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Memory-Enhanced distributed Accelerated algorithms for Coordinated Linear Computation

IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2025年 11卷 35-47页

作者： Ding, Shufen Meng, Deyuan Du, Mingjun Cai, Kaiquan Beihang Univ BUAA Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Beihang Univ BUAA Res Div 7 Beijing 100191 Peoples R China Beihang Univ BUAA State Key Lab CNS ATM Beijing 100191 Peoples R China Qilu Univ Technol Shandong Acad Sci Sch Informat & Automat Engn Jinan 250353 Peoples R China Beihang Univ BUAA Sch Elect & Informat Engn Beijing 100191 Peoples R China

In this paper, a memory-enhanced distributed accelerated algorithm is proposed for solving large-scale systems of linear equations within the context of multi-agent systems. By employing a local predictor consisting of a linear combination of the nodes' current and previous values, the inclusion of two memory taps can be characterized such that the convergence of the distributed solution algorithm for coordinated computation is accelerated. Moreover, consensus-based convergence results are established by leveraging an analysis of the spectral radius of an augmented iterative matrix associated with the error system that arises from solving the equation. In addition, the connection between the convergence rate and the tunable parameters is developed through an examination of the spectral radius of the iterative matrix, and the optimal mixing parameter is systematically derived to achieve the fastest convergence rate. It is shown that despite whether the linear equation of interest possesses a unique solution or multiple solutions, the proposed distributed algorithm exhibits exponential convergence to the solution, without dependence on the initial conditions. In particular, both the theoretical analysis and simulation examples demonstrate that the proposed distributed algorithm can achieve a faster convergence rate than conventional distributed algorithms for the coordinated linear computation, provided that adjustable parameters are appropriately selected.

关键词： Convergence distributed algorithms Signal processing algorithms Prediction algorithms Vectors Jacobian matrices Symmetric matrices Multi-agent systems Information processing distributed databases Convergence rate consensus distributed algorithms iterative method multi-agent systems

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distributed Ishikawa algorithms for seeking the fixed points of multi-agent global operators over time-varying communication graphs

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 457卷

作者： Liu, Xin Song, Xianhua Chen, Lili Zhao, Yanfeng Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China Harbin Univ Sci & Technol Dept Math Harbin 150080 Peoples R China

In this article, the problem of seeking fixed points for global operators over the time-varying graphs in a real Hilbert space is studied. The global operator is a linear combination of local operators, each local operator being accessed privately by one agent for less resource consumption. All agents form a network and they need to cooperate to solve problems. To this end, on the basis of the centralized Ishikawa iteration, the distributed Ishikawa algorithm (D-I) is first proposed. In the sequel, to predigest the calculational complexity, further considering the situation that only the random part of each operator coordinate is calculated in each iteration, the distributed block coordinate Ishikawa algorithm (D-BI) is also designed. The results indicate that the proposed D-I and D-BI algorithms can weakly converge to a fixed point of the multi- agent global operator. Eventually, we give a few numerical examples to illustrate practical benefits of the proposed algorithms.

关键词： distributed algorithms Ishikawa iteration Fixed point Random graphs

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ON THE GEOMETRIC CONVERGENCE OF BYZANTINE-RESILIENT distributed OPTIMIZATION algorithms

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SIAM JOURNAL ON OPTIMIZATION 2025年第1期35卷 210-239页

作者： Kuwaranancharoen, Kananart Sundaram, Shreyas Purdue Univ Elmore Family Sch Elect & Comp Engn W Lafayette IN 47907 USA

The problem of designing distributed optimization algorithms that are resilient to Byzantine adversaries has received significant attention. For the Byzantine-resilient distributed optimization problem, the goal is to (approximately) minimize the average of the local cost functions held by the regular (nonadversarial) agents in the network. In this paper, we provide a general algorithmic framework for Byzantine-resilient distributed optimization which includes some state-of-the-art algorithms as special cases. We analyze the convergence of algorithms within the framework, and derive a geometric rate of convergence of all regular agents to a ball around the optimal solution (whose size we characterize). Furthermore, we show that approximate consensus can be achieved geometrically fast under some minimal conditions. Our analysis provides insights into the relationship among the convergence region, distance between regular agents' values, step size, and properties of the agents' functions for Byzantine-resilient distributed optimization.

关键词： consensus algorithm convex optimization distributed algorithms distributed optimization fault tolerant systems linear convergence multiagent systems network security

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distributed algorithms for Array Signal Processing

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 4607-4622页

作者： Chen, Po-Chih Vaidyanathan, P. P. CALTECH Dept Elect Engn Pasadena CA 91125 USA

distributed or decentralized estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years, and applications in array processing have been indicated in some detail. Inspired by these, this paper provides a detailed development of several distributed algorithms for array processing. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares-ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, and distributed implementation of the spatial smoothing method for coherent sources. A distributed implementation of a recently proposed beamspace method called the convolutional beamspace (CBS) is also proposed. The proposed algorithms are fully distributed - an average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a recently reported finite-time version of AC which converges to the exact solution in a finite number of iterations. Numerical examples are given throughout the paper to show the effectiveness of the proposed algorithms.

关键词： Estimation Direction-of-arrival estimation distributed algorithms Array signal processing Signal processing algorithms Convergence Smoothing methods distributed or decentralized DOA estimation Capon beamforming convolutional beamspace root-MUSIC ESPRIT FOCUSS spatial smoothing

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distributed algorithms for Average Consensus of Input Data With Fast Convergence

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第5期51卷 2653-2664页

作者： Xie, Kan Cai, Qianqian Zhang, Zhaorong Fu, Minyue Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Guangdong Univ Technol Guangdong Key Lab Intelligent Decis & Cooperat Co Guangzhou 510006 Peoples R China Univ Newcastle Sch Elect Engn & Comp Sci Callaghan NSW 2308 Australia

This paper proposes fast convergent distributed algorithms for weighted average consensus of input data. For acyclic graphs, we give an algorithm that converges to the exact weighted average consensus in a finite number of iterations, equal to the graph diameter. For loopy (cyclic) graphs, we offer two remedies. In the first one, we give another distributed algorithm to enable our average consensus algorithm applicable to a loopy graph by converting it into a spanning tree. In the second one, we consider a slightly modified average consensus problem whose optimal solution approximates the consensus solution with arbitrary precision, and give a modified average consensus algorithm with guaranteed exponential convergence to the optimal solution. The proposed average consensus algorithms enjoy low complexities, robustness to transmission adversaries, and asynchronous implementation. Our algorithms are conceptually different from the popular graph Laplacian approach, and converge much faster than the latter approach.

关键词： distributed algorithms Convergence Consensus algorithm Nickel distributed databases Complexity theory Approximation algorithms Average consensus distributed algorithms distributed estimation networked control

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distributed algorithms for convexified bad data and topology error detection and identification problems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2016年 83卷 241-250页

作者： Weng, Yang Ilic, Marija D. Li, Qiao Negi, Rohit Stanford Univ Dept Civil & Environm Engn Stanford CA 94305 USA Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA Qualcomm Res New Jersey Bridgewater NJ 08807 USA

Large-scale smart grids call for online algorithms that are able to achieve the most accurate estimates. This paper shows how to achieve both the scalability and near globally optimal results for bad data and topology error detection and identification problems, by conducting fully distributed algorithms over convexified problem formulations. The proposed distributed decomposition is realized by (1) reducing a large network into much smaller network "cliques" which do not need extensive information exchange;(2) performing a Lagrangian dual decomposition in each clique and passing messages between cliques;and (3) conducting alternative coordinate descent optimization for robustness. To reduce the relaxation error in the convexification procedure, a nuclear norm penalty is added to approximate original problems. Finally, we propose a new metric to evaluate detection and identification results, which enables a system operator to characterize confidence for further system operations. We show that the proposed algorithms can be realized on IEEE test systems with improved accuracy in a short time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Power systems Bad data and topology error Detection and identification distributed algorithms Convexification Semidefinite programming

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distributed algorithms for Joint Channel Access and Rate Control in Ultrasonic Intra-Body Networks

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IEEE-ACM TRANSACTIONS ON NETWORKING 2016年第5期24卷 3109-3122页

作者： Guan, Zhangyu Santagati, G. Enrico Melodia, Tommaso Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

Most research in body area networks to date has focused on traditional RF wireless communications, typically along the body surface. However, the core challenge of enabling networked intra-body communications through body tissues is substantially unaddressed. RF waves are in fact known to suffer from high absorption and to potentially lead to overheating of human tissues. In this paper, we consider the problem of designing optimal network control algorithms for distributed networked systems of implantable medical devices wirelessly interconnected by means of ultrasonic waves, which are known to propagate better than radio-frequency electromagnetic waves in aqueous media such as human tissues. Specifically, we propose lightweight, asynchronous, and distributed algorithms for joint rate control and stochastic channel access designed to maximize the throughput of ultrasonic intra-body area networks under energy constraints. We first develop (and validate through testbed experiments) a statistical model of the ultrasonic channel and of the spatial and temporal variability of ultrasonic interference. Compared to in-air radio frequency (RF), human tissues are characterized by a much lower propagation speed, which further causes unaligned interference at the receiver. It is therefore inefficient to perform adaptation based on instantaneous channel state information (CSI). Based on this model, we formulate the problem of maximizing the network throughput by jointly controlling the transmission rate and the channel access probability over a finite time horizon based only on a statistical characterization of interference. We then propose a fully distributed solution algorithm, and through both simulation and testbed results, we show that the algorithm achieves considerable throughput gains compared with traditional algorithms.

关键词： distributed algorithms intra-body area networks stochastic channel access ultrasonic communications

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distributed algorithms for the Lovasz local lemma and graph coloring

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distributed COMPUTING 2017年第4期30卷 261-280页

作者： Chung, Kai-Min Pettie, Seth Su, Hsin-Hao Acad Sinica Taipei Taiwan Univ Michigan Ann Arbor MI 48109 USA MIT 77 Massachusetts Ave Cambridge MA 02139 USA

The Lovasz local lemma (LLL), introduced by Erdos and Lovasz in 1975, is a powerful tool of the probabilistic method that allows one to prove that a set of n "bad" events do not happen with non-zero probability, provided that the events have limited dependence. However, the LLL itself does not suggest how to find a point avoiding all bad events. Since the works of Alon (Random Struct algorithms 2(4): 367-378, 1991) and Beck (Random Struct algorithms 2(4): 343-365, 1991) there has been a sustained effort to find a constructive proof (i.e. an algorithm) for the LLL or weaker versions of it. In a major breakthrough Moser and Tardos (J ACM 57(2): 11, 2010) showed that a point avoiding all bad events can be found efficiently. They also proposed a distributed/parallel version of their algorithm that requires O(log(2) n) rounds of communication in a distributed network. In this paper we provide two new distributed algo-rithms for the LLL that improve on both the efficiency and simplicity of the Moser-Tardos algorithm. For clarity we express our results in terms of the symmetric LLL though both algorithms deal with the asymmetric version as well. Let p bound the probability of any bad event and d be the maximum degree in the dependency graph of the bad events. When epd(2) < 1 we give a truly simple LLL algorithm running in O(log(1/epd2) n) rounds. Under the weaker condition ep(d + 1) < 1, we give a slightly slower algorithm running in O(log(2) d . log(1/ep(d+1)) n) rounds. Furthermore, we give an algorithm that runs in sublogarithmic rounds under the condition p . f (d) < 1, where f (d) is an exponential function of d. Although the conditions of the LLL are locally verifiable, we prove that any distributed LLL algorithm requires Omega(log* n) rounds. In many graph coloring problems the existence of a valid coloring is established by one or more applications of the LLL. Using our LLL algorithms, we give logarithmic-time distributed algorithms for frugal coloring, defective c

关键词： Lovasz local lemma distributed algorithms Randomized algorithms Coloring Locality

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distributed algorithms for Constructing Approximate Minimum Spanning Trees in Wireless Sensor Networks

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IEEE TRANSACTIONS ON PARALLEL AND distributed SYSTEMS 2009年第1期20卷 124-139页

作者： Khan, Maleq Pandurangan, Gopal Kumar, V. S. Anil Virginia Tech Virginia Bioinformat Inst Network Dynam & Simulat Sci Lab Blacksburg VA 24061 USA Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

While there are distributed algorithms for the minimum spanning tree (MST) problem, these algorithms require relatively large number of messages and time, and are fairly involved, making them impractical for resource-constrained networks such as wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energy-efficient construction of an approximate MST in wireless networks. Assuming that the nodes are uniformly distributed, we show provable bounds on both the quality of the spanning tree produced and the energy needed to construct them. We show that while NNT produces a close approximation to the MST, it consumes asymptotically less energy than the classical message-optimal distributed MST algorithm due to Gallagery, Humblet, and Spira. Further, the NNTs can be maintained dynamically with polylogarithmic rearrangements under node insertions/deletions. We also perform extensive simulations, which show that the bounds are much better in practice. Our results, to the best of our knowledge, demonstrate the first tradeoff between the quality of approximation and the energy required for building spanning trees on wireless networks, and motivate similar considerations for other important problems.

关键词： distributed algorithms randomized approximation algorithms energy-efficient algorithms minimum spanning tree wireless networks sensor networks

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distributed algorithms for random graphs

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THEORETICAL COMPUTER SCIENCE 2015年 605卷 95-105页

作者： Krzywdzinski, K. Rybarczyk, K. Adam Mickiewicz Univ Poznan Poland

In this article we study statistical properties of a commonly used network model - an Erdos-Renyi random graph G(n, p). We are interested in the performance of distributed algorithms on large networks, which might be represented by G(n, p). We concentrate on classical problems from the field of distributed algorithms such as: finding a maximal independent set, a vertex colouring, an approximation of a minimum dominating set, a maximal matching, an edge colouring and an approximation of a maximum matching. We propose new algorithms, which with probability close to one as n -> infinity construct anticipated structures in G(n, p) in a low number of rounds. Moreover, in some cases, we modify known algorithms to obtain better efficiency on G(n, p). (C) 2015 Elsevier B.V. All rights reserved.

关键词： distributed algorithms Random graphs Colouring Independent set Dominating set Matching

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