed. Furthermore, the optimal matching scheme is obtained by transforming and solving the model according to the expected score, the linear weighting and the algorithm of “being as good as possible”. Finally, the practicability of the proposed two-sided matching method is verified by a transaction matching example. The novelty and key idea of the proposed method are as follows: (1) it combines the idea of closeness in TOPSIS method and the expected score in the new theory of TIFSs to measure the behavior factors of two-sided agents; (2) it builds a two-sided matching model considering the behavior factors under the preference of TIFSs; (3) according to the idea of “being as good as possible”, a novel algorithm for solving the two-sided matching model under TIFS preference is proposed. The major conclusion and advantage of this paper is that the obtained BM scheme using the proposed method can reflect agent behavior factors and maximize agents’ satisfaction as much as possible.

Workload balance-based dynamic two-sided matching decision-making approach for cloud manufacturing tasks and services under uncertain preferences

PurposeThis paper aims to develop a dynamic two-sided stable matching method based on preference information of the matching objects in uncertain environments, so as to solve the matching problem of cloud manufacturing tasks and services with load balancing.Design/methodology/approachFor dynamic two-sided matching, due to the complexity of social environment and the limitation of human cognition, hesitation and fuzziness always exist in the process of multi-criteria assessment. First, in order to obtain the accurate preference information of each matching object, uncertain linguistic variables, uncertain preference ordinal and incomplete complementary matrices are used to evaluate multi-criteria preference information. This process is undertaken by considering the probability of each possible matching pair. Second, the preference information at different times is integrated by using the time-series weight to obtain the comprehensive satisfaction degree matrices of the matching objects. Further, the load adjustment parameter is used to increase the satisfaction degree of the matching objects. Afterward, a dynamic two-sided stable matching optimization model is constructed by considering stable matching conditions. The model aims to maximize the satisfaction degree and minimizes the difference in the satisfaction degree of matching objects. The optimal stable matching results can be obtained by solving the optimization model. Finally, a numerical example and comparative analysis are presented to demonstrate the characteristics of the proposed method.FindingsUncertain linguistic variables, uncertain preference orders and incomplete complementary matrices are used to describe multi-criteria preference information of the matching objects in uncertain environments. A dynamic two-sided stable matching method is proposed, based on which a DTSMDM (dynamic two-sided matching decision-making) model of cloud manufacturing with load balancing can be constructed. The study proved that the authors can use the proposed method to obtain stable matching pairs and higher matching objective value through comparative analysis and the sensitivity analysis.Originality/valueA new method for the two-sided matching decision-making problem of cloud manufacturing with load balancing is proposed in this paper, which allows the matching objects to elicit language evaluation under uncertain environment more flexibly to implement dynamic two-sided matching based on preference information at different times. This method is suitable for dealing with a variety of TSMDM (two-sided matching decision-making) problems.

A centralized matching scheme to solve the role-partner allocation problem in collaborative networks

In the current constantly changing business and economic environment, partners (i.e., individuals and/or enterprises) create Collaborative Networks to join efforts and undertake new projects together, thus allowing them to face business opportunities that would not be possible if attempted by them individually. In this situation, an assignment problem arises, since these projects involve the performance of a group of tasks or processes (named roles) that have to be distributed among the partners. Specifically, this problem, called the Role-Partner Allocation (RPA) problem in Collaborative Networks is a two-sided matching problem with lower and upper quotas on the partner’s side, and incomplete and partially ordered preference lists on both sides. A matching problem, and thus also the RPA problem, should be solved by a centralized matching scheme. However, allocations in Collaborative Networks continue to be mainly created by ad hoc arrangements, which takes a long time and is hard work. Looking for a reliable and faster way of distributing roles among partners in a Collaborative Network, the existing centralized matching schemes expected to solve the RPA problem (e.g., DA algorithm, SOSM, CA-QL algorithm, and EADAM) are studied in this paper, concluding that none of them obtain a matching that properly meets the requirement of the RPA problem. Therefore, a new centralized matching scheme to solve the RPA problem is proposed, discussed and exemplified.

Delay and Energy-Efficiency-Balanced Task Offloading for Electric Internet of Things

With the development of the smart grid, massive electric Internet of Things (EIoT) devices are deployed to collect data and offload them to edge servers for processing. However, the task of offloading optimization still faces several challenges, such as the differentiated quality of service (QoS) requirements, decision coupling among multiple devices, and the impact of electromagnetic interference. In this paper, a low-complexity delay and energy-efficiency-balanced task offloading algorithm based on many-to-one two-sided matching is proposed for an EIoT. The proposed algorithm shows its novelty in the dynamic tradeoff between energy efficiency and delay as well as in low-complexity and stable task offloading. Specifically, we firstly formulate the minimization problem of weighted difference between delay and energy efficiency to realize the joint optimization of differentiated QoS requirements. Then, the joint optimization problem is transformed into a many-to-one two-sided matching problem. Through continuous iteration, a stable matching between devices and servers is established to cope with decision coupling among multiple devices. Finally, the effectiveness of the proposed algorithm is validated through simulations. Compared with two advanced algorithms, the weighted difference between the energy efficiency and delay of the proposed algorithm is increased by 29.01% and 45.65% when the number of devices is 120, and is increased by 11.57% and 22.25% when the number of gateways is 16.

Stable matching with uncertain pairwise preferences

We study a two-sided matching problem under preferences, where the agents have independent pairwise comparisons on their possible partners and these preferences may be uncertain. Preferences may be intransitive and agents may even have cycles in their preferences; e.g. an agent a may prefer b to c, c to d, and d to b, all with probability one. If an instance has such a cycle, then there may not exist any matching that is stable with positive probability. We focus on the computational problems of checking the existence of possibly and certainly stable matchings, i.e., matchings whose probability of being stable is positive or one, respectively. We show that finding possibly stable matchings is NP-hard, even if only one side can have cyclic preferences. On the other hand we show that the problem of finding a certainly stable matching is polynomial-time solvable if only one side can have cyclic preferences and the other side has transitive preferences, but that this problem becomes NP-hard when both sides can have cyclic preferences.

Myopic and farsighted stable sets in 2-player strategic-form games

This paper revisits the analysis of stable sets in two-player strategic-form games. Our two main contributions are (i) to establish a connection between myopic stable sets and the stable matchings of an auxiliary two-sided matching problem and (ii) to identify a structural property of 2-player games, called “the block partition property,” which helps characterize the strategy profiles that are indirectly dominated by a fixed profile. Our analysis also generalizes and unifies existing results on myopic and farsighted stable sets in 2-player games.

Assignment mechanisms: Common preferences and information acquisition

I study costly information acquisition in a two-sided matching problem, such as matching applicants to schools. An applicant's utility is a sum of common and idiosyncratic components. The idiosyncratic component is unknown to the applicant but can be learned at a cost. As applicants learn, their preferences over schools become more heterogeneous, improving match quality. In my stylized environment, too few applicants acquire information in an ordinal strategy-proof mechanism. Subsidies, disclosure of applicants' priorities, and affirmative action-like policies lead to higher information acquisition and Pareto improvements. Learning may also decrease when an ordinal strategy-proof mechanism replaces an Immediate Acceptance mechanism.

Energy-delay tradeoff for virtual machine placement in virtualized multi-access edge computing: a two-sided matching approach

By decoupling network functions from the underlying physical machines (PMs) at the edge of the networks, the virtualized multi-access edge computing (MEC) enables deployment of new network services and elastic network scaling to reduce the maintenance costs in a more flexible, scalable and cost-effective manner. Although there are appealing performance gains to be achieved, the placement of virtual machines (VMs) on top of the sharing PMs to support computation-intensive applications for smart mobile devices becomes a major challenge, especially for an increasing network scale. In this paper, we attempt to deal with the VM placement problem in virtualized MEC system, which is targeted for finding a performance balance between energy consumption and computing/offloading delay. To capture such a tradeoff for VM placement, we formulate a weighted sum based cost minimization problem as a pure 0–1 integer linear programming problem, which is NP-complete and very difficult to solve with lower complexity. Based on the one-to-one mapping relation constraint, the VM placement problem is then converted into a many-to-many two-sided matching problem between the VM instances and the PMs. Motivated by the student project allocation problem, we develop an extended two-sided matching algorithm with lower computational complexity for solving the matching problem. Simulation results are presented to show the effectiveness of our proposed algorithm, and the normalization factor is of great significance to obtain the lower total cost.

Two-sided matching model for assigning volunteer teams to relief tasks in the absence of sufficient information

In the wake of a large-scale disaster, volunteer teams provide invaluable assistance. There is a pressing need to design a suitable model to solve the problem of volunteer team dispatching. This paper proposes a novel approach from the perspective of two-sided matching, which could stimulate the enthusiasm of volunteers. However, it is almost impossible to use one or more fixed indicators to evaluate each volunteer team or rescue task. Even if the indicators can be determined, the values of some indicators are difficult to obtain. Therefore, the proposed approach uses the available information to recommend potential matching targets and revises some key targets based on the subjective preferences of participants. It effectively avoids the bias in decision-making caused by the unavailability of sufficient information and improves the satisfaction of bilateral participants. Furthermore, it can effectively solve the two-sided matching problem when the preference order is unknown. The proposed approach is illustrated with a simulation case that focuses on an explosion accident in China. The rationality and effectiveness of the approach is validated through comparisons and analyses of the experimental results.

Myopic and Farsighted Stable Sets in 2-Player Strategic-Form Games

This paper revisits analysis of stable sets in two-player strategic-form games. Our two main contributions are (i) to establish a connection between myopic stable sets and stable matchings of an auxiliary two-sided matching problem and (ii) to identify a structural property of 2-player games, called the block partition property, which helps characterize strategy profiles that are indirectly dominated by a fixed profile. Our analysis also generalizes and unifies existing results on myopic and farsighted stable sets in 2-player games.

Two-Sided Matching on Comprehensive Transportation Network Emergency Vehicles’ Allocation

In emergency rescue, the allocation of comprehensive transportation network emergency vehicles often affects the efficiency of the whole rescue process. In the context of disasters, this paper researches the one-to-many two-sided matching problem between the emergency vehicles and the materials to be transported. Firstly, based on the needs of both parties involved in the matching, the satisfaction evaluation systems are constructed; with the goal of maximizing the weighted satisfaction of the affected areas and vehicles, the optimization model of the materials and emergency vehicles matching is established; then, an improved National Intern Matching Program (NIMP) algorithm is designed to solve the model, which is based on the k: 1 experimental pairing and updating ideas, and can take into account the capacity and destination constraints of vehicles in the matching process. Finally, through the calculation of an example, the matching scheme can make the satisfaction of material transportation reach 0.7392, and the simulation analysis proves that the scheme keeps certain stability in risky conditions.