Pareto Order Research Articles

Finite multi-utility representable preferences and Pareto orderings

A characterization of the posets that admit a finite multi-utility representation is presented. This result is also connected to the concept of order dimension of a poset as defined by Dushnik and Miller (1941).

Joint Optimization of AoI, SINR, Completeness, and Energy in UAV-Aided SDCNs: Coalition Formation Game and Cooperative Order

As one of the most important representatives for the edge intelligence, Unmanned Aerial Vehicle (UAV) can be used to provide the intelligent edge service, such as performing data collection, computation and transmission tasks in the air-to-ground networks. In the considered Sensed Data Collection Networks (SDCNs), the UAV is in charge of collecting and computing the sensed data from mobile ground nodes, and multiple performance metrics need to be jointly optimized, including the collected data’s Age of Information (AoI) and the Signal to Interference plus Noise Ratio (SINR) at the UAV from mobile sensor nodes, the data collection areas’ completeness, and the mobile sensor nodes’ energy consumption. Due to the absence of such a joint optimization framework, this paper formulates the mobile sensing nodes deployment problem in the UAV-aided SDCNs. Afterwards, the formulated problem is transformed into a utility maximization problem from the perspective of Coalition Formation Game (CFG), where the orders, actions, rule, and stability in the coalitions are analyzed and proved. Then, two algorithms are put forward to reach the NE (Nash Equilibrium) of the CFG by determining the mobile sensor nodes’ coalitions and positions. Finally, extensive simulations are conducted with different parameters settings to evaluate the correctness and effectiveness of the proposed algorithms. Results have shown that the mobile sensor nodes, which adopt the proposed cooperative order to formulate the coalitions, could reach lower AoI, larger SINR, higher data completeness, and less energy consumption than the typical Pareto order.

Joint Task Assignment and Spectrum Allocation in Heterogeneous UAV Communication Networks: A Coalition Formation Game-Theoretic Approach

Coalition structure is an efficient networking architecture for task implementation in unmanned aerial vehicle (UAV) networks. However, both the formation of coalition and the spectrum resource for intra-coalition communication affect the reconnaissance performance. In this paper, we investigate a cooperative reconnaissance and spectrum access (CRSA) scheme for task-driven heterogeneous coalition-based UAV networks by jointly optimizing task layer and resource layer. Specifically, coalition formation game (CFG) is formulated to jointly optimize task selection and bandwidth allocation. In addition to the traditional Pareto order and selfish order, coalition expected altruistic order maximizing coalitions' utility is proposed. The CFG under the proposed order is proved to be an exact potential game (EPG). Then the existence of stable coalition partition is guaranteed with the help of Nash equilibrium (NE). We propose a joint bandwidth allocation and coalition formation (JBACF) algorithm to achieve stable coalition partition wherein an efficient gradient projection (GP) based method is applied to solve bandwidth allocation. The effectiveness of the proposed scheme and algorithms are demonstrated through in-depth numerical simulations. The results show that our proposed CRSA scheme is superior to non-joint optimization scheme. Also, the proposed order is superior to traditional Pareto order and selfish order.

Pricing Game With Complete or Incomplete Information About Spectrum Inventories for Mobile Virtual Network Operators

In network virtualization, mobile virtual network operators (MVNOs) lease spectrum resources from mobile network operators (MNOs) and offer certain wireless services to end users. Each MVNO competes with others using optimal price and spectrum inventory so as to profit. However, the inventory of one MVNO is private information and maybe unknown to others, which makes pricing decisions difficult for MVNOs. In this work, we first study the pricing strategy given others’ inventory information. We model the pricing decision problem using the non-cooperative game theory, and develop an optimal price setting algorithm based on an ordinal potential game. Then we put forward three cooperation strategies for MVNOs and analyze the impacts of the coalitions structure on pricing decision. For the situation where the inventory of one MVNO is unknown to others, we use the Bayesian coalition formation game to formulate the pricing decision problem and propose an optimal price setting algorithm based on the Minimum Mean-Square Error to resolve the conflicts resulting from the uncertainty. Next we define a Belief Pareto Order to characterize the preferences of MVNOs regarding the coalition structures. Then we devise a distributed coalition formation algorithm with the proposed belief Pareto order to achieve a Bayesian-Nash stable coalition structure that enables each MVNO to maximize its own revenue. Finally, simulation results demonstrate comprehensive performance evaluation of the proposed game model and provide a guidance on pricing strategies for MVNOs.

Hamiltonian Formalism for a Multicriteria Optimal Motion Control Problem

Statements of and solution methods for dynamic multicriteria optimization problems are considered. Although such problems are usually solved by reduction to the optimization of a scalar function of the criteria, in real-world vector problems one needs to introduce the Pareto frontier and describe its evolution. We propose an approach based on vector dynamic programming and similar to the classical approach. The method involves finding an extremum with respect to the Pareto ordering. A vector value function (the Pareto frontier) is introduced, for which an analog of the optimality principle is stated and the corresponding system of equations of the Hamilton-Jacobi-Bellman type is constructed. The control is sought in the form of synthesis. A method for constructing a guaranteed point estimate of the Pareto frontier is described, and solutions of problems of management by objectives obtained with the use of vector dynamic programming are presented.

Context Awareness Group Buying in D2D Networks: A Coalition Formation Game-Theoretic Approach

In this paper, we proposed a context-aware group buying mechanism to reduce users’ data cost based on the content similarity. Each user's cost is formulated as the combination of the content-aware data cost and location-aware sharing cost. Data cost is the payoff of the spectrum owner's channel to download files and sharing cost is the energy and time cost in transmitting files among the coalition. Compared with downloading data alone, users would like to form different groups and download the traffic data first and then share data among the group to achieve a lower cost. The cost reducing problem through group buying mechanism is modeled as a coalition formation game (CFG). Besides the traditional Pareto order, a coalition order maximizing the coalition's benefit and a selfish order maximizing users’ benefit are proposed. The CFGs with the two proposed orders are proved to be potential games, respectively, and the existence of the stable coalition partitions are also guaranteed by Nash equilibria. A cooperative exchange mechanism is designed, where users can make decisions cooperatively to achieve better performance. Simulation results show that the context awareness group buying reduces the cost and improves the benefit significantly compared with the situation without context awareness. The proposed orders both have better performance than the Pareto order.

A Coalition Formation Game Approach for Efficient Cooperative Multi-UAV Deployment

Unmanned aerial vehicle (UAV) cooperative control has been an important issue in UAV-assisted sensor networks, thanks to the considerable benefit obtained from the cooperative mechanism of UAVs being applied as a flying base station. In a coverage scenarios, the trade-off between coverage and transmission performance often makes deployment of UAVs fall into a dilemma, since both indexes are related to the distance between UAVs. To address this issue, UAV coverage and data transmission mechanism is analyzed in this paper; then, an efficient multi-UAV cooperative deployment model is proposed. The problem is modeled as a coalition formation game (CFG). The CFG with Pareto order is proved to have a stable partition. Then, an effective approach consisting of coverage deployment and coalition selection is designed, wherein UAVs can decide strategies cooperatively to achieve better coverage performance. Combining analysis of game approach, coalition selection and the position deployment algorithm based on Pareto order (CSPDA-PO) is designed to execute coverage deployment and coalition selection. Finally, simulation results are shown to validate the proposed approach based on an efficient multi-UAV cooperative deployment model.

Group Buying-Based Data Transmission in Flying Ad-Hoc Networks: A Coalition Game Approach

In scenarios such as natural disasters and military strikes, it is common for unmanned aerial vehicles (UAVs) to form groups to execute reconnaissance and surveillance. To ensure the effectiveness of UAV communications, repeated resource acquisition issues and transmission mechanism designs need to be addressed urgently. Since large-scale UAVs will generate high transmission overhead due to the overlapping resource requirements, in this paper, we propose a resource allocation optimization method based on distributed data content in a Flying Ad-hoc network (FANET). The resource allocation problem with the goal of throughput maximization is constructed as a coalition game framework. Firstly, a data transmission mechanism is designed for UAVs to execute information interaction within the coalitions. Secondly, a novel mechanism of coalition selection based on group-buying is investigated for UAV coalitions to acquire data from the central UAV. The data transmission and coalition selection problem are modeled as coalition graph game and coalition formation game, respectively. Through the design of the utility function, we prove that both games have stable solutions. We also prove the convergence of the proposed approach with coalition order and Pareto order. Based on simulation results, coalition order based coalition selection algorithm (CO-CSA) and Pareto order based coalition selection algorithm (PO-CSA) are proposed to explore the stable coalition partition of system model. CO-CSA and PO-CSA can achieve higher data throughput than the contrast onetime coalition selection algorithm (Onetime-CSA) (at least increased by 34.5% and 16.9%, respectively). Besides, although PO-CSA has relatively lower throughput gain, its convergence times is on average 50.9% less than that of CO-CSA, which means that the algorithm choice is scenario-dependent.

A Coalitional Formation Game for Physical Layer Security of Cooperative Compressive Sensing Multi-Relay Networks.

Cooperative relaying is an effective technology to improve the capacity of physical-layer security, in which the relay helps forward the received signal to the destination. In this paper, a cooperative compressive sensing and amplify-and-forward (CCS-AF) scheme, which combines the compressive sensing theory and amplify-and-forward strategy, is proposed to increase the secrecy capacity. To optimize the secrecy performance, a coalition formation algorithm based on coalitional game theory of optimal relay selection is proposed to maximize the secrecy capacity. Different to maximizing the individual utility based on the traditional pareto order, the max-coalition order rule is newly defined to guide the coalitional formation. Simulation results indicate that with the proposed algorithm, part of the relays could form a coalition to forward the information and the proposed algorithm could significantly improve the secrecy capacity of cooperative multi-relay networks.

PROFIT DISTRIBUTION IN MICRO-GRID

Smart-grids are advanced power systems that have capability control the power loading by saving the purchasing cost of extra electricity and alleviating power losses. The communication between the micro station (MS) and Micro-grid (MGs) is a key issue in smart grid where its performance affected by transmission pricing and extra exchanged power pricing that considers an efficient on the pricing stability of the smart micro-grids. Therefore, interchange mechanism is proposed in (MGs) integration, fulfilment of all requirements and enhanced routing of communication in smart-grids. We study the power consumption and the load-price mapping for coalitions with lower repetition time and equal contribution fulfil all requirements. This achieved by means of optimization problem that increment of total revenue, which based on the optimization tool function. We used Coalition Game Theoretical Formulation Strategy (CG-TFS) meet the high-speed routing of smart grid requirements and additional profits (ie, payoff) resulting from coalitions will be distributed by their equal participation role Equal Sharing Role to find optimal coalitions using the Pareto Order for power Transmission.

Parallel Processing Strategies for Skyline Queries Tolerant to Outliers

This paper deals with the problem of efficiently computing the most preferred objects, in the sense of Pareto ordering, in a set of multidimensional objects involving outliers. These outliers, for instance, odd data from ad sales websites, can hide interesting points, so it is important to limit their impact. To do this, we propose a graded Skyline based on the typicality of each object. Such an approach allows to supply an α-cut of the skyline containing both nondominated points, and almost nondominated but more representative points. The computational cost of a naive algorithm performing this task is very high, especially in high-dimensional spaces, due to the large number of comparisons between objects. Since common skyline optimizations cannot be used in our approach, we propose an implementation on parallel architectures, CUDA and OpenMP. Experimental results on both real-world and synthetic data sets show that this processing strategy makes the approach scalable.

A \u201cthree-sentence proof\u201d of Hansson\u2019s theorem

We provide a new proof of Hansson’s theorem: every preorder has a complete preorder extending it. The proof boils down to showing that the lexicographic order extends the Pareto order.

Coalition Formation for Interference Management in Visible Light Communication Networks

Visible light communication (VLC) can accomplish the two-fold goal of illumination and short-range communication with the advantages of low cost, free spectrum, natural confidentiality, and low energy consumption, whereas interference management is a major challenge in VLC networks. In this paper, we propose a coalition formation framework for interference management in VLC networks. VLC access points (APs) are designed to self-organize into cooperation coalitions for interference cancellation through orthogonal time or frequency domain. The performances of VLC APs with and without forming coalitions are both analyzed. Based on coalition formation game theory, a simple merge-and-split algorithm based on Pareto order is proposed. The convergence, stability, and complexity of the proposed algorithm are further discussed. Numerical results are given to illustrate the effectiveness of the proposed framework.

Collaborative Sub-channel Allocation with Power Control in Small Cell Networks

For enhancing the coverage of wireless networks and increasing the spectrum efficiency, small cell networks (SCNs) are considered to be one of the most prospective schemes. Most of the existing literature on resource allocation among non-cooperative small cell base stations (SBSs) has widely drawn close attention and there are only a small number of the cooperative ideas in SCNs. Based on the motivation, we further investigate the cooperative approach, which is formulated as a coalition formation game with power control algorithm (CFG-PC). First, we formulate the downlink sub-channel resource allocation problem in an SCN as a coalition formation game. Pareto order and utilitarian order are applied to form coalitions respectively. Second, to achieve more availability and efficiency power assignment, we expand and solve the power control using particle swarm optimization (PSO). Finally, with our proposed algorithm, each SBS can cooperatively work and eventually converge to a stable SBS partition. As far as the transmit rate of per SBS and the system rate are concerned respectively, simulation results indicate that our proposed CFG-PC has a significant advantage, relative to a classical coalition formation algorithm and the non-cooperative case.

Multi-Objective Influence Diagrams with Possibly Optimal Policies

The formalism of multi-objective influence diagrams has recently been developed for modeling and solving sequential decision problems under uncertainty and multiple objectives. Since utility values representing the decision maker's preferences are only partially ordered (e.g., by the Pareto order) we no longer have a unique maximal value of expected utility, but a set of them. Computing the set of maximal values of expected utility and the corresponding policies can be computationally very challenging. In this paper, we consider alternative notions of optimality, one of the most important one being the notion of possibly optimal, namely optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop a variable elimination algorithm for computing the set of possibly optimal expected utility values, prove formally its correctness, and compare variants of the algorithm experimentally.

Variância Intervalar das funções densidade de probabilidade com distribuições Exponencial, Pareto e Uniforme

<div><p class="SPabstract">A computação científica demanda de grande exatidão e ao se utilizar o sistema de ponto flutuante os resultados podem ser afetados por erros. Estes inviabilizam a confiabilidade nos resultados alcançados, com isto surge a necessidade da utilização da matemática intervalar. Esta cria limites que são os extremos do intervalo onde o valor real x está contido, controlando a propagação desses erros uma vez que resultados intervalares carregam consigo a segurança de sua qualidade. O cálculo da variância necessita de exatidão devido ao grande processamento de valores reais. O presente trabalho tem como objetivo definir a variância intervalar das funções de densidade de probabilidade com distribuições Exponencial, Pareto e Uniforme a fim de obter um controle automático de erros com limites confiáveis.</p></div>

Energy-Efficient Resource Sharing for Mobile Device-to-Device Multimedia Communications

Device-to-device (D2D) communications bring significant benefits to mobile multimedia services in local areas. However, these potential advantages hinge on intelligent resource sharing between potential D2D pairs and cellular users. In this paper, we study the problem of energy-efficient uplink resource sharing over mobile D2D multimedia communications underlaying cellular networks with multiple potential D2D pairs and cellular users. We first construct a novel analytical model of energy efficiency for different sharing modes, which takes into account quality-of-service (QoS) requirements and the spectrum utilization of each user. Then, we formulate the energy-efficient resource sharing problem as a nontransferable coalition formation game, with the characteristic function that accounts for the gains in terms of energy efficiency and the costs in terms of mutual interference. Moreover, we develop a distributed coalition formation algorithm based on the merge-and-split rule and the Pareto order. The distributed solution is characterized through novel stability notions and can be adapted to user mobility. From it, we obtain the energy-efficient sharing strategy on joint mode selection, uplink reusing allocation, and power management. Extensive simulation results are provided to demonstrate the effectiveness of our proposed game model and algorithm.

Computing the Moments of Order Statistics from Truncated Pareto Distributions Based on the Conditional Expectation

In this paper, closed form expressions for the moments of the truncated Pareto order statistics are obtained by using conditional distribution. We also derive some results for the moments which will be useful for moment computations based on ordered data.

Relay selection based on coalitional game for secure wireless networks

In this study, a two-stage decode-and-forward cooperative network is investigated consisting of a source, a corresponding destination, an eavesdropper and several intermediate nodes. In this study, the authors present an analysis of overall secrecy rate considering both distributed relay selection and secure beamforming problems. The achievable rate constraint is newly included into the system model. This modelling framework offers a more reliable approximation of the practical wireless channel. The relay selection is formulated as a coalitional game with transferable utility, which decreases the computation complexity in solving the distributed relay selection problem. A new ‘Max–Pareto order’ is constructed, which not only considers the player value, but also reflects the dominated weight of coalition value. Moreover, a distributed merge-and-split coalition formation algorithm is presented in this study. This algorithm achieves the system performance close to the theoretical upper limit, but it requires much less computation consumption.

Stochastic Duality of Markov Processes: A Study Via Generators

The article is devoted to a study of the duality of processes in the sense that for a certain f. This classical topic has well known applications in interacting particles, intertwining, superprocesses, stochastic monotonicity, exit – entrance laws, ruin probabilities in finances, etc. Aiming mostly at the case of f depending on the difference of its arguments, we develop a systematic approach to duality via the analysis of the generators of dual Markov processes and illustrate this approach by various examples, in particular, by giving a full characterization of duality arising from Pareto order in R d .