Stable Matching Research Articles

Modifying an instance of the super-stable matching problem

The topic of this paper is the stable matching problem in a bipartite graph. Super-stability is one of the stability concepts in the stable matching problem with ties. It is known that there may not exist a super-stable matching, and the existence of a super-stable matching can be checked in polynomial time. In this paper, we consider the problem of modifying an instance of the stable matching problem with ties by deleting some bounded number of agents in such a way that there exists a super-stable matching in the modified instance. First, we consider the setting where we are allowed to delete agents on only one side. We prove that, in this setting, our problem can be solved in polynomial time. Interestingly, this result is obtained by carefully observing the existing algorithm for checking the existence of a super-stable matching. Next, we consider the setting where we are given an upper bound on the number of deleted agents for each side, and we are allowed to delete agents on both sides. We prove that, in this setting, our problem is NP-complete.

On the existence of stable matchings with contracts

On the existence of stable matchings with contracts

Matching workers to firms facing budget constraints

We study a many-to-one matching model with salaries in which firms face budget constraints. Mongell and Roth (1986) show that when firms face a budget constraint, a stable matching may not exist. We introduce an algorithm to find a strong stable matching by changing the budget of firms such that the total budget remains the same and each firm’s budget change is bounded by the value of at most one worker for that firm.

Exploring the evolution and collaboration in two-sided matching: a comprehensive bibliometric and topic modeling analysis

PurposeThis study aims to provide a comprehensive analysis of two-sided matching (TSM) research, an interdisciplinary field that integrates both theoretical and practical perspectives. By examining 756 research articles from the Web of Science database, this paper seeks to identify key trends, collaboration patterns and emerging research topics within the TSM domain.Design/methodology/approachThe research utilizes bibliometric analysis combined with a structural topic model to analyze TSM-related articles published between January 1, 2000, and September 30, 2022. The study identifies leading subfields, journals, countries/regions and institutions based on publication volume, total citations and average citations per article. Interaction and collaboration patterns among these entities are examined through co-occurrence and coupling networks. Additionally, five major research topics are identified and explored using topic modeling and co-word networks. This hybrid knowledge mining approach better reveals the inherent structural changes in topic clusters. Topic distribution and network analysis are beneficial in capturing the attention allocation of different entities to knowledge.FindingsThe analysis reveals five prominent research topics in TSM: communication resource allocation, stable matching research, computing task assignment, TSM decision-making and market matching mechanism design. These topics represent the main directions of TSM research. The study also uncovers a shift in research focus from theoretical aspects to practical applications. Furthermore, the distribution of knowledge and interaction patterns among key entities align with the identified research trends.Originality/valueThis study offers a novel and detailed overview of TSM research highlighting significant trends and collaboration patterns within the field. By integrating bibliometric methods with structural topic modeling the study provides unique insights into the evolution of TSM research making it a valuable resource for both academic and professional communities.

Tiered matching model considering quality compatibility in two-sided markets

This paper explores how platforms can effectively match heterogeneous users within tiers to increase matches and profits in two-sided matching markets. With the rapid expansion of digital platforms, user preferences and quality have become increasingly differentiated, leading to market congestion, search frictions, and inequality among users of different levels. To address these issues, we propose a centralized matching model that dynamically estimates user popularity and adjusts acceptable match sets. The model incorporates a reciprocal recommender to reduce inequality in matching and avoid congestion from users intensively sending requests to higher-tier counterparts. By analyzing user recommendation lists, the model quantifies the impact of market thickness, congestion, and matching security on participant utility. We then establish integer linear programming models to solve the stable matching optimization problem, maximizing platform revenue and social welfare. Numerical experiments validate the effectiveness of the proposed approach, demonstrating that a soft-tiered strategy using a reciprocal recommender optimizes the distribution of matching pairs across different levels, significantly increasing matches for middle and lower-tier users while enhancing platform revenue and social welfare. The model provides decision support for platforms to optimize tiered strategies and assists regulatory agencies in monitoring potential social welfare losses from excessive segmentation. The findings highlight the importance of considering user heterogeneity and market characteristics in designing effective matching mechanisms for two-sided platforms.

Caught in Transition: Dynamics of Waithood Among Chinese and Japanese Youth

This paper investigates the dynamics of waithood among Chinese and Japanese youth, focusing on the unique aspects experienced in each country. Waithood, a period of prolonged transition into adulthood due to delayed milestones like stable employment and marriage, is increasingly prevalent due to high unemployment rates and evolving job markets. This paper presents the mental and social strain those experiencing waithood must endure, and examines government efforts to address these issues, comparing and contrasting the strategies implemented in China and Japan. Despite various initiatives, the findings suggest that current measures are insufficient to fully alleviate the challenges faced by young people. The paper argues for more comprehensive policies that address the root causes of waithood, emphasizing the need for innovative approaches to support youth in achieving independence. This research contributes to a deeper understanding of youth transitions in East Asia and underscores the urgency for effective interventions.

Effective data reduction for strongly stable matching in very sparse graphs

We provide a linear-time computable problem kernel of linear size for Strongly Stable Roommates parameterized by the feedback edge number of the acceptability graph (which encodes which agents may be matched to each other).

Impact of Islamic Financial Literacy, Money Attitude, and Social Environment on Young Muslim Couples' Financial Planning

Disciplined financial planning can create a more durable and financially stable marriage. However, many people still depend on fate, leading to financial planning being overlooked in daily life. Economic factors remain the second most common cause of divorce in Surabaya. Indonesia’s Sharia financial literacy index is only 8.93%, and only 6.3% of the population prepares for long-term financial goals. This study has the purpose of observing the modification theory of planned behavior with the variable Islamic financial literacy, attitude towards money, and social environment on family financial planning among young Muslim couples, especially in Surabaya. This research uses a quantitative approach used multiple linear regression analysis, utilizing IBM SPSS version 27 as the analytical tool. The subjects of this research are young Muslim couples in Surabaya, as younger generations often lack sufficient financial knowledge and tend to make poor financial decisions. The total sample consists of 75 respondents. The results show that Islamic financial literacy and social environment variables positively and significantly affect family financial planning. Meanwhile, the attitude towards money variable also shows an influence but is not statistically significant. These findings highlight the importance of improving Islamic financial literacy and leveraging the social environment to enhance family financial planning outcomes.

Improving the deferred acceptance algorithm for efficient sponsor-recipient matching

As the gap between rich and poor in China has become increasingly prominent, various charity platforms have emerged. However, due to information asymmetry, many recipients cannot receive effective donations, and the emergence of fraudulent donations also makes donors unable to fulfill their intentions. We designed some improvements to the delayed acceptance (DA) algorithm and applied it flexibly in the donation platform. This can improve the efficiency of matching between donors and recipients. The variant of the DA algorithm is designed to carry out multiple rounds of matching, give donors and recipients the opportunity to select the matching priority list based on various factors and use a reasonable matching mechanism to achieve Pareto efficient, strategy-proof, and stable matching. Therefore, the application of the variation of the DA algorithm in the donation problem can better match the needs, so that the platform can complete a more reasonable and efficient donation matching.

Designing stable ride-sharing for commuting trip chain with role flexibility

AbstractIn ride-sharing, fixing the roles of commuters with vehicles could come at an opportunity of missed balance between riders and drivers. The decisions made by commuters with vehicles about roles are related to both to-work travel and return-home travel. Commuters may choose not to drive when they have a confirmed ride back home. This study designs a stable ride-sharing model with role flexibility for the commuting trip chain. The preferences of commuters over matching partners in trip chains are formulated. A stable matching algorithm based on commuting trip chain is designed. To assess the performance of the proposed model and algorithm, real-life data from a resident trip survey in Dalian are used to design experimental cases. The results indicate that stable matching based on the trip chain is not a consequence of the repetition of successive one-period stable matching. Compared with matching in two phases, the matching rate of commuters increases by an average of 10%. When the number of commuters with role flexibility increases by four times, the matching rate of commuters increases by an average of 5.6%.

Stabilizing financial networks via mergers and acquisitions

A bi-level model is proposed to explore efficient policies for supporting negotiations on financial crisis resolution. In a principal–agent framework, this model minimizes the welfare loss function of a central authority (social planner, SP) through the simultaneous choice of subsidy levels and potential pairs of banks to merge. The SP’s choice of mergers needs to be incentive-compatible with the autonomous choices of banks, and the evaluation of the financial network must adhere to standard accounting principles. Incentive compatibility is enforced by two options for conditions, based on stable matching or competitive bidding. For the evaluation of the financial network, we employ an extended Eisenberg–Noe clearing payment equilibrium by considering bankruptcy costs and the seniority levels of liabilities. Additionally, liabilities are not cleared among solvent banks, and corporate bonds may be used for clearing payments. The bi-level model specifies conditions for the clearing equilibrium. For demonstration, we use major European banks, and a scenario linked to the adverse economic conditions used in the 2016 EU-wide stress testing.

Finding all stable matchings with assignment constraints

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives (Balinski and Ratier, 1997; Gutin et al., 2023), that determines if and when a given list of constraints is compatible with stability. Whenever there is a stable matching that satisfies the constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.

Adapting stable matchings to forced and forbidden pairs

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching M1, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to M1. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable.

The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing up Your Home?

We study housing markets as introduced by Shapley and Scarf. We investigate the computational complexity of various questions regarding the situation of an agent a in a housing market H: we show that it is [Formula: see text]-hard to find an allocation in the core of H in which (i) a receives a certain house, (ii) a does not receive a certain house, or (iii) a receives a house other than a’s own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of H in which agent a receives a house h, if the value of the house owned by a increases, then the resulting housing market admits an allocation in its core in which a receives either h or a house that a prefers to h; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that stable matchings in a one-sided market also respect improvement. Funding: This work was supported by the Hungarian Scientific Research Fund [Grants K124171, K128611]. I. Schlotter is supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2021-2) and its János Bolyai Research Scholarship. The research reported in this paper and carried out by T. Fleiner at the Budapest University of Technology and Economics was supported by the “TKP2020, National Challenges Program” of the National Research Development and Innovation Office [BME NC TKP2020 and OTKA K143858] and by the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of the Artificial Intelligence research area of the Budapest University of Technology and Economics (BME FIKP-MI/SC). P. Biró gratefully acknowledges financial support from the Hungarian Scientific Research Fund, OTKA [Grant K143858] and the Hungarian Academy of Sciences [Momentum Grant LP2021-2].

Manipulating the outcome of stable marriage and roommates problems

The stable marriage and stable roommates problems have been extensively studied due to their applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet certain requirements. In such cases, one might be interested in modifying the instance so that the existence of a stable outcome with the desired properties is ensured. We focus on three different modifications.1. In the stable roommates problem, we show that finding a smallest subset of agents whose removal results in an instance with a stable matching is NP-complete if the capacities are greater than one, or the deleted agents must belong to a fixed subset of vertices. We further show that analogous results hold for the stable marriage problem when one would like to achieve the existence of a stable and perfect matching through the deletion of vertices.2. We investigate how to modify the preferences of the agents as little as possible so that a given matching becomes stable. The deviation of the new preferences from the original ones can be measured in various ways; here, we concentrate on the ℓ1-norm. We show that, assuming the Unique Games Conjecture, the problem cannot be approximated within a factor smaller than 2. By relying on bipartite-submodular functions, we give a polynomial-time algorithm for the bipartite case. We also show that a similar approach leads to a 2-approximation for general graphs.3. Last, we consider problems where the preferences of agents are not fully prescribed, and the goal is to decide whether the preference lists can be completed so that a stable matching exists. We settle the complexity of several variants, including cases when some of the edges are required to be included or excluded from the solution.

Scarcity and market design: How effective matching can promote the peer-to-peer sharing economy

Scarcity is an essential issue in service marketing. This study examined scarcity in a game-theoretic setting. It focused on the role of customer evaluations, through satisfaction ratings, on a technology-enabled peer-to-peer sharing economy platform in achieving stable provider–user matching. The model shows that an appropriate market design employing a user-proposing version of Gale and Shapley's (1962) deferred acceptance algorithm for a ride-sharing platform where many users approach a few providers can help avoid congestion and ensure stable matching. To manage scarcity, the model uses a customer satisfaction rating system that modifies the widely used batch matching algorithm by matching highly rated riders much faster than their low-rated peers. A platform's ability to offer time-bound stable matching for highly-rated users during scarcity is likely to help it maintain a competitive edge.

A virtual-reality spatial matching algorithm and its application on equipment maintenance support: System design and user study

Equipment maintenance support is an important technical measure to maintain the equipment’s expected performance. However, the current maintenance supports are mainly completed by maintainers under the guidance of technical manual or additional experts, which may be insufficient for some advanced equipment with rapid update rate and complex inner structure. The rising technology of augmented reality (AR) provides a new solution for equipment maintenance support, while one of the key issues limiting the practical application of AR in maintenance field is the spatial matching issue between virtual space and reality space. In this paper, a virtual-reality spatial matching algorithm is designed to accurately superimpose the virtual information to the corresponding actual scene on the AR glasses. In this algorithm, two methods are proposed to help achieve the stable matching of virtual space and reality space. In detail, to obtain the saliency map with less background interference and improved saliency detection accuracy, a saliency detection method is designed based on the super-pixel segmentation. To deal with the problems of uneven distribution on the feature points and weak robustness to the light changes, a feature extraction and matching method is proposed for acquiring the feature point matching set with the utilization of the obtained saliency map. Finally, an immersive equipment maintenance support system (IEMSS) is developed based on this spatial matching algorithm, which provides the maintainers with immediate and immersive guidance to improve the efficiency and safety in the maintenance task, as well as offers maintenance training for inexperienced maintainers with expanded virtual information in case of limited experts. Several comparative experiments are implemented to verify the effectiveness of proposed methods, and a user study of real system application is carried out to further evaluate the superiority of these methods when applied in the IEMSS.

Research on the optimize doctor-patient matching in China

In China, patients are given the opportunity to know background information about their doctors, and patients choose their doctors to see. Due to the shortage of medical resources and the uncertainty of the quality of medical services, as well as some external factors, patients will prefer to choose well-known doctors in the hope of getting a better medical experience. In order to match the preferred healthcare resources, they may choose to lie to increase the chance of visiting the doctor. This study adopts a combination of theoretical modeling and algorithmic simulation. Through theoretical analysis, a framework model of doctor-patient matching is established. Doctors with different skills and experience, who select patients according to their conditions and their own preferences in the matching process, as well as patients with different conditions and preferences, who want to receive treatment by matching to a suitable doctor, are clarified. The Deferred Acceptance algorithm is written and operated to simulate the matching process where patients apply to doctors and doctors are screened based on their priorities. Analyze and evaluate the performance of Strategy-Proofness and Pareto Efficiency in matching by iterating the algorithm. In this case, the DA algorithm establishes a stable match between the patient and the physician despite the possibility that the patient may deceive his/her preferences. However, patient behavior may affect the efficiency and fairness of the matching process, highlighting the importance of transparency and integrity of the doctor-patient matching system.

ClusterMatch aligns single-cell RNA-sequencing data at the multi-scale cluster level via stable matching.

Unsupervised clustering of single-cell RNA sequencing (scRNA-seq) data holds the promise of characterizing known and novel cell type in various biological and clinical contexts. However, intrinsic multi-scale clustering resolutions poses challenges to deal with multiple sources of variability in the high-dimensional and noisy data. We present ClusterMatch, a stable match optimization model to align scRNA-seq data at the cluster level. In one hand, ClusterMatch leverages the mutual correspondence by canonical correlation analysis and multi-scale Louvain clustering algorithms to identify cluster with optimized resolutions. In the other hand, it utilizes stable matching framework to align scRNA-seq data in the latent space while maintaining interpretability with overlapped marker gene set. Through extensive experiments, we demonstrate the efficacy of ClusterMatch in data integration, cell type annotation, and cross-species/timepoint alignment scenarios. Our results show ClusterMatch's ability to utilize both global and local information of scRNA-seq data, sets the appropriate resolution of multi-scale clustering, and offers interpretability by utilizing marker genes. The code of ClusterMatch software is freely available at https://github.com/AMSSwanglab/ClusterMatch.

On the Convergence of Swap Dynamics to Pareto-Optimal Matchings

We study whether Pareto-optimal stable matchings can be reached via pairwise swaps in one-to-one matching markets with initial assignments. We consider housing markets, marriage markets, and roommate markets as well as three different notions of swap rationality. Our main results are as follows. While it can be efficiently determined whether a Pareto-optimal stable matching can be reached when defining swaps via blocking pairs, checking whether this is the case for all such sequences is computationally intractable. When defining swaps such that all involved agents need to be better off, even deciding whether a Pareto-optimal stable matching can be reached via some sequence is intractable. This confirms and extends a conjecture made by Damamme, Beynier, Chevaleyre, and Maudet (2015) who have shown that convergence to a Pareto-optimal matching is guaranteed in housing markets with single-peaked preferences. We prove that in marriage and roommate markets, single-peakedness is not sufficient for this to hold, but the stronger restriction of one-dimensional Euclidean preferences is.