Deferred Acceptance Algorithm Research Articles

Optimizing Geo-Distributed Data Processing with Resource Heterogeneity over the Internet

The traditional MapReduce frameworks were originally designed for processing data within a single cluster and are not suitable for handling geo-distributed data. Consequently, alternative approaches such as Hierarchical and Geo-Hadoop have been proposed to address this limitation. However, these approaches still face challenges in efficiently managing inter-cluster data transfer, particularly considering the heterogeneity of clusters and varying bandwidth among them. Moreover, the need to transmit results to a central global reducer for geo-distributed MapReduce operations adds unnecessary complexity. To tackle these issues, we introduce Extended Cross-MapReduce (ECMR), a framework that integrates resource heterogeneity and network links in geo-distributed MapReduce workflows. ECMR optimizes data management and determines the necessary data volume for generating final results. To enhance performance, ECMR leverages the overlap between data transfer and execution time by utilizing multiple global reducers and grouping temporary results that require data transfer over the Internet. In ECMR, we propose a bipartite graph and extend the Gale-Shapley algorithm to determine the optimal number of clusters and select the most suitable locations for global reducers. Through extensive experimental evaluations conducted on a real testbed, we demonstrate the effectiveness of our proposed ECMR method. The results exhibit significant improvements over traditional Hierarchical and Geo-Hadoop approaches, achieving reductions of up to 81% and 85% in overall makespan, respectively.

Respect for Improvements and Comparative Statics in Matching Markets

One of the oldest results in the theory of two-sided matching is the entry comparative static, which shows that under the Gale-Shapley deferred acceptance algorithm, adding a new agent to one side of the market makes all the agents on the other side weakly better off. Here, we give a new proof of the entry comparative static, by way of a well-known property of deferred acceptance called respect for improvements. Our argument extends to yield comparative static results in more general settings, such as matching with slot-specific preferences.

Optimization of industrial layout in airport economic zone through government-enterprise interaction

To avoid the issue of industrial layout plans in Airport Economic Zones (AEZs) being hard to implement due to mismatched the land supply and demand, it is necessary to clarify industrial layout factors that the government (land supplier) and locating enterprises (land demanders) focus on. This study constructs a AEZ's industrial layout optimization model from the government's perspective and enterprises’ locating utility. Based on the Gale-Shapley algorithm, aiming at eliminating blocking pairs, we establish government-enterprise interacting rules and coordinating mechanisms, corresponding to two types of government-enterprise interactions, namely public consultation and investment promotion joint meeting. According to government transparency and enterprise participation, the optimization model and Agent-Based Model are adopted in the combination to simulate the government-enterprise interactions in the decision-making of industrial layout in AEZ, under two interaction rules of “enterprises provide feedback in one go - the government makes revisions in one go” and “enterprises provide feedback one by one - the government makes revisions one by one”, respectively. By analyzing the changing curves of their objective functions, the equilibrium point where both parties can reach an agreement is identified, and the industrial layout scheme in AEZ is determined that will be mutually accepted. It is found that positive interaction with high government transparency and high enterprise participation will help improve the rationality of the industrial layout in AEZ, maximizing the efficiency of spatial allocation of elements and resources.

Stability vs. no justified envy

Stability and “no justified envy” are used almost synonymously in the matching theory literature. However, they are conceptually different and have logically separate properties. We generalize the definition of justified envy to environments with arbitrary school preferences, feasibility constraints, and contracts, and show that stable allocations may admit justified envy. When choice functions are substitutable, the outcome of the deferred acceptance algorithm is both stable and admits no justified envy.

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.

Exploring Trade-Offs for Online Mental Health Matching: Agent-Based Modeling Study.

Online mental health communities (OMHCs) are an effective and accessible channel to give and receive social support for individuals with mental and emotional issues. However, a key challenge on these platforms is finding suitable partners to interact with given that mechanisms to match users are currently underdeveloped or highly naive. In this study, we collaborated with one of the world's largest OMHCs; our contribution is to show the application of agent-based modeling for the design of online community matching algorithms. We developed an agent-based simulation framework and showcased how it can uncover trade-offs in different matching algorithms between people seeking support and volunteer counselors. We used a comprehensive data set spanning January 2020 to April 2022 to create a simulation framework based on agent-based modeling that replicates the current matching mechanisms of our research site. After validating the accuracy of this simulated replication, we used this simulation framework as a "sandbox" to test different matching algorithms based on the deferred acceptance algorithm. We compared trade-offs among these different matching algorithms based on various metrics of interest, such as chat ratings and matching success rates. Our study suggests that various tensions emerge through different algorithmic choices for these communities. For example, our simulation uncovered that increased waiting time for support seekers was an inherent consequence on these sites when intelligent matching was used to find more suitable matches. Our simulation also verified some intuitive effects, such as that the greatest number of support seeker-counselor matches occurred using a "first come, first served" protocol, whereas relatively fewer matches occurred using a "last come, first served" protocol. We also discuss practical findings regarding matching for vulnerable versus overall populations. Results by demographic group revealed disparities-underaged and gender minority groups had lower average chat ratings and higher blocking rates on the site when compared to their majority counterparts, indicating the potential benefits of algorithmically matching them. We found that some protocols, such as a "filter"-based approach that matched vulnerable support seekers only with a counselor of their same demographic, led to improvements for these groups but resulted in lower satisfaction (-12%) among the overall population. However, this trade-off between minority and majority groups was not observed when using "topic" as a matching criterion. Topic-based matching actually outperformed the filter-based protocol among underaged people and led to significant improvements over the status quo among all minority and majority groups-specifically, a 6% average chat rating improvement and a decrease in blocking incidents from 5.86% to 4.26%. Agent-based modeling can reveal significant design considerations in the OMHC context, including trade-offs in various outcome metrics and the potential benefits of algorithmic matching for marginalized communities.

Respecting priorities versus respecting preferences in school choice: When is there a trade-off?

A classic trade-off that school districts face when deciding which matching algorithm to use is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm (DA) respects priorities but can lead to inefficient allocations. We identify a new condition on school choice markets under which DA is efficient. Our condition generalizes earlier conditions by placing restrictions on how preferences and priorities relate to one another only on the parts that are relevant for the assignment. Whenever there is a unique allocation that respects priorities, our condition captures all the environments for which DA is efficient. We show through stylized examples and simulations that our condition significantly expands the range of known environments for which DA is efficient. We also discuss how our condition sheds light on existing empirical findings.

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.

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.

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.

Gale-Shapley Verified

This paper presents a detailed verification of the Gale-Shapley algorithm for stable matching (or marriage). The verification proceeds by stepwise transformation of programs and proofs. The initial steps are on the level of imperative programs, ending in a linear time algorithm. An executable functional program is obtained in a last step. The emphasis is on the stepwise development of the algorithm and the required invariants.

Research Design with Weighted Lotteries in School Choice

Centralized admissions are an integral part of parental school choice programs. Most districts use a version of the deferred acceptance algorithm to assign applicants to schools. Centralized admissions produce data with quasi-experimental variation in student assignment that is integral in program evaluation. Recent developments in research design consider the basic version of the deferred acceptance algorithm. However, most districts adapt advanced versions of the deferred acceptance algorithm to implement their diversity policy in admissions, such as favoring applicants from disadvantaged backgrounds in lottery tie-breaking. We develop research design for data from the deferred acceptance algorithm with weighted lotteries.

The Influences of Ties in Preference on Market Matching

The ties of preference and priorities are commonly seen and widely used in daily life. When the agent considers the priority order of some selected objects to be the same, the final matching result may be affected. People sometimes require strict preference ranking in order to facilitate the use of matching models, which can cause controversy and dissatisfaction with people in the matching. In order to effectively solve the above problems, this paper surveys what these impacts are and how they affect the final result of matching. According to the analysis, it is proven that when there is a preference of indifference, Pareto efficiency is unstable and the deferred acceptance algorithm cannot be used for market matching. In addition, the Pareto-improving draft mechanism has proven to be powerful without imposing a strict preference. This mechanism can also avoid the complex process and other negative consequences of handing ties arbitrarily.

Efficient matching under general constraints

We study indivisible goods allocation problems under constraints and provide algorithms to check whether a given matching is Pareto efficient. We first show that the serial dictatorship algorithm can be used to check Pareto efficiency if the constraints are matroid. To prove this, we develop a generalized top trading cycles algorithm. Moreover, we show that the matroid structure is necessary for obtaining all Pareto efficient matchings by the serial dictatorship algorithm. Second, we provide an extension of the serial dictatorship algorithm to check Pareto efficiency under general constraints. As an application of our results to prioritized allocations, we discuss Pareto improving the deferred acceptance algorithm.

Resource-aware fog service placement using deferred acceptance in edge computing

Fog computing aims at reducing network latency, bandwidth and processing delay by bringing computation resources closer to the data sources. Modern IoT applications, such as smart surveillance systems, remote health monitoring applications, ambient-aware applications etc., are time-critical and computationally intensive. For such applications, it is ideal to consider an intermediate layer of processing i.e a fog layer in addition to cloud. However, processing the workload of such IoT applications with an intermediate layer of fog nodes has several challenges. The significant challenges include the mobility of end-user nodes, dynamic patterns of workload generation leading to highly-variant resource requirements and sensitive quality of service (QOS) requirements. Hence a dynamic approach is required to precisely map the service requests from end-user devices to a suitable fog node. The optimality of a fog node for service placement depends on several factors, including location, resource utilization rates such as CPU, Memory and Disk utilization % and energy consumption. Several meta-heuristic techniques and evolutionary algorithms have been proposed in the past for optimal service placement among fog nodes. This paper investigates the applicability of a game theory-based approach called Deferred acceptance (DA) for the same. The DA algorithm, originally designed as a stable matching mechanism for the marriage market is adapted for service placement problems in fog-based IoT systems. The effectiveness of optimized service placement through the DA approach is validated experimentally. The experiment is carried out by creating a test bed that mimics a fog computing-based intelligent traffic management application. The proposed approach's performance is evaluated through parameters such as the startup time for the DA approach to produce outcomes, total execution time and handshake latency. The numerical results of the DA approach are compared with those of a simple scheduling algorithm ( FIFO) and a basic genetic algorithm-based approach. The DA approach appears to perform on par with the genetic algorithm in terms of start-up time, but exceeds the genetic algorithm with respect to stability of the outcomes produced.

Application of Gale-Shapley algorithm in optimal matching for healthcare facilities to elderly population: the case of Hangzhou, China

ABSTRACT This paper serves as the first empirical research applying the Nobel Prize winning Gale-Shapley algorithm to study optimal stable matching of healthcare facilities to elderly population living in residential neighbourhoods in main urban districts of Hangzhou, China. Through bilateral considerations of supply side attributes of healthcare facilities and demand side preferences of elderly population, this research shows that the Gale-Shapley matching is superior to unilateral spatial or non-spatial utility matching and can optimize stable matching for elderly population in a way similar to the Pareto optimal. Further, this study provides a conceptual model classifying urban spaces for healthcare services at various levels.

Analysis on the Mechanism of Chinese College Admission System

The college entrance examination has a history of more than fourty years in China. With the development of the society, the previous admission system has revealed more and more drawbacks, such as high scores and low admission which means the students who got the high score was not into the high reference college. Also, some schools are not full. In order to continue to exploring the entrance exams admission mechanisms. First, it describes the operation mechanism of the existing admission methods and analyzes the advantages and disadvantages, and then puts forward an application of foreign deferred acceptance (DA) algorithms to the college entrance examination and analyzing the advantages and disadvantages. The paper conducts a questionnaire to investigate the satisfaction of students and parents with the previous admission system and some privileges, and analyses the results of these data. In addition to this, the paper uses an example about Inner Mongolias university admission mechanisms and some drawback of this. Finally, this paper clarifies that the DA algorithm cannot be applied to the college entrance examination admission mechanism because of the large number of candidates and provinces in China.

Optimizing Social and Emotional Learning through Modified Gale-Shapley Algorithm for Collaborative and Competitive Education

Collaborative and competitive learning is essential in educational development, enhancing students’ social and emotional competencies critical for academic and personal success. This study explores the integration of the Gale-Shapley algorithm, initially designed for the stable marriage problem, to optimize student pairings in collaborative and competitive learning environments. The objective is to maximize the effectiveness of Social and Emotional Learning (SEL) interventions by fostering productive social interactions and essential skill development. We propose a modified version of the Gale-Shapley algorithm to handle a single list of students, utilizing compatibility scores based on inverse Euclidean distance, Jaccard similarity, and cosine similarity. Our methodology includes generating synthetic datasets to simulate various educational contexts and evaluate the algorithm’s performance. Results demonstrate the algorithm’s efficiency in forming stable and effective pairs, significantly enhancing the learning experience. This innovative approach aligns with SEL guidelines and contemporary educational requirements, offering a robust, personalized, and dynamic learning framework. Future research should focus on empirical validations in diverse educational settings to confirm the algorithm’s effectiveness and scalability.

Optimizing 5G Power Allocation With Device-to-Device Communication: A Gale-Shapley Algorithm Approach

Optimizing 5G Power Allocation With Device-to-Device Communication: A Gale-Shapley Algorithm Approach

Similarity propagation based semi-supervised entity alignment

Entity alignment aims to identify entities referring to the same real world object among multiple knowledge graphs. Current embedding based approaches suffer from the lack of labeled entity pairs as training data. Some works attempt to boost the training process with semi-supervised methods, which add confidently predicted entity pairs into training data iteratively. Though the effectiveness of this strategy has been confirmed, the current semi-supervised methods suffer from the problem of incorrect newly labeled entity pairs. This paper presents a novel semi-supervised entity alignment framework Similarity Propagation based Semi-supervised Entity Alignment (SPSEA), which improves the precision of labeled entity pairs by propagating alignment information from seed entity pairs to their direct neighbors. The key idea is to combine dependency between entities and entity embeddings to obtain entity similarities, which alleviates the problem of mislabeling when the entity embeddings are of low quality. And it finds aligned entities from direct neighbors of seed entity pairs with the help of relation alignment, which narrows the search space and not hurting the recall of true pairs. In addition, we propose novel deferred-acceptance algorithm and bilateral alignment strategy to further guarantee the quality of obtained entity pairs. Through extensive experiments, we show that the quality of labeled entity pairs obtained by SPSEA is high than current semi-supervised methods.