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## Asynchronous iterative computations with Web information retrieval structures: The PageRank case (2005)

Citations: | 10 - 0 self |

### Citations

3268 | The pagerank citation ranking: Bringing order to the web
- Page, Brin, et al.
- 1999
(Show Context)
Citation Context ...atics, Temple University, Philadelphia, USA 1. Introduction There are several ideas being used today for Web information retrieval, and specifically in Web search engines [20]. The PageRank algorithm =-=[22]-=- is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied to the set of pages returned by the Google search engine in response to posting a search quer... |

750 |
Introduction to the numerical solution of Markov chains
- Stewart
- 1994
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Citation Context ...α = 0.85. 1s2 The PageRank vector x is the solution of the linear system x = G x , (1) where the matrix G is an irreducible stochastic matrix, and thus its largest eigenvalue in magnitude is λmax = 1 =-=[26]-=-. Thus, the PageRank vector x is the eigenvector corresponding to λmax = 1, and when normalized, it is the stationary probability distribution over pages under a random walk on the Web, i.e., the inva... |

364 |
editors. The Grid, Blueprint for a New computing Infrastructure.
- Foster, Kesselman
- 1998
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Citation Context ...ations. The present research is part of our general objective, to explore the potential of asynchronous computational models as an underlying framework for very large scale computations over the Grid =-=[14]-=-. The area of “internet algorithmics” appears to offer many occasions for computations of unprecedent dimensionality that would be good candidates for this framework. After giving a formulation of Pag... |

167 | Extrapolation methods for accelerating PageRank computations. - Kamvar, Haveliwala, et al. - 2003 |

158 |
Parallel and distributed computation,
- Bertsekas, Tsitsiklis
- 1989
(Show Context)
Citation Context ... if many important pages include links to it. (ii) A page containing many links has reduced impact on the importance of the pages it links to. In this paper we focus on asynchronous iterative schemes =-=[9,15]-=- to compute PageRank over large sets of Web pages. The elimination of the synchronizing phases is expected to be advantageous on heterogeneous platforms. The motivation for a possible move to such lar... |

158 | Exploiting the block structure of the Web for computing PageRank. - Kamvar, Haveliwala, et al. - 2003 |

115 |
Graph structure in the Web: experiments and models
- Broder, Kumar, et al.
(Show Context)
Citation Context ...g set of four n × n matrices, where n is the number of pages being modeled. An adjacency matrix A can be obtained through a web crawl or synthetically generated using statistical results, e.g., as in =-=[10]-=-. Thus, Ai j = 1 iff page i points to page j, and Ai j = 0 otherwise. A transition matrix P has nonzero elements Pi j = Ai j/deg(i) when deg(i) �= 0, and zero otherwise (in which case page i is called... |

95 | A survey of eigenvector methods for web information retrieval.
- Langville, Meyer
- 2005
(Show Context)
Citation Context ...GREECE b Department of Mathematics, Temple University, Philadelphia, USA 1. Introduction There are several ideas being used today for Web information retrieval, and specifically in Web search engines =-=[20]-=-. The PageRank algorithm [22] is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied to the set of pages returned by the Google search engine in resp... |

89 | An analytical comparison of approaches to personalizing pagerank. Technical report 2003-35. Stanford InfoLab; - Haveliwala, Kamvar, et al. - 2003 |

73 | On asynchronous iterations”,
- Frommer, Szyld
- 2000
(Show Context)
Citation Context ... if many important pages include links to it. (ii) A page containing many links has reduced impact on the importance of the pages it links to. In this paper we focus on asynchronous iterative schemes =-=[9,15]-=- to compute PageRank over large sets of Web pages. The elimination of the synchronizing phases is expected to be advantageous on heterogeneous platforms. The motivation for a possible move to such lar... |

50 | Distributed pagerank for p2p systems.
- Sankaralingam, Sethumadhavan, et al.
- 2003
(Show Context)
Citation Context ... at the i th UE. Here Ri is a set of rows of the relaxed stochastic matrix R indexed by {i}, and bi is the corresponding set of elements of vector b. Also of interest are P2P computations of PageRank =-=[12,23,25,29]-=- These fall into the multiple UEs, message passing category and are asynchronous in nature. An important novelty in these studies is the dynamically generated link information through a notification p... |

35 | Fast Parallel PageRank: A Linear System Approach.
- Gleich, Zhukov, et al.
- 2004
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Citation Context ...tors and utilization of naturally occurring block structure in the adjacency matrix A can be found in [17–19]. For multiple UEs, message passing computation of PageRank using the formulation (2), see =-=[16]-=-. 4. Asynchronous PageRank Unfortunately, the necessary per-step synchronization of the synchronous algorithm described above grows into a significant overhead, especially as it is governed by the rat... |

31 | Fast PageRank Computation via a Sparse Linear System”.
- Corso, Gullí
- 2005
(Show Context)
Citation Context ... to a system of linear equations. Using the fact that x is normalized to unity, i.e., e T x = 1, equation (1) yields (I − R) x = b (2) where b = (1 − α) v and R = α S is the relaxed stochastic matrix =-=[13]-=-. 3. Synchronous PageRank To make the computation of x practical for the problem sizes we are considering, it is necessary to employ an iterative method, e.g. executing until convergence x(t + 1) ← f(... |

27 | Application of threshold partitioning of sparse matrices to Markov chains.
- Choi, Szyld
- 1996
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Citation Context ...tudy the performance of moving a clique-based (i.e., all-to-all) synchronous iterative method to an asynchronous, tree-based counterpart. We are also considering the use of suitable permutations (cf. =-=[11]-=-) as well as larger data sets. Acknowledgments The work of the first two authors was partially supported by a Hellenic Pythagoras-EPEAEK-II research grant. The work of the third author was partially s... |

16 |
Decentralized Convergence Detection Algorithm for Asynchronous Parallel Iterative Algorithms
- Bahi, Contassot-Vivier, et al.
- 2005
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Citation Context ...stributed protocols for global convergence detection (see, e.g., [28]) are flexible but rather complex to implement. They typically assume a specific underlying communication topology. For example in =-=[6]-=- a leader election protocol is used, which in turn assumes a tree topology. Our draft version of a practical centralized protocol, in part inspired by [7], is presented in Figure 1. It enforces persis... |

12 | Finite termination of asynchronous iterative algorithms, Parallel Comput
- Savari, Bertserkas
- 1996
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Citation Context ...rged, one can devise scenarios, where messages not yet delivered, could destroy local convergence. Both centralized and distributed protocols for termination detection can be found in the literature, =-=[24,8]-=-. In a centralized approach, a special UE acts as a monitor of the convergence process of other computing UEs; it keeps a log of the convergence status and issues STOP messages to all computing UEs wh... |

10 |
Jace : a java environment for distributed asynchronous iterative computations
- Bahi, Domas, et al.
- 2004
(Show Context)
Citation Context ...rlying communication topology. For example in [6] a leader election protocol is used, which in turn assumes a tree topology. Our draft version of a practical centralized protocol, in part inspired by =-=[7]-=-, is presented in Figure 1. It enforces persistence of convergence both at the computing UEs (for issuing a CONVERGE message) and at the monitor UE (for issuing a STOP message). Persistence is introdu... |

10 | The mystery of asynchronous iterations convergence when the spectral radius is one
- Szyld
- 1998
(Show Context)
Citation Context ...the misconception by some authors that for a nonnegative matrix B, spectral radius ρ(B) < 1 is a necessary condition for convergence of an asynchronous normalization-free power method can be found in =-=[27]-=-. On the other hand, process (7) involves a matrix R with ρ(R) < 1. Asynchronous iterations with such matrices are well known to converge to the true solution [9]. 3 (7)s4 computing UE monitor UE if(c... |

9 |
A method of terminating asynchronous iterative algorithms on message passing systems. Parallel Algorithms and Applications
- Baz
- 1996
(Show Context)
Citation Context ...rged, one can devise scenarios, where messages not yet delivered, could destroy local convergence. Both centralized and distributed protocols for termination detection can be found in the literature, =-=[24,8]-=-. In a centralized approach, a special UE acts as a monitor of the convergence process of other computing UEs; it keeps a log of the convergence status and issues STOP messages to all computing UEs wh... |

7 | PageRank: Three distributed algorithms
- Jager
- 2004
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Citation Context ... at the i th UE. Here Ri is a set of rows of the relaxed stochastic matrix R indexed by {i}, and bi is the corresponding set of elements of vector b. Also of interest are P2P computations of PageRank =-=[12,23,25,29]-=- These fall into the multiple UEs, message passing category and are asynchronous in nature. An important novelty in these studies is the dynamically generated link information through a notification p... |

3 |
A Chaotic, Asynhronous Algorithm for Computing the Fixed Point of a Nonnegative Matrix of Unit Spectral Radius
- Lubachevsky, Mitra
- 1986
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Citation Context ...×... × Xn(k). Then if x(0) ∈ X(0), the limit points of {x(t)} are fixed points of f , where {x(t)} are given by (5). Process (6) involves a nonnegative matrix of unit spectral radius; it is proved in =-=[21]-=- that the corresponding asynchronous iteration converges to the true solution within a multiplicative factor that can easily be factored out in the end by renormalization. A discussion on the misconce... |

3 | Distributed PageRank: Comparisons between a Simulation and a Peer-to-Peer Implementation of the Algorithm
- Tsimonou
- 2004
(Show Context)
Citation Context ... at the i th UE. Here Ri is a set of rows of the relaxed stochastic matrix R indexed by {i}, and bi is the corresponding set of elements of vector b. Also of interest are P2P computations of PageRank =-=[12,23,25,29]-=- These fall into the multiple UEs, message passing category and are asynchronous in nature. An important novelty in these studies is the dynamically generated link information through a notification p... |