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54
The EigenTrust Algorithm for Reputation Management in P2P Networks
 in Proceedings of the 12th International World Wide Web Conference (WWW 2003
, 2003
"... Peertopeer filesharing networks are currently receiving much attention as a means of sharing and distributing information. However, as recent experience with P2P networks such as Gnutella shows, the anonymous, open nature of these networks offers an almost ideal environment for the spread of self ..."
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Cited by 703 (21 self)
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Peertopeer filesharing networks are currently receiving much attention as a means of sharing and distributing information. However, as recent experience with P2P networks such as Gnutella shows, the anonymous, open nature of these networks offers an almost ideal environment for the spread of selfreplicating inauthentic files.
Deeper inside pagerank
 Internet Mathematics
, 2004
"... Abstract. This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existe ..."
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Cited by 142 (4 self)
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Abstract. This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research. 1.
Extrapolation Methods for Accelerating PageRank Computations
 In Proceedings of the Twelfth International World Wide Web Conference
, 2003
"... We present a novel algorithm for the fast computation of PageRank, a hyperlinkbased estimate of the "importance" of Web pages. The original PageRank algorithm uses the Power Method to compute successive iterates that converge to the principal eigenvector of the Markov matrix representing the Web li ..."
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Cited by 134 (13 self)
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We present a novel algorithm for the fast computation of PageRank, a hyperlinkbased estimate of the "importance" of Web pages. The original PageRank algorithm uses the Power Method to compute successive iterates that converge to the principal eigenvector of the Markov matrix representing the Web link graph. The algorithm presented here, called Quadratic Extrapolation, accelerates the convergence of the Power Method by periodically subtracting off estimates of the nonprincipal eigenvectors from the current iterate of the Power Method. In Quadratic Extrapolation, we take advantage of the fact that the first eigenvalueof a Markov matrix is known to be 1 to compute the nonprincipal eigenvectorsusing successiveiterates of the Power Method. Empirically, we show that using Quadratic Extrapolation speeds up PageRank computation by 50300% on a Web graph of 80 million nodes, with minimal overhead.
A survey of eigenvector methods of web information retrieval
 SIAM Rev
"... Abstract. Web information retrieval is significantly more challenging than traditional wellcontrolled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Web’s hyperlink structure. This structure has bee ..."
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Cited by 66 (6 self)
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Abstract. Web information retrieval is significantly more challenging than traditional wellcontrolled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Web’s hyperlink structure. This structure has been exploited by several of today’s leading Web search engines, particularly Google and Teoma. In this survey paper, we focus on Web information retrieval methods that use eigenvector computations, presenting the three popular methods of HITS, PageRank, and SALSA.
A survey on pagerank computing
 Internet Mathematics
, 2005
"... Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. T ..."
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Cited by 64 (0 self)
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Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. This defines the importance of the model and the data structures that underly PageRank processing. Computing even a single PageRank is a difficult computational task. Computing many PageRanks is a much more complex challenge. Recently, significant effort has been invested in building sets of personalized PageRank vectors. PageRank is also used in many diverse applications other than ranking. We are interested in the theoretical foundations of the PageRank formulation, in the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability. We also review alternative models that lead to authority indices similar to PageRank and the role of such indices in applications other than web search. We also discuss linkbased search personalization and outline some aspects of PageRank infrastructure from associated measures of convergence to link preprocessing. 1.
Adaptive Methods for the Computation of PageRank
 STANFORD UNIVERSITY
, 2003
"... We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while relatively few pages take a much longer time to converge. Furthermore, we observe that these slowconverging pages ar ..."
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Cited by 49 (0 self)
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We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while relatively few pages take a much longer time to converge. Furthermore, we observe that these slowconverging pages are generally those pages with high PageRank. We use this observation to devise a simple algorithm to speed up the computation of PageRank, in which the PageRank of pages that have converged are not recomputed at each iteration after convergence. This
A fast twostage algorithm for computing pagerank and its extensions
, 2003
"... We present a fast twostage algorithm for computing the PageRank vector [16]. The algorithm exploits the following observation: the homogeneous discretetime Markov chain associated with PageRank is lumpable, with the lumpable subset of nodes being the dangling nodes [13]. Time to convergence is onl ..."
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Cited by 34 (0 self)
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We present a fast twostage algorithm for computing the PageRank vector [16]. The algorithm exploits the following observation: the homogeneous discretetime Markov chain associated with PageRank is lumpable, with the lumpable subset of nodes being the dangling nodes [13]. Time to convergence is only a fraction of what’s required for the standard algorithm employed by Google [16]. On data of 451,237 webpages, convergence was achieved in 20 % of the time. Our algorithm also replaces a common practice which is in general incorrect. Namely, the practice of ignoring the dangling nodes until the last stages of computation [16] does not necessarily accelerate convergence. In comparison, our algorithm is provable, generally applicable, and achieves the desired speedup. The paper ends with a discussion of possible extensions that generalize the divideandconquer theme. We describe two variations that incorporate a multistage algorithm. In the first variation, the ordinary PageRank vector is computed. In the second variation, the algorithm computes a generalized version of PageRank where webpages are divided into several classes, each incorporating a different personalization vector. The latter represents a major modeling extension and introduces greater flexibility and a potentially more refined model for web traffic.
Generalizing pagerank: Damping functions for linkbased ranking algorithms
 In Proceedings of ACM SIGIR
"... This paper introduces a family of linkbased ranking algorithms that propagate page importance through links. In these algorithms there is a damping function that decreases with distance, so a direct link implies more endorsement than a link through a long path. PageRank is the most widely known ran ..."
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Cited by 29 (8 self)
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This paper introduces a family of linkbased ranking algorithms that propagate page importance through links. In these algorithms there is a damping function that decreases with distance, so a direct link implies more endorsement than a link through a long path. PageRank is the most widely known ranking function of this family. The main objective of this paper is to determine whether this family of ranking techniques has some interest per se, and how different choices for the damping function impact on rank quality and on convergence speed. Even though our results suggest that PageRank can be approximated with other simpler forms of rankings that may be computed more efficiently, our focus is of more speculative nature, in that it aims at separating the kernel of PageRank, that is, linkbased importance propagation, from the way propagation decays over paths. We focus on three damping functions, having linear, exponential, and hyperbolic decay on the lengths of the paths. The exponential decay corresponds to PageRank, and the other functions are new. Our presentation includes algorithms, analysis, comparisons and experiments that study their behavior under different parameters in real Web graph data. Among other results, we show how to calculate a linear approximation that induces a page ordering that is almost identical to PageRank’s using a fixed small number of iterations; comparisons were performed using Kendall’s τ on large domain datasets.
Fast Parallel PageRank: A Linear System Approach
, 2004
"... In this paper we investigate the convergence of iterative stationary and Krylov subspace methods for the PageRank linear system, including the convergence dependency on teleportation. We demonstrate that linear system iterations converge faster than the simple power method and are less sensitive to ..."
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Cited by 23 (2 self)
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In this paper we investigate the convergence of iterative stationary and Krylov subspace methods for the PageRank linear system, including the convergence dependency on teleportation. We demonstrate that linear system iterations converge faster than the simple power method and are less sensitive to the changes in teleportation. In order to perform this study we developed a framework for parallel PageRank computing. We describe the details of the parallel implementation and provide experimental results obtained on a 70node Beowulf cluster.
A Reordering for the PageRank problem
 SIAM J. SCI. COMPUT
, 2004
"... We describe a reordering particularly suited to the PageRank problem, which reduces the computation of the PageRank vector to that of solving a much smaller system, then using forward substitution to get the full solution vector. We compare the theoretical rates of convergence of the original Page ..."
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Cited by 18 (3 self)
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We describe a reordering particularly suited to the PageRank problem, which reduces the computation of the PageRank vector to that of solving a much smaller system, then using forward substitution to get the full solution vector. We compare the theoretical rates of convergence of the original PageRank algorithm to that of the new reordered PageRank algorithm, showing that the new algorithm can do no worse than the original algorithm. We present results of an experimental comparison on five datasets, which demonstrate that the reordered PageRank algorithm can provide a speedup as much as a factor of 6. We also note potential additional benefits that result from the proposed reordering.