A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations

Silvestre, Daniel; Hespanha, João P.; Silvestre, Carlos

doi:10.23919/acc.2018.8431212

Cited by 26 publications

(14 citation statements)

References 23 publications

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“…Distributed processing of data over networks has been studied extensively, and they find applications in different problem formulations ranging from distributed sensor localization [35]- [38] and controlling network of agents [39], [40] to opinion dynamics [41] and PageRank computations [42], [43]. One particular purpose of distributed algorithms is to obtain a consensus among the agents of the underlying network, and the value of the consensus is designed to be the optimal solution of the objective function of interest [44]- [46].…”

Section: A the Random Asynchronous Modelmentioning

confidence: 99%

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Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Teke

Vaidyanathan

2021

IEEE Access

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In graph signal processing signals are defined over a graph, and filters are designed to manipulate the variation of signals over the graph. On the other hand, time domain signal processing treats signals as time series, and digital filters are designed to manipulate the variation of signals in time. This study focuses on the notion of vertex-time filters, which manipulates the variation of a time-dependent graph signal both in the time domain and graph domain simultaneously. The key aspects of the proposed filtering operations are due to the random and asynchronous behavior of the nodes, in which they follow a collectcompute-broadcast scheme. For the analysis of the randomized vertex-time filtering operations, this study first considers the random asynchronous variant of linear discrete-time state-space models, in which each state variable gets updated randomly and independently (and asynchronously) in every iteration. Unlike previous studies that analyzed similar models under certain assumptions on the input signal, this study considers the model in the most general setting with arbitrary time-dependent input signals, which lay the foundations for the vertex-time graph filtering operations. This analysis shows that exponentials continue to be eigenfunctions in a statistical sense in spite of the random asynchronous nature of the model. This study also presents the necessary and sufficient condition for the mean-squared stability and shows that stability of the underlying state transition matrix is neither necessary nor sufficient for the mean-squared stability of the randomized asynchronous recursions. Then, the proposed filtering operations are proven to be mean-square stable if and only if the filter, the graph operator and the update probabilities satisfy a certain condition. The results show that some unstable vertex-time graph filters (in the synchronous case) can be implemented in a stable manner in the presence of randomized asynchronicity, which is also demonstrated by numerical examples.INDEX TERMS Autonomous networks, asynchronous updates, randomized iterations, vertex-time filters.

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Section: A the Random Asynchronous Modelmentioning

confidence: 99%

“…The input noise affects the error correlation matrix through the term Q n defined by the equation (42). By vectorizing both sides of (42), a numerical solution to Q n can be obtained as follows:…”

Section: ) Error Due To the Noisementioning

confidence: 99%

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Teke

Vaidyanathan

2021

IEEE Access

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“…This problem is of distinguished importance due to its wide range of applications. Examples of applications are such as distributed optimization [35,36]; motion coordination tasks (e.g., flocking, leader following) [37,38]; rendezvous problems [39]; computer networks resource allocation [40]; and even in computing relative importance of webpages in the PageRank algorithm [41].…”

Section: Problem Statementmentioning

confidence: 99%

Distributed design of deterministic discrete-time privacy preserving average consensus for multi-agent systems through network augmentation

Ramos¹,

Aguiar²,

Kar³

et al. 2021

Preprint

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Average consensus protocols emerge with a central role in distributed systems and decision-making such as distributed information fusion, distributed optimization, distributed estimation, and control. A key advantage of these protocols is that agents exchange and reveal their state information only to their neighbors. Yet, it can raise privacy concerns in situations where the agents' states contain sensitive information. In this paper, we propose a novel (noiseless) privacy preserving distributed algorithms for multi-agent systems to reach an average consensus. The main idea of the algorithms is that each agent runs a (small) network with a crafted structure and dynamics to form a network of networks (i.e., the connection between the newly created networks and their interconnections respecting the initial network connections). Together with a re-weighting of the dynamic parameters dictating the inter-agent dynamics and the initial states, we show that it is possible to ensure that the value of each node converges to the consensus value of the original network. Furthermore, we show that, under mild assumptions, it is possible to craft the dynamics such that the design can be achieved in a distributed fashion. Finally, we illustrate the proposed algorithm with examples.

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“…Bu algoritmaların ortak özelliği, denklem sisteminin tamamının bilindiği varsayımına sahip olmalarıdır ve bu nedenle merkezileştirilmiş algoritmalar olarak adlandırılırlar. Ancak kısmi türevli diferansiyel denklemler [4], hesaplamalı akışkanlar dinamiği [5], elektromanyetik hesaplamaları [6], güç sistemleri tahminlemesi [7] ve arama motorları için geliştirilen pagerank algoritmaları [8] gibi birçok pratik uygulamada denklem sistemindeki bilinmeyen sayısı çok fazladır ve merkezileştirilmiş algoritmaların bu denklem sistemlerini çözmesi pratik değildir. Bunun yanında, doğrusal denklem sistemini oluşturan denklemler birbirinden çok farklı fiziksel konumlarda ortaya çıkabileceği için merkezileştirilmiş bir algoritmanın kullanılabilmesi için tüm denklemlerin merkezi işlemci tarafından tek bir yerde toplanması gerekmektedir.…”

Section: Introductionunclassified

Distributed Solution of Road Lighting Problem Over Multi-Agent Networks

Cihan

2020

Sakarya University Journal of Computer and Information Sciences

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In this study, we consider the solution of the road lighting problem by distributed algorithms over multi-agent networks where the objective is to determine the powers of the lamps that provide the desired road lighting level for a given road profile. The road is modeled as multiple road sections each with a length of 50 meters where a lighting pole is located in the middle of each section. Under given assumptions, the illumination levels of the road sections are expressed as linear functions of the powers of the lamps. When the processing units in the lighting poles can communicate wirelessly with the neighboring processing units and make simple calculations, it is shown that the power levels of the lamps that provide the desired lighting level for each road section can be calculated in a distributed manner. Finally, the model and the proposed solution has been verified by a numerical example.

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A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations

Cited by 26 publications

References 23 publications

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

Distributed design of deterministic discrete-time privacy preserving average consensus for multi-agent systems through network augmentation

Distributed Solution of Road Lighting Problem Over Multi-Agent Networks

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