Optimal Matching Problem Research Articles

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.

Multi-person dance tiered posture recognition with cross progressive multi-resolution representation integration.

Recognizing postures in multi-person dance scenarios presents challenges due to mutual body part obstruction and varying distortions across different dance actions. These challenges include differences in proximity and size, demanding precision in capturing fine details to convey action expressiveness. Robustness in recognition becomes crucial in complex real-world environments. To tackle these issues, our study introduces a novel approach, i.e., Multi-Person Dance Tiered Posture Recognition with Cross Progressive Multi-Resolution Representation Integration (CPMRI) and Tiered Posture Recognition (TPR) modules. The CPMRI module seamlessly merges high-level features, rich in semantic information, with low-level features that provide precise spatial details. Leveraging a cross progressive approach, it retains semantic understanding while enhancing spatial precision, bolstering the network's feature representation capabilities. Through innovative feature concatenation techniques, it efficiently blends high-resolution and low-resolution features, forming a comprehensive multi-resolution representation. This approach significantly improves posture recognition robustness, especially in intricate dance postures involving scale variations. The TPR module classifies body key points into core torso joints and extremity joints based on distinct distortion characteristics. Employing a three-tier tiered network, it progressively refines posture recognition. By addressing the optimal matching problem between torso and extremity joints, the module ensures accurate connections, refining the precision of body key point locations. Experimental evaluations against state-of-the-art methods using MSCOCO2017 and a custom Chinese dance dataset validate our approach's effectiveness. Evaluation metrics including Object Keypoint Similarity (OKS)-based Average Precision (AP), mean Average Precision (mAP), and Average Recall (AR) underscore the efficacy of the proposed method.

Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models

Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays’ problems, however, well assessed model translation techniques exhibit scalability issues that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is nontrivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.

Research on user requirements preprocessing of imaging reconnaissance satellites

Aiming at how to solve the problem of optimal matching between imaging reconnaissance user requirements and satellite resources, this paper conducts research on the preprocessing of imaging reconnaissance satellite requirements. First, considering the remote sensor type and resolution of imaging satellites, a requirement-resource matching matrix is constructed to realize the preliminary matching between user requirements and imaging reconnaissance satellite resources. Secondly, starting from the time constraints, by calculating the observation time window of requirement and resources, the time requirements of satellite resources and user requirements are matched. Finally, in order to solve the problem that the same observation task can be completed by multiple imaging satellites, a conflict resolution method based on resource consumption is proposed, which effectively improves the preprocessing ability of user requirements.

An optimization framework for analyzing dual‐donor organ exchange

We study an optimal matching problem in the context of dual‐donor organ exchange, where a portion of two living donors' organs are transplanted to a single patient. This dual‐donor transplant technique is becoming more widespread for lung and liver transplants. However, multiple medical compatibility criteria pose a serious challenge for matching a patient with two compatible donors. In the United States and many other countries, laws prohibit commercial (for‐profit) deals for human organs, so donor exchanges are run by nonprofit organizations connecting donors with people in need of organs, with the goal of increasing transplant matches. We propose a simple chain mechanism in dual‐donor organ exchange to increase the number of patient–dual‐donor matches, which would maximize the number of patients receiving transplants. Based on this objective, we propose a general simple chain optimization framework for finding the maximum patient matching, taking into account multiple compatibility criteria (e.g., blood type and weight), and determine the complexity status of the problem. We provide theoretical results on the structures of simple chains, as well as a polynomial time algorithm to obtain the maximum patient matching simple chain with blood type compatibility. Through a numerical study for multiple compatibility criteria, we show that in many scenarios, a simple chain substantially increases the number of patients matched with dual donors for transplants, as opposed to exchange cycles. We also address the problem of maximizing the number of patients matched for dual‐donor organ transplants via two‐way and three‐way exchange cycles, subject to donors' and recipients' medical compatibility criteria, along with a discussion of their computational complexity. Finally, we characterize the general configurations of large n‐way exchange cycles and provide theoretical insights for their structural properties. Our findings provide general optimization models for dual‐donor organ exchange operators to increase the number of patients matched for transplant, given multiple compatibility criteria. In addition, we show how exchange operators, using simple chains, can increase patient matches and reduce simultaneous surgical resource requirements over exchange cycles.

Long-Term Matching Optimization With Federated Neural Temporal Difference Learning in Mobility-on-Demand Systems

Efficient bipartite graph matching of orders and drivers is a central operational problem in industrial mobility-on-demand (MOD) systems. Traditional studies adopt pure combinatorial optimization models for order-and-driver matching, which do not consider the long-term rewards of the dynamic MOD decision making process. Toward long-term optimization, this article presents a systemic paradigm of online matching with federated neural temporal difference learning (FedTDLearning), which encompasses learning and matching phases. During the learning phase, the long-term matching process is modeled as a Markov decision process, which is typically solved by employing data-driven reinforcement learning in an offline central training scheme. Massive amounts of data would be generated on the network by industrial MOD systems. It is impossible to send all the large-scale industrial data to the cloud server for centralized model training due to network bandwidth limitations and safety concerns. Therefore, a generic and innovative FedTDLearning is proposed to achieve long-term matching in a distributed manner. During the matching phase, a real-time bipartite matching optimization problem is formulated to maximize the learned spatiotemporal value and minimize the pickup distance, which is reducible to the minimum-cost maximum weight bipartite graph matching problem. A distance-learned-value ratio algorithm is proposed to find an optimal matching in the bipartite graph based on the joint optimization of FedTDLearning and the combinatorial fractional programming approach. Furthermore, to pursue optimal computation efficiency, we solve the real-time matching problem by constructing a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k$ </tex-math></inline-formula> NN) bipartite graph where each order is connected with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> NN drivers. Using openly available real-world data, the prototype system and experimental evaluations show that our proposed algorithms have effective problem-solving capability in practice.

The Way to Invest: Trading Strategies Based on ARIMA and Investor Personality

In the field of financial investment, accurate prediction of financial market values can increase investor profits. Investor personality affects specific portfolio solutions, which keeps them symmetrical in the process of investment competition. However, information is often asymmetric in financial markets, and this information bias often results in different future returns for investors. Nowadays, machine learning algorithms are widely used in the field of financial investment. Many advanced machine learning algorithms can effectively predict future market changes and provide a scientific basis for investor decisions. The purpose of this paper is to study the problem of optimal matching of financial investment by using machine learning algorithms combined with finance and to reduce the impact of information asymmetry for investors effectively. Moreover, based on the model results, we study the effects of different investor personalities on factors such as expected investment returns and the number of transactions. Based on the time-series characteristics of price data, through multi-model comparison, we select the ARIMA model combined with particle swarm algorithm to determine the optimal prediction model and introduce the concepts of mean-variance model, Sharpe ratio, and efficient frontier to find the balance point of risk and return. In this study, we use gold and bitcoin price data from 2016–2021 to develop optimal investment strategies and study the impact of investor behavior on trading strategies.

Multicontractor multiproject matching optimization for planning modular school construction programs

In a practical context of construction management, a number of special contractors are selected to deliver a multiproject program in a definitive time frame. Research has yet to address how well contractors are matched to projects in scheduling and how to evaluate this criterion in scheduling optimization analysis. This research formulates a novel resource scheduling optimization problem termed multicontractor multiproject matching optimization problem (MCMPMO) based on the current practice of planning modular school development programs. The particular goal of MCMPMO is to determine which contractor is a better match for delivering which project in such a way that the program would be completed by available resources in time, resulting in the highest chances of completing the whole program to the satisfaction of all the stakeholders. A bi-objective optimization formulation for MCMPMO is proposed in the application context of planning modular school development programs. A computer program was prototyped to identify a Pareto front of the MCMPMO problem in a case study.

A fluctuation result for the displacement in the optimal matching problem

The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given by the solution to the linearized equation that is, the Poisson equation. Moreover, we prove that at all mesoscopic scales, this displacement is close in suitable negative Sobolev spaces to a curl-free Gaussian free field. For this, we combine a quantitative estimate on the difference between the displacement and the linearized object, which is based on the large-scale regularity theory recently developed in collaboration with F. Otto, together with a qualitative convergence result for the linearized problem.

A Lightweight Top-Down Multi-Person Pose Estimation Method Based on Symmetric Transformation and Global Matching

The top-down human pose estimation method usually faces the following problems: (i) The target detection result is not well applied in the pose estimation network. (ii) Difficulty of human detection in the crowded state. (iii) The complicated model leads to a long training time. Aiming at the issues above, a lightweight multi-person pose estimation method based on symmetric transformation and global matching is proposed. Symmetric transformation module adds spatial transformation network(STN) and spatial de-transformer network(SDTN) before and after the single-person pose estimation(SPPE) to extract high-quality single-person pose regions from inaccurate human candidate frames. Global matching method is used to transform the key point prediction problem into the optimal matching problem of the human body-key point graph, and solve the questions of misjudgment and error detection of pose estimation in the crowded state. Finally, depth wise separable convolution and inverted residual model are used to reduce the complexity of model, so as to improve the running speed while balancing the accuracy of the algorithm. Experiments show that the algorithm proposed in this paper not only enhance the overall performance of the multi-person posture estimation network in the crowded state, but also improves the running speed significantly, which further confirms the effectiveness and competitiveness of this algorithm.

An energy efficient scheme by exploiting multi-hop D2D communications for 5G networks

The multi-hop Device-to-Device (M-D2D) communication has a potential to serve as a promising technology for upcoming 5G networks. The prominent reason is that the M-D2D communication has the potential to improve coverage, enhanced spectrum efficiency, better link quality, and energy-efficient communication. One of the major challenges for M-D2D communication is the mitigation of interference between the cellular user (CUs) and M-D2D users. Considering this mutual interference constraint, this work investigates the problem of optimal matching of M-D2D links and CUs to form spectrum-sharing partners to maximize overall sum rates of the cell under QoS and energy efficiency (EE) constraints. In this paper, we investigate the interference management for multi-hop (more than one-hop) D2D communication scenarios where we propose a channel assignment scheme along with a power allocation scheme. The proposed channel assignment scheme is based on the Hungarian method in which the channel assignment for M-D2D pairs is done by minimum interference value. The power allocation scheme is based on Binary Particle swarm optimization (BPSO). This scheme calculates the specific power values for all the individual M-D2D links. We have done a comprehensive simulation and the result portrays that our proposed scheme performs better compared to the previous work mentioned in the literature. The results clearly indicate that the proposed scheme enhances the EE of up to 13% by producing the optimal assignment of channels and power for the CUs and M-D2D users.

Polymatching algorithm in observational studies with multiple treatment groups

Matched designs are commonly used in non-randomized studies to evaluate causal effects for dichotomous treatment. Optimal matching algorithms have been devised to form matched pairs or sets between treatment and control groups in various designs, including 1-k matching and full matching. With multiple treatment arms, however, the optimal matching problem cannot be solved in polynomial-time. This is a major challenge for implementing matched designs with multiple arms, which are important for evaluating causal effects with different dose levels or constructing evidence factors with multiple control groups. A polymatching framework for generating matched sets among multiple groups is proposed. An iterative multi-way algorithm for implementation is developed, which takes advantage of the existing optimal two-group matching algorithm repeatedly. An upper bound for the total distance attained by our algorithm is provided to show that the distance result is close to the optimal solution. Simulation studies are conducted to compare the proposed algorithm with the nearest neighbor algorithm under different scenarios. The algorithm is also used to construct a difference-in-difference matched design among four groups, to examine the impact of Medicaid expansion on the health status of Ohioans.

On the scaling of wind turbine rotors

Abstract. This paper formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on the subscaling problem, i.e., on the design of a smaller-sized model that mimics a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial, and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a subscaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, the article continues by considering the problem of designing scaled rotors that match desired indicators of a full-scale reference. To better illustrate the challenges implicit in scaling and the necessary tradeoffs and approximations, two different approaches are contrasted. The first consists in a straightforward geometric zooming. An analysis of the consequences of zooming reveals that, although apparently simple, this method is often not applicable in practice, because of physical and manufacturing limitations. This motivates the formulation of scaling as a constrained optimal aerodynamic and structural matching problem of wide applicability. Practical illustrations are given considering the scaling of a large reference 10 MW wind turbine of about 180 m in diameter down to three different sizes of 54, 27, and 2.8 m. Results indicate that, with the proper choices, even models characterized by very significant scaling factors can accurately match several key performance indicators. Additionally, when an exact match is not possible, relevant trends can at least be captured.

Optimal matching investigation of marine contra-rotating propellers for energy consumption minimization

To minimize the energy consumption of contra-rotating propellers (CRPs), the optimal matched rotational speeds of the forward propeller (FP) and rear propeller (RP) of CRP are investigated based on the potential-based panel method. The optimal matching problem of a set of CRP405 is investigated. The open-water hydrodynamic performances of CRP405 with the FP and RP having the same rotational speed are calculated and the method is validated. The hydrodynamic characteristics of CRP405 with changing FP and RP rotational speeds are investigated. The cubic spline interpolation method is used to determine the equal thrust line at which CRP405 generates the target thrust while keeping the inflow velocity constant. A series of equal thrust points on the equal thrust line is selected for the analysis of the delivered power. The rotational speeds of the FP and RP corresponding to the minimal delivered power are the optimal matched rotational speeds of CRP405. The optimal matching calculations are carried out at different inflow velocities. The results show that, under the condition of a low inflow velocity, properly increasing the rotational speed of the FP and decreasing the rotational speed of the RP are the most direct and efficient ways to reduce the energy consumption and avoid the negative effect of the net torque of the CRP on the transverse stability.

Socially Aware Device-to-multi-device User Grouping for Popular Content Distribution

The distribution of popular videos incurs a large amount of traffic at the base stations (BS) of networks. Device-to-multi-device (D2MD) communication has emerged an efficient radio access technology for offloading BS traffic in recent years. However, traditional studies have focused on synchronous user requests whereas asynchronous user requests are more common. Hence, offloading BS traffic in case of asynchronous user requests while considering their time-varying characteristics and the quality of experience (QoE) of video request users (VRUs) is a pressing problem. This paper uses social stability (SS) and video loading duration (VLD)-tolerant property to group VRUs and seed users (SUs) to offload BS traffic. We define the average amount of data transmission (AADT) to measure the network’s capacity for offloading BS traffic. Based on this, we formulate a time-varying bipartite graph matching optimization problem. We decouple the problem into two subproblems which can be solved separately in terms of time and space. Then, we propose the socially aware D2MD user selection (SA-D2MD-S) algorithm based on finite horizon optimal stopping theory, and propose the SA-D2MD user matching (SA-D2MD-M) algorithm to solve the two subproblems. The results of simulations show that our algorithms outperform prevalent algorithms.

Dynamic asymmetric assignment problem in open multi-agent systems

The purpose of the work is to develop models and algorithms for optimizing matching in dynamically generated graphs of asymmetric relations in coordinated open systems of interacting agents with centralized and collective control. The dynamic asymmetric matching optimization problem arises here as a result of a compromise approximation of the mapping of the dynamic programming method onto a stream of known open assignment problems or several traveling salesmen. However, the branching alternatives presented in this way for independent tasks do not take into account the interdependence of real relationships between agents and their tasks, including their relationship to time. Ignoring the dependence of branching alternatives leads to a delay in the moment or to a loss in the quality of assignment of tasks to coordinated agents. The main idea of the proposed implementation of the principle known for effective control is to postpone the moment the final decision is made to the latest moment, taking into account the susceptibility of the system to local changes in state variables. The interdependence of states is revealed on the basis of the analysis of the correspondence of the graph of the current matching with the optimal solution on the subgraph of perfect matching. The transition between states is implemented by the incremental version of the reoptimization algorithm for solving linear problems of assigning the shortest replenishing path using the method. The space of search states is a dynamically generated bipartite sparse graph of alternatives for a combination of agents and tasks, represented by a list of arcs. To highlight the sets of changed arcs, it is proposed to supplement the weight of the arcs with the boundaries of the stability intervals of the solution, optionally formed in the background. By default, the weight of the modified arc matches the boundary of the stability interval. On each correction cycle of the lists of agents, tasks, and their associations, subsets of elements are selected for which reconsideration of matching is required. An enhanced condition for the selection of such elements is to go beyond the boundaries of the stability interval. In this case, the asymmetry of the assignment problem is taken into account by choosing the adjacency structure for the fraction of the graph with a minimum of vertices. As a result, the reaction time of procedures for solving the assignment problem is reduced by an order of magnitude.

Geometry consistency aware confidence evaluation for feature matching

Most existing approaches prune wrong matches via estimating an image transformation or solving a graph-based global matching optimization problem, which usually suffers from varying local transformations and outliers. Inspired by the insight that neighboring true matches usually hold consistent local topological structures across images, in this paper we propose a new approach to evaluate the confidence of each putative match based on how well its two keypoints can predict each other by exploring the geometric constraint with its neighboring matches. With the evaluation, a two-stage approach combining recursively false match pruning and correct match incrementing is presented to obtain the reliable matches. Experiments on various image pairs demonstrate that our approach can conduct robust feature matching in challenging conditions and outperform state-of-the-art approaches.

Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics

We explore upper bounds on Kantorovich transport distances between probability measures on the Euclidean spaces in terms of their Fourier-Stieltjes transforms, with focus on non-Euclidean metrics. The results are illustrated on empirical measures in the optimal matching problem on the real line.

On optimal matching of Gaussian samples III

This article is a continuation of the papers [8,9] in which the optimal matching problem, and the related rates of convergence of empirical measures for Gaussian samples are addressed. A further step in both the dimensional and Kantorovich parameters is achieved here, proving that, given $X_1, \ldots, X_n$ independent random variables with common distribution the standard Gaussian measure $\mu$ on $\mathbb{R}^d$, $d \geq 3$, and $\mu_n \, = \, \frac 1n \sum_{i=1}^n \delta_{X_i}$ the associated empirical measure, $$ \mathbb{E} \big( \mathrm {W}_p^p (\mu_n , \mu )\big ) \, \approx \, \frac {1}{n^{p/d}} $$ for any $1\leq p < d$, where $\mathrm {W}_p$ is the $p$-th Kantorovich metric. The proof relies on the pde and mass transportation approach developed by L. Ambrosio, F. Stra and D. Trevisan in a compact setting.

Optimal Matching Problem for Ride-Sharing Considering Users’ Schedule Rearrangement

This paper proposed an optimal matching problem between drivers and riders for ride-sharing. The model assumes that all Space-time Extended Network (STEN) links have measurable utility based on the activity desired by each user. The ride-sharing service is designed to maximise the social utility of all users while considering the capacity constraints of vehicles. As user activity over the entire study period is taken into account, the model accommodates changes, and even cancellations, in the timing of user activity without addition of any further parameters. Furthermore, the model allows evaluation of the diffusion effects of autonomous vehicles used for ride-sharing. A case study using a hypothetical network confirmed that autonomous vehicle diffusion not only reduced detours during pick-up, but also encouraged riders to travel. Vehicle diffusion increased total user utility and helped to equalise opportunities for user activities. Although autonomous vehicle diffusion may increase total travel time, this can be mitigated by vehicle-sharing.