Stable Matching Research Articles

Platform-based stable truck matching problem with trailer-swapping mode

This study investigates the platform-based stable truck-matching problem with trailer-swapping mode (STMP-TSM). The TSM is a novel collaborative transportation approach in which trucks participate in trailer swapping, significantly decreasing the rate of empty trucks and reducing transportation costs. In the STMP-TSM, a platform delivers a trailer-swapping scheme that satisfies all participating trucks. Correspondingly, an integer linear programming model is developed to maximize the total truck utility of the STMP-TSM. A specific preference list based on a chain-data structure is meticulously constructed to obtain a stable matching scheme. The preference list enables more generalized truck matching. In addition, a series of acceleration strategies is proposed to expedite the generation of a preference list while effectively reducing its length. An iterative preference-list-trim heuristic algorithm is designed, which strategically trims chains in the preference list to solve the STMP-TSM efficiently. As a benchmark, an integer linear programming model is developed based on the preference list to solve the truck-matching problem using the TSM. Finally, a series of numerical experiments are conducted to evaluate the performance of the proposed algorithm, assess the practicality of the TSM, and analyze the influences of the key parameters.

Design an intermediary mobility-as-a-service (MaaS) platform using many-to-many stable matching framework

Mobility-as-a-service (MaaS) provides seamless door-to-door trips by integrating different transport modes. Although many MaaS platforms have emerged in recent years, most of them remain at a limited integration level. This study investigates the assignment and pricing problem for a MaaS platform as an intermediary in a multi-modal transportation network, which purchases capacity from service operators and sells multi-modal trips to travelers. The analysis framework of many-to-many stable matching is adopted to decompose the joint design problem and to derive the stability condition such that both operators and travelers are willing to participate in the MaaS system. To maximize the flexibility in route choice and remove boundaries between modes, we design an origin–destination pricing scheme for MaaS trips. On the supply side, we propose a wholesale purchase price for service capacity. Accordingly, the assignment problem is reformulated and solved as a bi-level program, where MaaS travelers make multi-modal trips to minimize their travel costs meanwhile interacting with non-MaaS travelers in the multi-modal transport system. We prove that, under the proposed pricing scheme, there always exists a stable outcome to the overall many-to-many matching problem. Further, given an optimal assignment and under some mild conditions, a unique optimal pricing scheme is ensured. Numerical experiments conducted on the extended Sioux Falls network also demonstrate that the proposed MaaS system could create a win-win-win situation—the MaaS platform is profitable and both traveler welfare and transit operator revenues increase from a baseline scenario without MaaS.

Stable Matching on the Job? Theory and Evidence on Internal Talent Markets

Stable Matching on the Job? Theory and Evidence on Internal Talent Markets

Estimating separable matching models

SummaryMost recent empirical applications of matching with transferable utility have imposed a natural restriction: that the joint surplus be separable in the sources of unobserved heterogeneity. We propose here two simple methods to estimate models in this class. The first method is a minimum distance estimator that relies on the generalized entropy of matching. The second applies to the more special but popular Choo and Siow model, which reformulates as a generalized linear model with two‐way fixed effects. Neither method requires solving for the stable matching. Both methods are easy to apply and perform very well.

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.

Bandit learning based stable matching for decentralized task offloading in dynamic fog computing networks

Bandit learning based stable matching for decentralized task offloading in dynamic fog computing networks

Efficiency and maximality in anonymous two-sided economies

We study efficiency and maximality in anonymous two-sided economies, where each agent only cares about trading with a desired number of partners from the opposite side. For both homogeneous and heterogeneous economies, we provide a necessary and sufficient condition that ensures the efficiency of all pairwise stable matchings. In addition, we provide a sufficient condition for maximality in heterogeneous economies. These conditions have implications for the design of anonymous markets that function optimally without the continuous intervention of a social planner.

Stable container-route matching in multimodal transport: A case of Yangtze River Economic Belt

Multimodal transport is promoted along the Yangtze River Economic Belt to facilitate transport between rivers and seas. This paper introduces a container-route matching problem with choice behavior in multimodal transport of the Yangtze River Economic Belt. The concept of stable matching is used to assign containers to multimodal routes in which shippers have preferences over multimodal routes and multimodal routes have preferences over shipment groups. The preference is formed as a combination of self-preference regarding freight rates and transport time, and other-preference regarding cooperation. A stable container-route matching model is formulated to tailor the non-independent preferences of shippers and route operators. A local search algorithm is designed to solve the stable container-route matching problem. The multimodal transport along the Yangtze River Economic Belt including river-sea combined transport, river-sea transport and rail-sea combined transport is used to validate the proposed model. Extensive computational experiments show that it costs to keep the cooperative relationship to avoid the risks from market fluctuations. When shipments of cooperative partners need to be transported, the total capacity utilization of routes reduces by 26 %. For high-value cargo and time-sensitive cargo, the time preference of shippers has a greater impact than the freight preference. River-sea transport is more competitive than rail-sea combined transport.

Not all is lost: Sorting and self-stabilizing sets

It is well known that in the absence of transfers, stable matchings are positive assortative when agents' preferences are strictly monotonic in each other's types and types are commonly known. Instead, monotonicity is consistent with the existence of stable matchings that exhibit negative sorting when types on one side of the market are private information. This paper sheds light on the scope and meaning of this consistency by showing that within familiar monotonic markets we cannot conclude that a stable matching is negative, and not positive, assortative.

Many-to-one matching based cooperative spectrum sharing in overlay cognitive radio networks

Cooperative Spectrum Sharing (CSS) is a Dynamic Spectrum Access mechanism aimed at providing incentives for both primary users (PUs) and secondary users (SUs) through cooperative communication. This paper addresses the pairing problem among multiple PUs and SUs to allocate optimal fractions of spectrum resources in terms of access time, using the CSS technique. Inspired by Matching Theory, we model the CSS between PUs and SUs as a Two-sided Matching Market and explore different market equilibria. Cooperative strategies among SUs are employed to maximize the gross utility of cooperative SUs and overall utility of the secondary network, in exchange for relay services rendered to PUs. We propose a polynomial-time based many-to-one matching scheme that favors groups of collaborative SUs to attract favorable PUs from the opposite side, leading to optimal matching for SUs. On the other hand, each PU achieves stable matching when paired with a group of cooperative SUs. We provide necessary proofs for the achieved matching equilibrium. Furthermore, we formulate an optimization framework for the optimal usage of PU access time among stable PU-SU pairs and propose a near-optimal solution, achieving 96% accuracy compared to the optimal allocation yield from the benchmark method (analytical). Our proposed many-to-one matching scheme outperforms similar existing schemes and the one-to-one matching scheme in terms of SU utility, satisfaction, participation, and throughput fairness index.

Active mixing of two-component viscoelastic silicone ink at molecular level for spatiotemporally controlled 3D/4D printing of cellular silicones

3D printed silicones have demonstrated great potential in diverse areas such as soft robots, tissue engineering, flexible sensors and energy dissipation. However, most silicone inks face inevitable curing issue once it is prepared. During the materials extrusion based printing process, the curing-related viscosity change in silicone inks hamper the ink stability and printing controllability, leading to complex relationship among ink properties and printing parameters, as well as printing structures and material properties of final products. Herein, this work presents active mixing of two component silicone ink to realize stable printing, achieving exact and continuous match of ink properties and printing parameters. Using a specially formulated ink containing separate starting components with reactive groups, catalyst and thixotropic agents, this work studies the active mixing process thoroughly for the first time from molecular level to materials performances under various conditions regarding inlet flow rates, impeller rotation speed and component ratios. Besides, cellular silicones with controlled distribution of component ratios and tailored gradient structures are printed, leading to integrated manufacturing of compression performance and shape morphing property. This work will pave way for active mixing and printing of two-component silicones, and provide guidance for other reactive multi-material 3D printing systems.

Blockchain-based cooperative game bilateral matching architecture for shared storage

The development of IPFS (InterPlanetary File System) and blockchain-based distributed storage projects has brought new possibilities to the field of storage. This paper proposes a blockchain-based cooperative game bilateral matching architecture as a novel approach for shared storage networks. In traditional competitive (non-cooperative) game models, the allocation of storage resources is centered around pricing, leading to a scenario where node providers often engage in price competition to obtain greater rewards, resulting in an imbalance in resource allocation for both buyers and sellers. In contrast, a distributed storage model based on cooperative game theory can better facilitate cooperation and resource sharing among node providers. This paper designs a storage resource allocation algorithm based on the stable marriage matching algorithm, demonstrating the stability of this algorithm as a matching solution. The paper also analyzes the differences between cooperative and non-cooperative game models in the market, and explores an equilibrium pricing mechanism guided by supply and demand. Furthermore, the paper introduces a trading mechanism for storage resources, including publication standards and matching schemes, ensuring efficient and trustworthy interaction between storage suppliers and demanders in a decentralized network centered around storage resources, thus enabling the circulation of the value of storage resources. A prototype of a blockchain-based shared storage trading system is implemented in this paper, utilizing bilateral matching for tradings. System evaluation and experimental testing are conducted, with results showing that the average utility value of the matching trading mechanism proposed in this paper outperforms the Double Auction-based matching model under any Poisson distribution (λ = 0.1, 0.2, 0.3, …, 0.9) conditions set in the experiments. Additionally, compared to the traditional approach of directly storing complete data content on the chain, the design proposed in this paper effectively reduces on-chain storage consumption by approximately 27.06%.

The Levels of Psychological Well-Being among Married Couples in Selected Parishes in the Catholic Archdiocese of Nairobi, Kenya

A stable marriage is crucial for establishment of a prosperous community, but this depends on psychological well-being of the couples. This study investigated the levels of psychological well-being among couples in selected parishes in the Catholic Archdiocese of Nairobi (CAN), Kenya. The study was guided by Adlerian Theory and employed concurrent convergent mixed methods research design. The target population was 19,828 Catholic faithful, who have exchanged their marital vows in CAN within the last 5 to 25 years. A sample of 784 married men and women were selected by multistage sampling and used as respondents. The psychological well-being questionnaire was used to collect data, which were analyzed descriptively using frequency counts and percentages. Findings revealed that psychological well-being of the married couples was in three levels thus low, moderate and high. It is recommended that policy should be made by the government of Kenya through the office of the Attorney general by formulating a legal framework to ensure all newly married couples are trained on various aspects of psychological well-being so as to ensure stable marriage.

A Map of Diverse Synthetic Stable Matching Instances

Focusing on Stable Roommates (SR), we contribute to the toolbox for conducting experiments for stable matching problems. We introduce the polynomial-time computable mutual attraction distance to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar with respect to our mutual attraction distance to each other. Subsequently, we conduct several illustrative experiments and depict their results on the map, illustrating the map’s usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures. Lastly, we extend our approach to the bipartite Stable Marriage problem.

Postsynaptic receptors regulate presynaptic transmitter stability through transsynaptic bridges

Stable matching of neurotransmitters with their receptors is fundamental to synapse function and reliable communication in neural circuits. Presynaptic neurotransmitters regulate the stabilization of postsynaptic transmitter receptors. Whether postsynaptic receptors regulate stabilization of presynaptic transmitters has received less attention. Here, we show that blockade of endogenous postsynaptic acetylcholine receptors (AChR) at the neuromuscular junction destabilizes the cholinergic phenotype in motor neurons and stabilizes an earlier, developmentally transient glutamatergic phenotype. Further, expression of exogenous postsynaptic gamma-aminobutyric acid type A receptors (GABAA receptors) in muscle cells stabilizes an earlier, developmentally transient GABAergic motor neuron phenotype. Both AChR and GABAA receptors are linked to presynaptic neurons through transsynaptic bridges. Knockdown of specific components of these transsynaptic bridges prevents stabilization of the cholinergic or GABAergic phenotypes. Bidirectional communication can enforce a match between transmitter and receptor and ensure the fidelity of synaptic transmission. Our findings suggest a potential role of dysfunctional transmitter receptors in neurological disorders that involve the loss of the presynaptic transmitter.

The law of large numbers for large stable matchings

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges’ preferences while allowing students’ preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.

Text recuperated using ontology with stable marriage optimization technique and text visualization using AR

Text recuperated using ontology with stable marriage optimization technique and text visualization using AR

Stable Matchings in Practice: A Constraint Programming Approach

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

Improved Bandits in Many-to-One Matching Markets with Incentive Compatibility

Two-sided matching markets have been widely studied in the literature due to their rich applications. Since participants are usually uncertain about their preferences, online algorithms have recently been adopted to learn them through iterative interactions. An existing work initiates the study of this problem in a many-to-one setting with responsiveness. However, their results are far from optimal and lack guarantees of incentive compatibility. We first extend an existing algorithm for the one-to-one setting to this more general setting and show it achieves a near-optimal bound for player-optimal regret. Nevertheless, due to the substantial requirement for collaboration, a single player's deviation could lead to a huge increase in its own cumulative rewards and a linear regret for others. In this paper, we aim to enhance the regret bound in many-to-one markets while ensuring incentive compatibility. We first propose the adaptively explore-then-deferred-acceptance (AETDA) algorithm for responsiveness setting and derive an upper bound for player-optimal stable regret while demonstrating its guarantee of incentive compatibility. This result is a significant improvement over existing works. And to the best of our knowledge, it constitutes the first player-optimal guarantee in matching markets that offers such robust assurances. We also consider broader substitutable preferences, one of the most general conditions to ensure the existence of a stable matching and cover responsiveness. We devise an online DA (ODA) algorithm and establish an upper bound for the player-pessimal stable regret for this setting.

An efficient two-heuristic algorithm for the student-project allocation with preferences over projects

The Student-Project Allocation with preferences over Projects problem is a many-to-one stable matching problem that aims to assign students to projects in project-based courses so that students and lecturers meet their preference and capacity constraints. In this paper, we propose an efficient two-heuristic algorithm to solve this problem. Our algorithm starts from an empty matching and iteratively constructs a maximum stable matching of students to projects. At each iteration, our algorithm finds an unassigned student and assigns her/his most preferred project to her/him to form a student-project pair in the matching. If the project or the lecturer who offered the project is over-subscribed, our algorithm uses two heuristic functions, one for the over-subscribed project and the other for the over-subscribed lecturer, to remove a student-project pair in the matching. To reach a stable matching of a maximum size, our two heuristics are designed such that the removed student has the most opportunities to be assigned to some project in the next iterations. Experimental results show that our algorithm is efficient in execution time and solution quality for solving the problem.