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.
The concept of proportionally fair markets for transportation networks is studied. The goal is to find methods for flow allocation to origin/destination pairs in urban communities which is fair, efficient, and able to...
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The concept of proportionally fair markets for transportation networks is studied. The goal is to find methods for flow allocation to origin/destination pairs in urban communities which is fair, efficient, and able to dynamically adapt to the changes in origin/destinations and traffic network. Two flow markets are designed and studied. distributed and dynamic algorithms are developed to find the proportional fair allocation of flow among competing origin/destinations. Additionally, existence, uniqueness and stability of the equilibrium points are proved for both markets. Our numerical simulations supplement the stability and practicality of our proposed algorithms.
The dispersion problem on graphs asks k <= n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct no...
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The dispersion problem on graphs asks k <= n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing, and relocation of self-driven electric cars (robots) to recharge stations (nodes). In this paper, we consider dispersion using the global communication model where a robot can communicate with any other robot in the graph (but the graph is unknown to robots). We provide two novel deterministic algorithms for arbitrary graphs in a synchronous setting where all robots perform their actions in every time step. Our first algorithm is based on a DFS traversal and guarantees (i) O(k Delta) steps runtime using O (log(k + Delta))) bits at each robot and (ii) O(min(m, k Delta)) steps runtime using O(Delta + log k) bits at each robot, where m is the number of edges and Delta is the maximum degree of the graph. The second algorithm is based on a BFS traversal and guarantees O ((D + k)Delta(D + Delta)) steps runtime using O (log D + Delta log k)) bits at each robot, where D is the diameter of the graph. Our results complement the existing results established using the local communication model where a robot can communication only with other robots present at the same node. (C) 2021 Elsevier Inc. All rights reserved.
We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing a...
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We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity;in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. We also provide an example of a natural testing problem where interactivity helps.
In this article, we study methods to solve a Sylvester equation in the form of AX + XB = C for given matrices A, B, C is an element of R-nxn, inspired by the distributed linear equation flows. The entries of A. B. and...
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In this article, we study methods to solve a Sylvester equation in the form of AX + XB = C for given matrices A, B, C is an element of R-nxn, inspired by the distributed linear equation flows. The entries of A. B. and C are separately partitioned into a number of pieces (or sometimes we permit these pieces to overlap), which are allocated to nodes in a network. Nodes hold a dynamic state shared among their neighbors defined from the network structure. Natural partial or full row , column partitions and block partitions of the data A, B, and C are formulated by use of the vectorized matrix equation. We show that existing network flows for distributed linear algebraic equations can be extended to solve this special form of matrix equations over networks. A "consensus + projection + symmetrization" flow is also developed for equations with symmetry constraints on the matrix variables. We prove the convergence of these flows and obtain the fastest convergence rates that these flows can achieve regardless of the choices of node interaction strengths and network structures.
This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to ...
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This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player' local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations.
Nowadays, Wireless Sensor Networks are one of the fundamental infrastructures for IoT technology. Although WSN has been researched for a decade, providing energy efficiency for resource-constrained sensor nodes is sti...
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Nowadays, Wireless Sensor Networks are one of the fundamental infrastructures for IoT technology. Although WSN has been researched for a decade, providing energy efficiency for resource-constrained sensor nodes is still a hot topic given the widespread usage of real-time WSN applications. For ensuring scalability, recent studies focus on multi-hop routing schemes. In this paper, a fully distributed, multi-hop intra and inter-cluster communication based static clustering scheme (MI(2)RSDiC) is proposed for WSNs. Differently from the studies in literature, MI(2)RSDiC suggests a limited re-evaluation opportunity to the nodes in clustering phase for optimized decision, an adaptive threshold-based cluster head alteration for energy efficiency and a multi-hop communication at every transmission stage for supporting large-scale WSNs. The proposed approach is compared with recent approaches and the results show that MI(2)RSDiC yields the highest lifetime of the network with achieving the least energy consumption and the largest amount of collected data among the equivalent approaches.
We design the first fully distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direc...
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We design the first fully distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the aggregate decision. The algorithm is derived by integrating dynamic tracking into a projected pseudo-gradient algorithm. The convergence analysis relies on the framework of monotone operator splitting and the Krasnosel'skii-Mann fixed-point iteration with errors.
This article investigates the problem of distributed cooperative energy management of multiple energy bodies with the consideration of both the optimal energy generation/consumption of each participant within single e...
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This article investigates the problem of distributed cooperative energy management of multiple energy bodies with the consideration of both the optimal energy generation/consumption of each participant within single energy body and the optimal energy distribution on the interconnected lines between any pair of energy bodies. First, we define the physical and communication structure of the system formed by many energy bodies, each of which is viewed as a multienergy prosumer. Then, a distributed energy management model is proposed to achieve not only maximum profits of overall energy generation and consumption, but also minimum cost of energy delivery. To address this issue, a distributed double-Newton descent (DDND) algorithm is proposed, which possesses two advantages. On the one hand, by employing second-order information, the concept of Newton descent is embedded into the implementation of the proposed algorithm, resulting in faster convergence speed. On the other hand, the proposed algorithm performs in a fully distributed fashion. As a consequence, each participant can locally obtain its optimal operation as well as the global energy market clearing prices;meanwhile, each energy router can locally obtain the optimal exchanged energy with its neighbor energy routers. Moreover, we prove that the proposed DDND algorithm can asymptotically converge to the global optimal point. As a result, the correctness of the DDND algorithm can be guaranteed in theory. Finally, simulation results validate the effectiveness of the proposed algorithm.
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