We design distributed algorithms to compute approximate solutions for several related graph optimization problems. All our algorithms have round complexity being logarithmic in the number of nodes of the underlying gr...
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We design distributed algorithms to compute approximate solutions for several related graph optimization problems. All our algorithms have round complexity being logarithmic in the number of nodes of the underlying graph and in particular independent of the graph diameter. By using a primal-dual approach, we develop a 2(1 + epsilon)-approximation algorithm for computing the coreness values of the nodes in the underlying graph, as well as a 2(1 + epsilon)-approximation algorithm for the min-max edge orientation problem, where the goal is to orient the edges so as to minimize the maximum weighted in-degree. We provide lower bounds showing that the aforementioned algorithms are tight both in terms of the approximation guarantee and the round complexity. Additionally, motivated by the fact that the densest subset problem has an inherent dependency on the diameter of the graph, we study a weaker version that does not suffer from the same limitation. Finally, we conduct experiments on large real-world graphs to evaluate the effectiveness of our algorithms. (C) 2020 Elsevier Inc. All rights reserved.
This article proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It i...
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This article proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the algorithm converges to a weight-balanced solution at sublinear rate. The analysis builds upon a new metric inspired by positional system representations, which characterizes the dynamics of information exchange over the network, and on a novel step-size rule. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each timeslot, finite rate simplex communications between adjacent nodes-some bits for the weight-balancing problem and others for the average consensus. Convergence of the proposed quantized consensus algorithm to the average of the node's unquantized initial values is established, both almost surely and in the moment generating function of the error;and a sublinear convergence rate is proved for sufficiently large step-sizes. Numerical results validate our theoretical findings.
In this article, a discrete-time distributed optimization algorithm is proposed for solving the economic dispatch (ED) problem with some groups of generator units to communicate over a connected graph, which is indepe...
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In this article, a discrete-time distributed optimization algorithm is proposed for solving the economic dispatch (ED) problem with some groups of generator units to communicate over a connected graph, which is independent of the power system. The ED problem is converted to a distributed optimization problem with an objective of the sum of individual convex functions and constraints of local generators. Based on the optimal conditions, a class of distributed algorithms is designed to find the solution to the ED problem. The distributed algorithm can be realized as a multiagent system with a connected graph, whose convergence can be proved using the dynamic analysis method. Moreover, experiments with simulations are presented to demonstrate the performance of the proposed algorithm.
Noncooperative game-theoretic methods have been widely utilized in system-level engineering applications as they are capable of aggregating interests, information, and behaviors of many independent, self-interested en...
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Noncooperative game-theoretic methods have been widely utilized in system-level engineering applications as they are capable of aggregating interests, information, and behaviors of many independent, self-interested entities with conflicting objectives via payoffs. Another major advantage is the existence of adaptive learning dynamics that involve realistic, constrained decision making, and converge to Nash equilibrium. If players are not fully rational (e.g., constrained or regulated), such convergence is generally not guaranteed except in some special games, such as potential games (PGs). Within each PG, there exists a potential function that connects the global objective with players' payoffs and actions such as optimizers of the global objective align with Nash equilibrium. Therefore, PGs have been widely utilized in many engineering domains and recently to power grids. This article summarizes the state-of-the-art existing literature on applying various PG models in power grids and provides an overlook of potential models and algorithms that have not received sufficient attention but possess unique capabilities to solve existing challenges in power grids.
This paper considers the problem of sequential binary hypothesis testing based on observations from a network of m sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average ...
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This paper considers the problem of sequential binary hypothesis testing based on observations from a network of m sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average sample number required to reach a certain level of error probability is selected as the performance metric of the system. We propose an asymptotically optimal voting algorithm for the sensor network with a fusion center and generalize it to fully-distributed networks, where the algorithm stays asymptotically optimal under the weak assumption that the sensor network is connected. Moreover, we prove that both of the proposed algorithms are asymptotically optimal in the presence of Byzantine sensors, in the sense that each of them forms a Nash equilibrium with the worst-case attack (flip-attack). Compared to existing distributed detection strategies, the proposed scheme has a low message complexity, which is independent of the error probability and the sample number, by taking advantage of the sparsity of votes. The results are corroborated by numerical simulations.
distributed stochastic optimization has important applications in the practical implementation of machine learning and signal processing setup by providing means to allow interconnected network of processors to work t...
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distributed stochastic optimization has important applications in the practical implementation of machine learning and signal processing setup by providing means to allow interconnected network of processors to work towards the optimization of a global objective with intermittent communication. Existing works on distributed stochastic optimization predominantly assume all the processors storing related data to perform updates for the optimization task in each iteration. However, such optimization processes are typically executed at shared computing/data centers along with other concurrent tasks. Therefore, it is necessary to develop efficient optimization methods that possess the flexibility to share the computing resources with other ongoing tasks. In this work, we propose a new first-order framework that allows this flexibility through a probabilistic computing resource allocation strategy while guaranteeing the satisfactory performance of distributed stochastic optimization. Our results, both analytical and numerical, show that by controlling a flexibility parameter, our suite of algorithms (designed for various scenarios) can achieve the lower computation and communication costs of distributed stochastic optimization than their inflexible counterparts. This framework also enables the fair sharing of the common resources with other concurrent tasks being processed by the processing network.
Integrated energy systems become more and more important to realize the energy complementary property. Micro-integrated energy system, served as the terminal integrated energy system, will have the electricity deliver...
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Integrated energy systems become more and more important to realize the energy complementary property. Micro-integrated energy system, served as the terminal integrated energy system, will have the electricity delivered directly to the local customers by energy hubs (EHs). Here, the data and information of the EHs during the operation are confidential and should be kept by each owner. Therefore, this article designs a dual-decomposition-based distributed algorithm to address this problem, where the optimal consensus problem is used for the dual problem to update the multipliers. The primary and dual problems are alternatively solved until the Karush-Kuhn-Tucher condition is satisfied. For the proposed distributed algorithm, the feasibility can be strictly guaranteed during the iteration process. Moreover, theorems and lemmas are proved for the linear convergence rate. The numerical results verify the effectiveness of the proposed algorithm.
This article studies the distributed composite optimization problem over relay-assisted networks (DCOP-RNs). By combining the local primal-dual updates with a data fusion strategy, an effective distributed algorithm i...
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This article studies the distributed composite optimization problem over relay-assisted networks (DCOP-RNs). By combining the local primal-dual updates with a data fusion strategy, an effective distributed algorithm is developed to solve the DCOP-RN. Compared with the existing linearized alternating direction method of multipliers (ADMMs), this article provides a novel interpretation of the proposed algorithm. More specifically, it is shown that the proposed algorithm can be interpreted as a simplified proximal augmented Lagrangian method. Within this framework, a simplified convergence analysis of the algorithm is conducted, based on which the convergence to an optimal solution to the DCOP-RN is proved. Further, taking into account the limited bandwidth in real networks, this article proposes a quantized distributed algorithm to solve the DCOP-RN. Especially, a relationship between the quantization resolution and the convergence accuracy of the algorithm is established. Finally, simulation examples verify the theoretical results.
This article studies a distributed average tracking (DAT) problem, in which a collection of agents work collaboratively, subject to local communication, to track the average of a set of reference signals, each of whic...
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This article studies a distributed average tracking (DAT) problem, in which a collection of agents work collaboratively, subject to local communication, to track the average of a set of reference signals, each of which is available to a single agent. Our primary objective is to seek a design methodology for DAT under possibly weight-unbalanced directed networks-the most general and thus most challenging case from the network topology perspective, which has few results in the literature. For this purpose, we propose a distributed algorithm based on a chain of two integrators that are coupled with a distributed estimator. It is found that the convergence depends on not only the network topology but also the deviations among the reference signal accelerations. Another primary interest of this article stems from the dynamics perspective-a point perceived as a main source of control design difficulty for multiagent systems. Indeed, we devise a nonlinear algorithm that is capable of achieving DAT under weight-unbalanced directed networks for agents subject to high-order integrator dynamics. The results show that the convergence to the vicinity of the average of the reference signals is guaranteed as long as the signals' states and control inputs are all bounded. Both algorithms are robust to initialization errors, i.e., DAT is insured even if the agents are not correctly initialized, enabling the potential applications in a wider spectrum of application domains.
Computing shortest paths from a single source is one of the central problems studied in the CONGEST model of distributed computing. After many years in which no algorithmic progress was made, Elkin [STOC '17] prov...
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Computing shortest paths from a single source is one of the central problems studied in the CONGEST model of distributed computing. After many years in which no algorithmic progress was made, Elkin [STOC '17] provided the first improvement over the distributed Bellman-Ford algorithm. Since then, several improved algorithms have been published. The state-of-the-art algorithm for weighted directed graphs (with polynomially bounded non-negative integer weights) requires (O) over tilde (min{root nD(1/2), root nD(1/4) + n(3/5) + D}) rounds [Forster and Nanongkai, FOCS '18], which is still quite far from the known lower bound of (Omega) over tilde(root n + D) rounds [Elkin, STOC '04];here D is the diameter of the underlying network and n is the number of vertices in it. For the (1+ o(1))-approximate version of this problem and the same class of graphs, Forster and Nanongkai [FOCS 18] obtained a better upper bound of (O) over tilde (root nD(1/4) + D) rounds. In the same paper, they stated that achieving the same bound for the exact case remains a major open problem. In this paper we resolve the above mentioned problem by devising a new randomized algorithm for computing shortest paths from a single source in (O) over tilde (root nD(1/4) + D) rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute approximate distances that preserve a certain form of the triangle inequality for the edges in the graph.
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