Deferred Acceptance Algorithm 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.

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 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.

Performance Assessment of a Rehabilitation Transportation Reservation Matching Service with Market Design Mechanisms

Government agencies provide huge amount of subsidies to support the rehabilitation transportation service over the past decade in eastern Taiwan; however, low demand request fulfillment rate, limited medical and transportation resources, long travel distances, and an extremely high percentage of dead mileages are still the main challenges faced by rehabilitation transportation service providers. This study applies the market design theory to match the rehabilitation buses with the requests of patients, so as to improve resource utilization efficiency in rural areas. The developed market design mechanisms aim to allocate resources to those who need them most in a matching manner, by using the deferred acceptance algorithm and the top trading cycle approach. The model is initialized with the requests of those who choose the rehabilitation bus based on their desired boarding time slots. On the other hand, the service providers of the rehabilitation bus would determine patients’ schedule based on their disability level, willingness to share the ride, number of fulfilled appointments during this month, and the travel distance of this trip as the order of preference. Since the current vehicle dispatching rule is to reserve seats of a rehabilitation bus on the “first-come-first-served” basis, and it cannot fully satisfy patients need. In accordance with the historical data, 63 of 72 demand requests could successfully reserve the seats. In the “first-come, first-served” mode, 48 requests obtained the first-ranking shift (i.e., their desired time slots), and the sum of their disability level score is 155. In the market design matching mode, 57 requests obtained the first-ranking shift, and the sum of their disability level score is 170, which demonstrates that the proposed market design matching mechanism outperforms than the conventional rules.

Comparative Analysis on Benefits of Elective System at Universities Based on Triangle-dynamic-matching System

Nowadays, the development of education can improve the level of human capital and significantly promote economic development. As part of the education system, more and more students care about the college admissions, but few of them pay attention to the benefits of a good elective system, which also might influence their whole university life. Taking Chinese elective system as an example, the paper proposes a new elective system at universities with a specific formula: Triangle - dynamic - matching system, which combines the advantages the Auction mechanism, the Wharton Business School Mechanism and the Deferred acceptance algorithm with the true preferences of students, teachers and the schools recommendation dynamically. Through the Systematic Literature Review and Analytical Method, the paper aims to analyse the benefits of a good elective system, its utility, the algorithm and problem in the elective system. This is a new system promising Pareto-efficiency and strategy proof, which might helps to save the school's human, material and financial resources, and greatly enhances the efficiency of students' course selection.

Contemporary challenges and AI solutions in port operations: applying Gale–Shapley algorithm to find best matches

Artificial intelligence (AI) developments enable human capability to deliver the same outcome at a lower cost. This research performs a high-level matching between AI solutions and challenges within the port area by developing a novel academic approach. This way, the matching is carried out more structured than when one (manager, developer, challenge owner, etc.) fulfils it based on their opinion without following any structured approach. Therefore, the study defines first a comprehensive typology of port stakeholders' challenges, which can be solved via AI solutions. This typology presents challenges, including their main issues, widespread impact, and potential solutions. A state-of-the-art review of AI solutions that can address these challenges is carried out in parallel. Secondly, this review clearly distinguishes between AI solutions based on their technology and functionality. Thirdly, this research selects an appropriate AI solution for addressing each identified challenge in the port operation by upgrading the Gale–Shapley algorithm. Finally, it shows that the most critical presented AI solutions in this study use various machine learning (ML) techniques. Besides, concerning the AI solution's reusability feature and the result of high-level matching, this research shows that the implementation phase effort can be drastically reduced by using the recently developed matching algorithm.

A task matching model of photovoltaic storage system under the energy blockchain environment - based on GA-CLOUD-GS algorithm

Photovoltaic storage system (PVSS) has been spawned with the combined application of photovoltaic (PV), energy storage (ES) and energy blockchain (EB), which has also made important contributions to the energy structure adjustment, energy transaction security and ecological environment protection. The establishment of a reasonable task matching mechanism can further improve the operation efficiency and quality of the system under the EB environment, and this paper consequently constructs a task matching model of PVSS based on GA-CLOUD-GS algorithm. Firstly, the decision-making committee is set up and the index system is determined for the to-be-matched task. Secondly, the Genetic Algorithm (GA) comprehensive weighting method is introduced to integrate the subjective and objective weights to achieve the weight optimization. Thirdly, the cloud model is used to obtain the preference order and priority order of the to-be-matched subjects. Fourthly, the Gale-Shapley (GS) algorithm is used to obtain the task matching results. Finally, the operability, the stability and the effectiveness of the model are separately verified through numerical simulation, sensitivity analysis and comparative analysis. Corresponding suggestions for the task matching of PVSS in the EB environment are also put forward according to the research content.

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.

Beam Selection for Cell-Free Millimeter-Wave Massive MIMO Systems: A Matching-Theoretic Approach

In this letter, we consider beam selection in cell-free millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. To address the beam selection of all access points in the network for cell-free operation, a beam selection problem that maximizes the minimum of spectral efficiencies of all user equipments is formulated. We propose an extended deferred acceptance algorithm for beam selection based on the matching theory. Additionally, we propose two intuitive beam selection algorithms. System-level simulation results demonstrate the advantage of the proposed matching theory-based beam selection method in terms of spectral efficiency for cell-free mmWave massive MIMO systems.

K -Best Egalitarian Stable Marriages for Task Assignment

In a two-sided market with each agent ranking individuals on the other side according to their preferences, such as location or incentive, the stable marriage problem calls to find a perfect matching among the two sides such that no pair of agents prefers each other to their assigned matches. Recent studies show that the number of solutions can be large in practice. Yet the classic solution by the Gale-Shapley (GS) algorithm is optimal for agents on the one side and pessimal for those on the other side. Some algorithms find a stable marriage that optimizes a measure of the cumulative satisfaction of all agents, such as egalitarian cost. However, in many real-world circumstances, a decision-maker needs to examine a set of solutions that are stable and attentive to both sides and choose among them based on expert knowledge. With such a disposition, it is necessary to identify a set of high-quality stable marriages and provide transparent explanations for any reassigned matches to the decision-maker. In this paper, we provide efficient algorithms that find the k -best stable marriages by egalitarian cost. Our exhaustive experimental study using real-world data and realistic preferences demonstrates the efficacy and efficiency of our solution.

Energy Minimization for UAV Swarm-Enabled Wireless Inland Ship MEC Network With Time Windows

This paper establishes a new unmanned aerial vehicle (UAV) swarm-enabled wireless inland ship mobile edge computing (MEC) network with time windows, where UAVs are deployed to support time-constrained and low-resource unmanned surface vehicles (USVs) communication and computation. We aim to minimize UAV swarm energy consumption subject to numerous constraints. To tackle the challenging formulated problem, we decompose the original challenging problem into a list of sub-problems according to block coordinate descent (BCD) method and propose a heuristic algorithm to solve subproblems in an iterative manner. Specifically, the optimization of USVs offloading decisions is formulated as mixed-integer non-linear programming and then a modified deferred acceptance algorithm is proposed. The joint consideration of UAVs flight speed and UAV swarm stability is converted into a single-objective optimization problem after determining UAV control system’s latency requirements, and then Lagrangian multiplier method with Karush-Kuhn-Tucker (KKT) conditions is proposed. Successive convex approximations (SCA)-based algorithm is proposed to convert the non-convex constraints to convex ones, and then UAVs hovering coordinates can be obtained by solving the convex approximation problem. Numerical results verify the effectiveness of jointly considering USVs offloading decisions, UAVs flight speed, UAVs horizontal hovering coordinates and the number of UAVs for energy efficiency in comparison with several advanced baseline algorithms without optimization design.

CATCHMENT AREAS, STRATIFICATION, AND ACCESS TO BETTER SCHOOLS

AbstractSchool Choice provides students with the opportunity to attend better schools than those in their neighborhood. This is crucial for students from disadvantaged areas where schools may be of lower quality. Our theoretical model and numerical simulations show that the widely used Deferred Acceptance (DA) algorithm has limitations in providing access to better schools (ABS). When schools have varying levels of quality and when there are priorities linked to neighborhood schools, the DA algorithm experiences significant limitations in providing ABS. Top Trading Cycles, when compared to DA, offers greater ABS, particularly for disadvantaged students.

Multi-Satellite Cooperative Communication: Exploiting Time Asynchrony in Non-Orthogonal Transmissions

The ever-increasing densification of the low-Earth orbit constellation makes it possible to boost the data rate via multi-satellite cooperative transmission. However, the large spatial scale of satellite networks makes the time asynchrony non-negligible. In this paper, we exploit the asynchronous non-orthogonal transmission for multi-satellite cooperative communication to improve the fairness-aware rate. The asynchronous capacity is extended to the multi-satellite cooperation scenario and then utilized to formulate the optimization problem, which jointly considers the satellite-to-terminal association, power allocation, and decoding order. To dissect those coupled variables, we propose a preference-list-based algorithm that iterates between the following two stages. First, the many-to-many two-sided matching is solved by a Gale-Shapley algorithm based strategy given prespecified preference lists. Then, transmit power and decoding order are jointly optimized by a Dinkelbach-like algorithm. Based on the above results, the preference lists are updated to reflect the inter-satellite interference for iterative refinement. Simulation results show that introducing cooperative transmission improves the fairness rate by 12%, and exploiting time asynchrony provides another 7% gain.