Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Tran, Thi-Minh-Dung; Kibangou, Alain

doi:10.3182/20140824-6-za-1003.02428

Cited by 27 publications

(22 citation statements)

References 22 publications

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“…The most difficult part is to normalize the vector in a distributed way. In [37], [40], [41], the authors circumvent the problem of calculating eigenvectors during eigenvalue computation by means of a novel matrix deflation, an affine transformation and a distributed optimization, respectively. Average consensus is utilized to estimate the vector length but at the cost of infinite time to converge [39].…”

Section: Related Workmentioning

confidence: 99%

Distributed Identification of the Most Critical Node for Average Consensus

Líu

Cao

et al. 2015

IEEE Trans. Signal Process.

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In communication networks, cyber attacks, such as resource depleting attacks, can cause failure of nodes and can damage or significantly slow down the convergence of the average consensus algorithm. In particular, if the network topology information is learned, an intelligent adversary can attack the most critical node in the sense that deactivating it causes the largest destruction, among all the network nodes, to the convergence speed of the average consensus algorithm. Although a centralized method can undoubtedly identify such a critical node, it requires global information and is computationally intensive and, hence, is not scalable. In this paper, we aim to identify the most critical node in a distributed manner. The network algebraic connectivity is used to assess the destruction caused by node removal and further the importance of a node. We propose three low-complexity algorithms to estimate the descent of the algebraic connectivity due to node removal and theoretically analyze the corresponding estimation errors. Based on these estimation algorithms, distributed power iteration, and maximum-consensus, we propose a fully distributed algorithm for the nodes to iteratively find the most critical one. Extensive simulation results demonstrate the effectiveness of the proposed methods.Index Terms-Consensus, critical node identification, algebraic connectivity, Fiedler vector, distributed algorithm. 1053-587X

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Section: Related Workmentioning

confidence: 99%

Distributed Identification of the Most Critical Node for Average Consensus

Líu

Cao

et al. 2015

IEEE Trans. Signal Process.

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“…. In [35], the authors have proposed a leave-one-out method to retrieve the non-zero Laplacian eigenvalues.…”

Section: Laplacian Eigenvalues Estimation From the Averaging Matrix Fmentioning

confidence: 99%

Collaborative Network Monitoring by Means of Laplacian Spectrum Estimation and Average Consensus

Tran

Kibangou

2019

Int. J. Control Autom. Syst.

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This paper concerns collaborative monitoring of the robustness of networks partitioned into sub-networks. We consider the critical threshold of a network and the effective graph resistance (Kirchhoff index) of a subgraph characterizing the interconnection of sub-networks, that are partitioned from the given network as robustness metric. In which, the critical threshold depends only on the two first moments of the degree distribution while the Kirchhoff index can be computed with Laplacian eigenvalues. Therefore, we show how to estimate jointly the Laplacian eigenvalues and the two first moments of the degree distribution in a distributed way. * Thi Minh Dung Tran is with the Faculty

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“…(ii) We can let Ł = Ł G /λ max {Ł G }. The network needs λ max {Ł G } to configure this matrix but a preprocessing to retrieve λ max {Ł G } is possible [18].…”

Section: A Notation and Basic Assumptionsmentioning

confidence: 99%

Improved Convergence Rates for Distributed Resource Allocation

Nedić

Olshevsky

Shi

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation problem in a network of n agents, where the agent objectives are decoupled while the resource constraints are coupled. The agents communicate over a connected undirected graph, and they want to collaboratively determine a solution to the overall network problem, while each agent only communicates with its neighbors. We first study the connection between the decentralized resource allocation problem and the decentralized consensus optimization problem. Then, using a class of algorithms for solving consensus optimization problems, we propose a novel class of decentralized schemes for solving resource allocation problems in a distributed manner. Specifically, we first propose an algorithm for solving the resource allocation problem with an o(1/k) convergence rate guarantee when the agents' objective functions are generally convex (could be nondifferentiable) and per agent local convex constraints are allowed; We then propose a gradient-based algorithm for solving the resource allocation problem when per agent local constraints are absent and show that such scheme can achieve geometric rate when the objective functions are strongly convex and have Lipschitz continuous gradients. We have also provided scalability/network dependency analysis. Based on these two algorithms, we have further proposed a gradient projectionbased algorithm which can handle smooth objective and simple constraints more efficiently. Numerical experiments demonstrates the viability and performance of all the proposed algorithms. DRAFT n i=1 (R i x i − r i ) ∈ K where K is a convex cone and R i is a matrix that couples local resources. It was required that the interior of K is nonempty which does not apply to (1b).The authors recently removed such nonempty interior requirement on K during our preparation of this paper. We also would like to point out that our rates are non-ergodic and the measures/criteria used for our rates have some advantages in practical uses (see the comments following Theorem 2). Based December 18, 2018 DRAFT

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Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Cited by 27 publications

References 22 publications

Distributed Identification of the Most Critical Node for Average Consensus

Distributed Identification of the Most Critical Node for Average Consensus

Collaborative Network Monitoring by Means of Laplacian Spectrum Estimation and Average Consensus

Improved Convergence Rates for Distributed Resource Allocation

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