Showing papers on "Distributed algorithm published in 2012"

Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

Abstract: The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent coordination, estimation in sensor networks, and large-scale machine learning. We develop and analyze distributed algorithms based on dual subgradient averaging, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our analysis allows us to clearly separate the convergence of the optimization algorithm itself and the effects of communication dependent on the network structure. We show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network, and confirm this prediction's sharpness both by theoretical lower bounds and simulations for various networks. Our approach includes the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.

Optimal distributed online prediction using mini-batches

Abstract: Online prediction methods are typically presented as serial algorithms running on a single processor. However, in the age of web-scale prediction problems, it is increasingly common to encounter situations where a single processor cannot keep up with the high rate at which inputs arrive. In this work, we present the distributed mini-batch algorithm, a method of converting many serial gradient-based online prediction algorithms into distributed algorithms. We prove a regret bound for this method that is asymptotically optimal for smooth convex loss functions and stochastic inputs. Moreover, our analysis explicitly takes into account communication latencies between nodes in the distributed environment. We show how our method can be used to solve the closely-related distributed stochastic optimization problem, achieving an asymptotically linear speed-up over multiple processors. Finally, we demonstrate the merits of our approach on a web-scale online prediction problem.

Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach

Abstract: A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept.

Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication

Abstract: The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy intersensor communication. It introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the NU (with its linear counterpart LU) and the NLU. Their update rule combines a consensus step (where each sensor updates the state by weight averaging it with its neighbors' states) and an innovation step (where each sensor processes its local current observation). This makes the three algorithms of the consensus + innovations type, very different from traditional consensus. This paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value), efficiency, and asymptotic unbiasedness. For LU and NU, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms LU and NU are analyzed in the framework of stochastic approximation theory; algorithm NLU exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in this paper.

Fuzzy-Logic-Based Clustering Approach for Wireless Sensor Networks Using Energy Predication

Abstract: In order to collect information more efficiently, wireless sensor networks (WSNs) are partitioned into clusters. Clustering provides an effective way to prolong the lifetime of WSNs. Current clustering approaches often use two methods: selecting cluster heads with more residual energy, and rotating cluster heads periodically, to distribute the energy consumption among nodes in each cluster and extend the network lifetime. However, most of the previous algorithms have not considered the expected residual energy, which is the predicated remaining energy for being selected as a cluster head and running a round. In this paper, a fuzzy-logic-based clustering approach with an extension to the energy predication has been proposed to prolong the lifetime of WSNs by evenly distributing the workload. The simulation results show that the proposed approach is more efficient than other distributed algorithms. It is believed that the technique presented in this paper could be further applied to large-scale wireless sensor networks.

Network aware resource allocation in distributed clouds

Abstract: We consider resource allocation algorithms for distributed cloud systems, which deploy cloud-computing resources that are geographically distributed over a large number of locations in a wide-area network. This distribution of cloud-computing resources over many locations in the network may be done for several reasons, such as to locate resources closer to users, to reduce bandwidth costs, to increase availability, etc. To get the maximum benefit from a distributed cloud system, we need efficient algorithms for resource allocation which minimize communication costs and latency. In this paper, we develop efficient resource allocation algorithms for use in distributed clouds. Our contributions are as follows: Assuming that users specify their resource needs, such as the number of virtual machines needed for a large computational task, we develop an efficient 2-approximation algorithm for the optimal selection of data centers in the distributed cloud. Our objective is to minimize the maximum distance, or latency, between the selected data centers. Next, we consider use of a similar algorithm to select, within each data center, the racks and servers where the requested virtual machines for the task will be located. Since the network inside a data center is structured and typically a tree, we make use of this structure to develop an optimal algorithm for rack and server selection. Finally, we develop a heuristic for partitioning the requested resources for the task amongst the chosen data centers and racks. We use simulations to evaluate the performance of our algorithms over example distributed cloud systems and find that our algorithms provide significant gains over other simpler allocation algorithms.

Economics of Electric Vehicle Charging: A Game Theoretic Approach

Abstract: In this paper, the problem of grid-to-vehicle energy exchange between a smart grid and plug-in electric vehicle groups (PEVGs) is studied using a noncooperative Stackelberg game. In this game, on the one hand, the smart grid, which acts as a leader, needs to decide on its price so as to optimize its revenue while ensuring the PEVGs' participation. On the other hand, the PEVGs, which act as followers, need to decide on their charging strategies so as to optimize a tradeoff between the benefit from battery charging and the associated cost. Using variational inequalities, it is shown that the proposed game possesses a socially optimal Stackelberg equilibrium in which the grid optimizes its price while the PEVGs choose their equilibrium strategies. A distributed algorithm that enables the PEVGs and the smart grid to reach this equilibrium is proposed and assessed by extensive simulations. Further, the model is extended to a time-varying case that can incorporate and handle slowly varying environments.

Distributed Computing by Oblivious Mobile Robots

Abstract: The study of what can be computed by a team of autonomous mobile robots, originally started in robotics and AI, has become increasingly popular in theoretical computer science (especially in distributed computing), where it is now an integral part of the investigations on computability by mobile entities. The robots are identical computational entities located and able to move in a spatial universe; they operate without explicit communication and are usually unable to remember the past; they are extremely simple, with limited resources, and individually quite weak. However, collectively the robots are capable of performing complex tasks, and form a system with desirable fault-tolerant and self-stabilizing properties. The research has been concerned with the computational aspects of such systems. In particular, the focus has been on the minimal capabilities that the robots should have in order to solve a problem. This book focuses on the recent algorithmic results in the field of distributed computing by oblivious mobile robots (unable to remember the past). After introducing the computational model with its nuances, we focus on basic coordination problems: pattern formation, gathering, scattering, leader election, as well as on dynamic tasks such as flocking. For each of these problems, we provide a snapshot of the state of the art, reviewing the existing algorithmic results. In doing so, we outline solution techniques, and we analyze the impact of the different assumptions on the robots' computability power. Table of Contents: Introduction / Computational Models / Gathering and Convergence / Pattern Formation / Scatterings and Coverings / Flocking / Other Directions

Economics of Electric Vehicle Charging: A Game Theoretic Approach

Abstract: In this paper, the problem of grid-to-vehicle energy exchange between a smart grid and plug-in electric vehicle groups (PEVGs) is studied using a noncooperative Stackelberg game. In this game, on the one hand, the smart grid that acts as a leader, needs to decide on its price so as to optimize its revenue while ensuring the PEVGs' participation. On the other hand, the PEVGs, which act as followers, need to decide on their charging strategies so as to optimize a tradeoff between the benefit from battery charging and the associated cost. Using variational inequalities, it is shown that the proposed game possesses a socially optimal Stackelberg equilibrium in which the grid optimizes its price while the PEVGs choose their equilibrium strategies. A distributed algorithm that enables the PEVGs and the smart grid to reach this equilibrium is proposed and assessed by extensive simulations. Further, the model is extended to a time-varying case that can incorporate and handle slowly varying environments.

Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case

Abstract: This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization.

Distributed Verification and Hardness of Distributed Approximation

Abstract: We study the verification problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would l...

Residential Load Control: Distributed Scheduling and Convergence With Lost AMI Messages

Abstract: This paper deals with load control in a multiple-residence setup. The utility company adopts a cost function representing the cost of providing energy to end-users. Each residential end-user has a base load, two types of adjustable loads, and possibly a storage device. The first load type must consume a specified amount of energy over the scheduling horizon, but the consumption can be adjusted across different slots. The second type does not entail a total energy requirement, but operation away from a user-specified level results in user dissatisfaction. The research issue amounts to minimizing the electricity provider cost plus the total user dissatisfaction, subject to the individual constraints of the loads. The problem can be solved by a distributed subgradient method. The utility company and the end-users exchange information through the Advanced Metering Infrastructure (AMI)-a two-way communication network-in order to converge to the optimal amount of electricity production and the optimal power consumption schedule. The algorithm finds near-optimal schedules even when AMI messages are lost, which can happen in the presence of malfunctions or noise in the communications network. The algorithm amounts to a subgradient iteration with outdated Lagrange multipliers, for which convergence results of wide scope are established.

Dynamic Resource Allocation in MIMO-OFDMA Systems with Full-Duplex and Hybrid Relaying

Abstract: In this paper, we formulate a joint optimization problem for resource allocation and scheduling in full-duplex multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) relaying systems with amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Our problem formulation takes into account heterogeneous data rate requirements for delay sensitive and non-delay sensitive users. We also consider a theoretically optimal hybrid relaying scheme as a performance benchmark, which allows a dynamic selection between AF relaying and DF relaying protocols with full-duplex and half-duplex relays. We show that under some mild conditions the optimal transmitter precoding and receiver post-processing matrices jointly diagonalize the MIMO-OFDMA relay channels for all considered relaying protocols transforming the resource allocation and scheduling problem into a scalar optimization problem. Dual decomposition is employed to solve this optimization problem and a distributed iterative resource allocation and scheduling algorithm with closed-form power and subcarrier allocation is derived. Simulation results not only illustrate that the proposed distributed algorithm converges to the optimal solution in a small number of iterations, but also demonstrate the potential performance gains achievable with full-duplex relaying protocols.

An energy-aware distributed clustering protocol in wireless sensor networks using fuzzy logic

Abstract: Clustering is an effective approach for organizing a network into a connected hierarchy, load balancing, and prolonging the network lifetime. On the other hand, fuzzy logic is capable of wisely blending different parameters. This paper proposes an energy-aware distributed dynamic clustering protocol (ECPF) which applies three techniques: (1) non-probabilistic cluster head (CH) elections, (2) fuzzy logic, and (3) on demand clustering. The remaining energy of the nodes is the primary parameter for electing tentative CHs via a non-probabilistic fashion. A non-probabilistic CH election is implemented by introducing a delay inversely proportional to the residual energy of each node. Therefore, tentative CHs are selected based on their remaining energy. In addition, fuzzy logic is employed to evaluate the fitness (cost) of a node in order to choose a final CH from the set of neighboring tentative CHs. On the other hand, every regular (non CH) node elects to connect to the CH with the least fuzzy cost in its neighborhood. Besides, in ECPF, CH elections are performed sporadically (in contrast to performing it every round). Simulation results demonstrate that our approach performs better than well known protocols (LEACH, HEED, and CHEF) in terms of extending network lifetime and saving energy.

Distributed Basis Pursuit

Abstract: We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP) BP finds the least l1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multi- pliers We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms

Decentralized Plug-in Electric Vehicle Charging Selection Algorithm in Power Systems

Abstract: This paper uses a charging selection concept for plug-in electric vehicles (PEVs) to maximize user convenience levels while meeting predefined circuit-level demand limits. The optimal PEV-charging selection problem requires an exhaustive search for all possible combinations of PEVs in a power system, which cannot be solved for the practical number of PEVs. Inspired by the efficiency of the convex relaxation optimization tool in finding close-to-optimal results in huge search spaces, this paper proposes the application of the convex relaxation optimization method to solve the PEV-charging selection problem. Compared with the results of the uncontrolled case, the simulated results indicate that the proposed PEV-charging selection algorithm only slightly reduces user convenience levels, but significantly mitigates the impact of the PEV-charging on the power system. We also develop a distributed optimization algorithm to solve the PEV-charging selection problem in a decentralized manner, i.e., the binary charging decisions (charged or not charged) are made locally by each vehicle. Using the proposed distributed optimization algorithm, each vehicle is only required to report its power demand rather than report several of its private user state information, mitigating the security problems inherent in such problem. The proposed decentralized algorithm only requires low-speed communication capability, making it suitable for real-time implementation.

Distance Based Thresholds for Cluster Head Selection in Wireless Sensor Networks

Abstract: Central to the cluster-based routing protocols is the cluster head (CH) selection procedure that allows even distribution of energy consumption among the sensors, and therefore prolonging the lifespan of a sensor network We propose a distributed CH selection algorithm that takes into account the distances from sensors to a base station that optimally balances the energy consumption among the sensors NS-2 simulations show that our proposed scheme outperforms existing algorithms in terms of the average node lifespan and the time to first node death

On Cooperative Patrolling: Optimal Trajectories, Complexity Analysis, and Approximation Algorithms

Abstract: The subject of this paper is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory and propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.

Acknowledgment-Based Broadcast Protocol for Reliable and Efficient Data Dissemination in Vehicular Ad Hoc Networks

Abstract: We propose a broadcast algorithm suitable for a wide range of vehicular scenarios, which only employs local information acquired via periodic beacon messages, containing acknowledgments of the circulated broadcast messages. Each vehicle decides whether it belongs to a connected dominating set (CDS). Vehicles in the CDS use a shorter waiting period before possible retransmission. At time-out expiration, a vehicle retransmits if it is aware of at least one neighbor in need of the message. To address intermittent connectivity and appearance of new neighbors, the evaluation timer can be restarted. Our algorithm resolves propagation at road intersections without any need to even recognize intersections. It is inherently adaptable to different mobility regimes, without the need to classify network or vehicle speeds. In a thorough simulation-based performance evaluation, our algorithm is shown to provide higher reliability and message efficiency than existing approaches for nonsafety applications.

Agent Based Restoration With Distributed Energy Storage Support in Smart Grids

Abstract: The goal of this paper is to present a new and completely distributed algorithm for service restoration with distributed energy storage support following fault detection, location, and isolation. The distributed algorithm makes use of intelligent agents, which possess three key characteristics, namely autonomy, local view, and decentralization. The switch agents will detect, locate and isolate the fault, then restore the load. The distributed energy storage agent will support the system in grid-connected as well as islanded operation. Important restoration issues such as load priority restoration and islanding coordination of multiple distributed energy storage systems will be discussed. Two case studies on the modified IEEE 34 node test feeder will be presented.

Average Consensus on General Strongly Connected Digraphs

Abstract: We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. Our contribution is that in both cases, the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs; in particular, this graphical condition does not require that the network be balanced or symmetric, thereby extending many previous results in the literature. The key novelty of our approach is to augment an additional variable for each agent, called "surplus", whose function is to locally record individual state updates. For convergence analysis, we employ graph-theoretic and nonnegative matrix tools, with the eigenvalue perturbation theory playing a crucial role.

Distributed Control for Optimal Economic Dispatch of a Network of Heterogeneous Power Generators

Abstract: In this paper, we present a simple, distributed algorithm for frequency control and optimal economic dispatch of power generators. In this algorithm, each generator independently adjusts its power-frequency set-points of generators to correct for generation and load fluctuations using only the aggregate power imbalance in the network, which can be observed by each generator through local measurements of the frequency deviation on the grid. In the absence of power losses, we prove that the distributed algorithm eventually achieves optimality, i.e., minimum cost power allocations, under mild assumptions (strict convexity and positivity of cost functions); we also present numerical results from simulations to compare its performance with traditional (centralized) dispatch algorithms. Furthermore, we show that the performance of the algorithm is robust in the sense that, even with power losses, it corrects for frequency deviations, and, for low levels of losses, it still achieves near-optimal allocations; we present an approximate analysis to quantify the resulting suboptimality.

Distributed algorithms for optimal power flow problem

Abstract: Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so that its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured problems. The computation time grows linearly with the problem size with the cumulative approach while the distributed one can have size-independent computation time.

Distributed Traffic Signal Control for Maximum Network Throughput

Abstract: We propose a distributed algorithm for controlling traffic signals. Our algorithm is adapted from backpressure routing, which has been mainly applied to communication and power networks. We formally prove that our algorithm ensures global optimality as it leads to maximum network throughput even though the controller is constructed and implemented in a completely distributed manner. Simulation results show that our algorithm significantly outperforms SCATS, an adaptive traffic signal control system that is being used in many cities.

Distributed Computation of Equilibria in Monotone Nash Games via Iterative Regularization Techniques

Abstract: We consider the development of single-timescale schemes for the distributed computation of equilibria associated with Nash games in which each player solves a convex program. Equilibria associated with such games are wholly captured by the solution set of a variational inequality. Our focus is on a class of games, termed monotone Nash games, that lead to monotone variational inequalities. Distributed extensions of standard approaches for solving such variational problems are characterized by two challenges: (1) Unless suitable assumptions (such as strong monotonicity) are imposed on the mapping arising in the specification of the variational inequality, iterative methods often require the solution of a sequence of regularized problems, a naturally two-timescale process that is harder to implement in practice. (2) Additionally, algorithm parameters for all players (such as steplengths and regularization parameters) have to be chosen centrally and communicated to all players; importantly, these parameters c...

A new class of distributed optimization algorithms: application to regression of distributed data

Abstract: In a distributed optimization problem, the complete problem information is not available at a single location but is rather distributed among different agents in a multi-agent system. In the problems studied in the literature, each agent has an objective function and the network goal is to minimize the sum of the agents’ objective functions over a constraint set that is globally known. In this paper, we study a generalization of the above distributed optimization problem. In particular, the network objective is to minimize a function of the sum of the individual objective functions over the constraint set. The ‘outer’ function and the constraint set are known to all the agents. We discuss an algorithm and prove its convergence, and then discuss extensions to more general and complex distributed optimization problems. We provide a motivation for our algorithms through the example of distributed regression of distributed data.

A flexible distributed framework for realising electric and plug-in hybrid vehicle charging policies

Abstract: Motivated by the problems of charging a number of electric vehicles via limited capacity infrastructure, this article considers the problem of individual load adjustment under a total capacity constraint. For reasons of scalability and simplified communications, distributed solutions to this problem are sought. Borrowing from communication networks (AIMD algorithms) and distributed convex optimisation, we describe a number of distributed algorithms for achieving relative average fairness whilst maximising utilisation. We present analysis and simulation results to show the performance of these algorithms. In the scenarios examined, the algorithm's performance is typically within 5% of that achievable in the ideal centralised case, but with greatly enhanced scalability and reduced communication requirements.

Cooperative Patrolling via Weighted Tours: Performance Analysis and Distributed Algorithms

Abstract: This paper focuses on the problem of patrolling an environment with a team of autonomous agents. Given a set of strategically important locations (viewpoints) with different priorities, our patrolling strategy consists of 1) constructing a tour through the viewpoints, and 2) driving the robots along the tour in a coordinated way. As performance criteria, we consider the weighted refresh time, i.e., the longest time interval between any two visits of a viewpoint, weighted by the viewpoint's priority. We consider the design of both optimal trajectories and distributed control laws for the robots to converge to optimal trajectories. First, we propose a patrolling strategy and we characterize its performance as a function of the environment and the viewpoints priorities. Second, we restrict our attention to the problem of patrolling a nonintersecting tour, and we describe a team trajectory with minimum weighted refresh time. Third, for the tour patrolling problem and for two distinct communication scenarios, namely the Passing and the Neighbor-Broadcast communication models, we develop distributed algorithms to steer the robots toward a minimum weighted refresh time team trajectory. Finally, we show the effectiveness and robustness of our control algorithms via simulations and experiments.