Deferred Acceptance Algorithm Research Articles

An Energy-Delay Trade-Off in Wireless Visual Sensor Networks Based on Two-Sided Matching

Wireless visual sensor networks (WVSNs) comprise a large number of battery-powered visual sensors with limited processing and transmission capacity in the field of interest. Hence, energy conservation is an important issue in resource-constrained WVSNs. In-network data fusion, clustering networks has been proved to be an effective scheme in reducing energy consumption. However, in most clustering algorithms, clustering may introduce bottlenecks to WVSNs which bring extra delay in the processes of data collection and forwarding. Such delay can be reduced by the design of routing schemes. In this paper, we propose an approach of energy-delay trade-off (EDT) based on two-sided matching theory. First, we determine a balance clustering structure which can balance energy consumption and delay in random-densely-deployed WVSNs. Then, the problem formulation of EDT problem in the balance clustering structure is provided. Moreover, the transformation strategy based on two-sided matching (TS-TSM) is proposed. After the TS-TSM, the EDT problem is transformed into a stable two-sided matching (STSM) problem with single objective function and the computational complexity is reduced. Furthermore, most of floating-point operations in original EDT problem are converted into integer operations which are easy to parallel compute. Finally, an improved deferred-acceptance algorithm (IDAA) is provided to generate a stable matching solution as the EDT scheme. Evaluation results demonstrate that the EDT approach can reduce delay in data aggregation processes and keep the total energy consumption at low levels. Further simulations show that the EDT approach is a fast approach, and it is not inferior to the existing algorithms.

Stable User Association and Resource Allocation Based on Stackelberg Game in Backhaul-Constrained HetNets

In heterogeneous networks (HetNets), user association approaches should be able to achieve load balancing among base stations (BSs). This paper investigates the joint optimization of user association and resource allocation in Backhaul-constrained HetNets for capacity enhancements. We consider two major limitations in HetNets: the backhaul bottleneck of BSs and the capability of user equipment (UE). We establish a framework based on a multi-leader multi-follower Stackelberg game, in which resource allocation is formulated as a follower-level game and user association is cast as a leader-level game. Because of the backhaul bottleneck of small BSs, the given preference order of users renders the final association result unstable. Thus, the resident-oriented Gale-Shapley (GS) algorithm is included in the proposed framework to obtain a stable single-BS association. Furthermore, congestion factors are introduced to reflect the relative backhaul congestion degrees of BSs, which enables load balancing among the small BSs in the proposed algorithm. The study considers user association and resource allocation with and without limitations on the number of serving users for small BSs in HetNets. Extensive simulation results suggest that the proposed algorithm can adaptively respond to a wide variety of network situations.

An Efficient Resource Allocation Algorithm for Device-To-Device Communications

In order to solve the problem of interference and spectrum optimization caused by D2D (device-to-device) communication multiplexing uplink channel of heterogeneous cellular networks, the allocation algorithm based on the many-to-one Gale-Shapley (M21GS) algorithm proposed in this paper can effectively solve the resource allocation problem of D2D users multiplexed cellular user channels in heterogeneous cellular network environments. In order to improve the utilization of the wireless spectrum, the algorithm allows multiple D2D users to share the channel resources of one cellular user and maintains the communication service quality of the cellular users and D2D users by setting the signal to interference and noise ratio (SINR) threshold. A D2D user and channel preference list are established based on the implemented system’s capacity to maximize the system total capacity objective function. Finally, we use the Kuhn–Munkres (KM) algorithm to achieve the optimal matching between D2D clusters and cellular channel to maximize the total capacity of D2D users. The MATLAB simulation is used to compare and analyze the total system capacity of the proposed algorithm, the resource allocation algorithm based on the delay acceptance algorithm, the random resource allocation algorithm and the optimal exhaustive search algorithm, and the maximum allowable access for D2D users. The simulation results show that the proposed algorithm has fast convergence and low complexity, and the total capacity is close to the optimal algorithm.

Behavioral Habits-Based User Identification Across Social Networks

Social networking is an interactive Internet of Things. The symmetry of the network can reflect the similar friendships of users on different social networks. A user’s behavior habits are not easy to change, and users usually have the same or similar display names and published contents among multiple social networks. Therefore, the symmetry concept can be used to analyze the information generated by the user for user identification. User identification plays a key role in building better information about social network user profiles. As a consequence, it has very important practical significance in many network applications and has attracted a great deal of attention from researchers. However, existing works are primarily focused on rich network data and ignore the difficulty involved in data acquisition. Display names and user-published content are very easy to obtain compared to other types of user data across different social networks. Therefore, this paper proposes an across social networks user identification method based on user behavior habits (ANIUBH). We analyzed the user’s personalized naming habits in terms of display names, then utilized different similarity calculation methods to measure the similarity of the features contained in the display names. The variant entropy value was adopted to assign weights to the features mentioned above. In addition, we also measured and analyzed the user’s interest graph to further improve user identification performance. Finally, we combined one-to-one constraint with the Gale–Shapley algorithm to eliminate the one-to-many and many-to-many account-matching problems that often occur during the results-matching process. Experimental results demonstrated that our proposed method enables the possibility of user identification using only a small amount of online data.

Centralized Admissions for Engineering Colleges in India

The authors designed a process, based on the Deferred Acceptance algorithm, to allocate undergraduate admissions to over 500 programs in 80 technical universities in India. They also addressed complex rules regarding affirmative action by incorporating algorithmic innovations.

A stable marriage requires communication

In 1976, Knuth asked whether the worst-case running-time of the Gale-Shapley algorithm for the Stable Marriage Problem can be improved when non-sequential access to the input is allowed. Partial negative answers were given by Ng and Hirschberg and as part of Segal's general communication-complexity analysis. We give a far simpler, yet significantly more powerful, argument showing that Ω(n2) Boolean queries of any type are required for finding a stable — or even approximately stable — marriage. Unlike Segal's lower bound, our lower bound generalizes additionally to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's and men's respective preferences profiles, (C) related problems, e.g. whether a given pair is married in every/some stable marriage, (D) whether a proposed marriage is stable or far from stable. To analyze “approximately stable” marriages, we introduce the notion of “distance to stability” and provide an efficient algorithm for its computation.

Partners in Crime: Manipulating the Deferred Acceptance Algorithm through an Accomplice

We introduce a new manipulation strategy available to women in the men-proposing stable matching, called manipulation through an accomplice. In this strategy, a woman can team up with a potential male “accomplice” who manipulates on her behalf to obtain a better match for her. We investigate the stability of the matching obtained after this manipulation, provide an algorithm to compute such strategies, and show its benefit compared to single-woman manipulation strategies.

On the Existence of Stable Allocations in Matching Games with Infinite Contracts: Leveraging the Deferred Acceptance Algorithm

In classic matching games, individuals choose their partners and each pair chooses a contract from a finite set of feasible contracts; the existence of stable allocations then follows from the (generalized) Deferred Acceptance algorithm. We consider an extension where the contract set is a compact subset of a Banach space (e.g., R^k or C[0, 1]) and establish, using only elementary methods, that this algorithm continues to ensure the existence of stable allocations.

Energy trading framework for electric vehicles: an assignment matching‐theoretic game

Electric Vehicles (EVs) can be considered as a flexible source of energy which can receive some benefit in terms of incentives for selling their energy. For efficient and economic trading amongst the EV owners, various researchers have proposed a variety of preference based matching algorithms like College Admission Framework (CAF), Max-weight, Merge and Split, Gale-Shapley Algorithm and Brute-Force Algorithm etc, where buyer and seller EVs can exchange energy and receive better payoffs. Unlike the above mentioned algorithms, in this paper the participating entities do not submit the preferences menu (which contains preferred choices of sellers (of a buyer) and of buyers (for a seller)) to a central authority.) However, this paper proposes an assignment energy trading game where no central authority is needed, the matching algorithm is hosted on cloud which matches charging and discharging of EVs based on their aspiration level and bids. The contribution of the work is to deduce the bids and aspiration level of charging and discharging EVs which is not considered in any of the existing work. Another contribution of the work is the behavioral assignment game that eludes the need of integer linear programming problem and deduces the convergence of game by adjustments of aspiration levels. Futhermore, the entire algorithm is cloud hosted with no middleman hence trading EVs identities are concealed from each other making the system unbiased. The proposed game helps both the buyer and the seller side of EVs to achieve their best bids as well as by reducing grid dependency it boosts the profit margin of the charging stations (CS).

A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem

The paper develops a new extension of the sequential preference condition, which leads to unique stable matching in all subpopulations, obtained by consistent restrictions of the marriage matching problem. Under the new condition, the Gale–Shapley algorithm is stable, consistent, strategy-proof, Pareto optimal for men, and Pareto optimal for women.

Two Problems in Max-Size Popular Matchings

We study popular matchings in the many-to-many matching problem, which is given by a graph $$G = (V,E)$$ and, for every agent $$u\in V$$ , a capacity $$\textsf {cap}(u) \ge 1$$ and a preference list strictly ranking her neighbors. A matching in G is popular if it weakly beats every matching in a majority vote when agents cast votes for one matching versus the other according to their preferences. First, we show that when $$G = (A\cup B,E)$$ is bipartite, e.g., when matching students to courses, every pairwise stable matching is popular. In particular, popular matchings are guaranteed to exist. Our main contribution is to show that a max-size popular matching in G can be computed in linear time by the 2-level Gale–Shapley algorithm, which is an extension of the classical Gale–Shapley algorithm. We prove its correctness via linear programming. Second, we consider the problem of computing a max-size popular matching in $$G = (V,E)$$ (not necessarily bipartite) when every agent has capacity 1, e.g., when matching students to dorm rooms. We show that even when G admits a stable matching, this problem is $$\mathsf {NP}$$ -hard, which is in contrast to the tractability result in bipartite graphs.

Are Affirmative Action Policies so Impossible?

Les politiques de discriminations positives sont un outil utilisé par nombre de décideurs politiques. Un de leurs objectifs est d’améliorer le bien-être d’un groupe ciblé d’étudiants lors d’une procédure d’admission au sein des écoles. Cependant, il est bien connu au sein de la littérature sur les problèmes d’affectation que ces politiques peuvent avoir des effets pervers : les étudiants ciblés peuvent être heurtés par cette dernière. Dans cet article, nous prenons une perspective de bien être interim et montrons que, dans l’environnement particulier de préférences alignées et d’écoles indifférentes, le fameux algorithme à Acceptation Différée ne nuit jamais au bien être des étudiants minoritaires une fois qu’une politique de discrimination positive est mise en place. Nous soulignons les effets sur le bien-être que peuvent avoir l’ordre dans lequel les places au sein des écoles sont affectées au cours de l’algorithme, appelé precedence order . Notre preuve principale montre deux effets d’un renforcement d’une politique de discrimination positive. Un effet direct où la politique augmente la probabilité qu’un étudiant minoritaire a d’être affecté au sein des écoles dans lesquelles la politiques est renforcée. Et un effet indirect : la politique diminue la compétition entre étudiants minoritaires au sein des écoles qui donnent priorité aux minoritaires mais qui n’ont pas vu leur politique être renforcée ; cela augmente l’espérance d’utilité conditionnelle d’un étudiant minoritaire une fois qu’il a été rejeté par les écoles qui ont vu leur politique renforcée. Nous fournissons également des contres exemples montrant que l’environnement que nous considérons est un domaine maximal pour obtenir des effets positifs des politiques de discrimination positives. Enfin, nous réalisons des simulations pour étudier les effets sur le bien-être interim des politiques de discrimination positives quand nous quittons l’environnement i) des préférences alignées et ii) d’écoles indifférentes. Les résultats soulignent que le plus les préférences des étudiants sont corrélées, meilleures sont les performances de ces politiques et le moins les écoles sont indifférentes, pire sont les performances. Elles soulignent également que la règle utilisée pour casser les indifférences des priorités au sein des écoles peuvent avoir des effets différents : la règle de Casse Multiple d’Indifférences tend à heurter moins d’étudiants minoritaires qu’une règle Casse Unique d’Indifférences .

Pairing clients and psychologists using stable marriage problem approach

Health is an important thing in human life, it includes not only physical health, but also mental health. Choosing the right psychologist will help individuals with mental problem to overcome the problem. Choosing a psychologist is important, because the psychologist’s personality will influence the process of psychotherapy. This research paper will describe our approach in building a Decision Support System model that will compute the pairing of clients and psychologists. In this study, Weighted Sum Model is adopted to calculate the preference value of each individual, both psychologists and clients. Then based on this preference value, the client-psychologist pairing will be calculated using the Stable Marriage Problem approach. The Gale-Shapley Algorithm is used in this system to solve the Stable Marriage Problem and has been able to produce a stable matching between one set of Clients and one set of Psychologists, and there is no blocking pair from the results of this algorithm.

Measuring the External Stability of the One-to-One Matching Generated by the Deferred Acceptance Algorithm

In this paper, we consider a one-to-one matching model where the population expands with the arrival of a man and a woman. Individuals in this population are matched, before and after the expansion, according to a version of the deferred acceptance algorithm (Gale and Shapley, 1962) where men propose and women reject or (tentatively or permanently) accept. Using computer simulations of this model, we study how the percentage of matches disrupted (undisrupted) with the expansion of the population is affected when the initial size of the population and the size of correlation in the preferences of individuals change.

The Success of the Deferred Acceptance Algorithm Under Heterogenous Preferences with Endogenous Aspirations

In this paper, we consider a one-to-one matching model with two phases; an adolescence phase where individuals meet a number of dates and learn about their aspirations, followed by a matching phase where individuals are matched according to a version of Gale and Shapley's (1962) deferred acceptance (DA) algorithm. Using simulations of this model, we study how the likelihoods of matching and divorce, and also the balancedness and the speed of matching associated with the outcome of the DA algorithm are affected by the size of correlation in the preferences of individuals and by the frequency individuals update their aspirations in the adolescence phase.

QoE-Oriented Rate Control and Resource Allocation for Cognitive M2M Communication in Spectrum-Sharing OFDM Networks

With the development of wireless communication systems, it is particularly essential to maximize the quality of experience (QoE) of machine-to-machine (M2M) communication. In this paper, we propose a new QoE-oriented uplink rate control and resource allocation scheme for the Internet of Things (IoT) network, by introducing an evaluation model based on mean opinion score (MOS) for different machine-type communication (MTC) devices. The existing works are only dedicated to solving the short-term resource allocation problems by considering the current transmission time slots, which cannot handle long-standing problems. To this end, based on the recently developed Lyapunov optimization, we convert the original long-term optimization problem into the admission rate control subproblem and the resource allocation subproblem in each time slot. To solve the joint power optimization and sub-channel selection subproblems, Gale-Shapley algorithm is utilized to formulate it as a two-dimensional matching problem, and the preference lists are established by the transmission rate and signal to interference plus noise ratio (SINR). In the proposed algorithms, a priority mechanism is employed to ensure fairness. The simulation results demonstrate that without prior knowledge of the data arrivals and sub-channel statistics, the proposed algorithms can significantly improve the overall perceived quality from the users' perspective.

Learning Management through Matching: A Field Experiment Using Mechanism Design

We place young professionals into established firms to shadow middle managers. Using random assignment into program participation, we find positive average effects on wage employment, but no average effect on the likelihood of self-employment. We match individuals to firms using a deferred-acceptance algorithm, and show how this allows us to identify heterogeneous treatment effects by firm and intern characteristics. We find striking heterogeneity in self-employment effects, and show that some assignment mechanisms can substantially outperform random matching in generating employment and income effects. These results demonstrate the potential for matching algorithms to improve the design of field experiments.

Utility-Based Stable Matching For Large Scale EH Relay Networks With Finite-Alphabet Inputs

The computational complexity of utility optimization for a large scale energy harvesting (EH) relay network is extremely high, especially when inputting finite-alphabet signals. This paper investigates the utility optimization for large scale EH relay networks with finite-alphabet inputs by the stable matching scheme. First, we divide the nodes, which may act as a user or a relay, into multiple clusters, and perform optimization strategy within the clusters. Second, the optimal power bought from the relay node to maximize the utility of the user is derived. Then, the mutual preference matrices between the users and relays by the maximum utility criterion are established. Base on the mutual preference matrices, an improved Gale-Shapley (GS) algorithm is proposed to get a sub-optimal result. The simulation results demonstrate that the proposed algorithm can bring significant performance improvements and achieve higher energy efficiency compared with the conventional algorithms. In contrast to the exhausted Search (ES) method, it costs much less time and accomplishes an approximative utility output. Moreover, the proposed scheme incurs low signaling overhead which makes it practical to be implemented.

A Two-Stage Energy-Efficient Approach for Joint Power Control and Channel Allocation in D2D Communication

A large number of mobile multimedia terminals are prominent features of smart cities. Device-to-device (D2D) communication takes advantage of the limited bandwidth resources of cellular networks to accommodate more mobile devices. However, when D2D pairs reuse cellular users channels, serious interference leads to energy consumption, which dissatisfies the requirements of green communication. This paper focuses on energy efficiency maximization of D2D communication under the constraints of both D2D pairs and cellular users quality of service. The formulated resource allocation problem is NP-hard, which is usually difficult to solve within polynomial time. To make the problem easy to handle, we divide it into power control and channel allocation sub-problems. In particular, we propose a power control algorithm based on the Lambert W function to maximize the energy efficiency of a single D2D pair. The preference values of D2D pairs and cellular users are calculated using the power control results, respectively. A channel allocation scheme based on the Gale-Shapley algorithm utilizes preference values to match two sides, which aims at maximizing the signal to interference plus noise ratio of cellular users and the energy efficiency of D2D pairs. The simulation results show that the proposed algorithm could not only guarantee the transmission rate of cellular users but also improve the system and D2D pairs energy efficiency.

Sorting On-Line and On-Time

Using proprietary data from a Chilean online job board, we find strong, positive assortative matching at the worker-position level, both along observed dimensions and on unobserved characteristics (OLS Mincer residual wages). We also find that this positive assortative matching is robustly procyclical. Since we use information on job applications instead of final matches, we use the generalized deferred-acceptance algorithm to simulate tentative final allocations. Under all considered scenarios for the algorithm, positive assortative matching is preserved from the application stage to the realized matches.