Distributed PageRank computation based on iterative aggregation-disaggregation methods

Zhu, Yangbo; Ye, Shaozhi; Li, Xing

doi:10.1145/1099554.1099705

Cited by 54 publications

(37 citation statements)

References 24 publications

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“…Aggregation or Disaggregation iterative method is used to expeditiously compute PageRank vector than the Power Method as studied by Zhu, Yu and Li [10]. Aggregation or Disaggregation iterative approach develop from the concept of Markov chains.…”

Section: Aggregation or Disaggregation Iterative Approachmentioning

confidence: 99%

A Survey and Comparative Study of Different PageRank Algorithms

Jilani¹,

Fatima²,

Baig³

et al. 2015

IJCA

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Searching the World Wide Web is an NP complete problem with sparse hyperlink matrices. Thus searching the significant search results is a challenge. Google's PageRank attempted to solve this problem using computing of principle Eigenvalues termed as PageRank vector. After this, a number of techniques were developed to speed up the convergence patterns of pages in the PageRank algorithm. This is paper, we have reviewed a number of of PageRank computation techniques. The main objective of all these techniques is the convergence rate along with space and time complexities. In this paper, a comparative study is presented among Standard Power method, Adaptive Power Method and Aitken's method using SNAP Google web pages dataset.

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Section: Aggregation or Disaggregation Iterative Approachmentioning

confidence: 99%

A Survey and Comparative Study of Different PageRank Algorithms

Jilani¹,

Fatima²,

Baig³

et al. 2015

IJCA

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“…2.1, the coarsescale aggregated stationary probability vector is given by x 14) with the matrix elements of B c given by In matrix form, Eq. (2.15) can be written as 17) with matrix P given by 18) and diag(x) denoting the diagonal matrix of appropriate dimension with diagonal entries x i . In analogy with multigrid terminology, we call matrix P an interpolation operator, because it interpolates from the coarse to the fine level, and its transpose P T a restriction operator.…”

Section: Problem Formulation Let B ∈ Rmentioning

confidence: 99%

“…We mention three examples here: for so-called nearly completely decomposable Markov chains, the aggregates are normally chosen to be the fine-level blocks that are nearly decoupled [7,8]; in [16], one of the coarse states is an aggregate that contains the dangling nodes of a webgraph; and, in [17], aggregates are formed by the nodes of the webgraph that reside on the same compute node in a distributed computing environment for web ranking. In contrast, in the approach we propose, the aggregation process does not employ any explicit advance knowledge of the topology of the Markov chain, but aggregation is done automatically, based solely on some measure of strength of connection in the stochastic matrix.…”

mentioning

confidence: 99%

Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking

Sterck¹,

Manteuffel²,

McCormick³

et al. 2008

SIAM J. Sci. Comput.

104

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Abstract. A multilevel adaptive aggregation method for calculating the stationary probability vector of an irreducible stochastic matrix is described. The method is a special case of the adaptive smooth aggregation and adaptive algebraic multigrid methods for sparse linear systems, and is also closely related to certain extensively studied iterative aggregation/disaggregation methods for Markov chains. In contrast to most existing approaches, our aggregation process does not employ any explicit advance knowledge of the topology of the Markov chain. Instead, adaptive agglomeration is proposed that is based on strength of connection in a scaled problem matrix, in which the columns of the original problem matrix at each recursive fine level are scaled with the current probability vector iterate at that level. Strength of connection is determined as in the algebraic multigrid method, and the aggregation process is fully adaptive, with optimized aggregates chosen in each step of the iteration and at all recursive levels. The multilevel method is applied to a set of stochastic matrices that provide models for web page ranking. Numerical tests serve to illustrate for which types of stochastic matrices the multilevel adaptive method may provide significant speedup compared to standard iterative methods. The tests also provide more insight into why Google's PageRank model is a successful model for determining a ranking of web pages.

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“…The lion's share of such literature is given by PageRank implementations [9], with even a large number of distributed versions [7,14,13].…”

Section: Related Workmentioning

confidence: 99%

Decentralized Network Analysis: A Proposal

Montresor

2008

2008 IEEE 17th Workshop on Enabling Technologies: Infrastructure for Collaborative Enterprises

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In recent years, the peer-to-peer paradigm has gained momentum in several application areas: file-sharing and VoIP applications have been able to attract millions of end users, while large-scale distributed computing frameworks, including the Grid, have proven their ability of attacking large scientific problems. We believe, however, that the potential of the P2P approach has not been completely exploited yet. The goal of this position paper is to propose another scientific area where the P2P cooperation paradigm could be profitably adopted: network analysis, i.e. the mathematical characterization of the main graph-theoretic properties of a large-scale network. We discuss the potential issues that must be confronted with when a decentralized approach to network analysis is taken, and we propose a preliminary research plan.

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Distributed PageRank computation based on iterative aggregation-disaggregation methods

Cited by 54 publications

References 24 publications

A Survey and Comparative Study of Different PageRank Algorithms

A Survey and Comparative Study of Different PageRank Algorithms

Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking

Decentralized Network Analysis: A Proposal

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