PageRank Problem, Survey And Future Research Directions

In this survey, we provide the most important computational methods to find the PageRank. This is a new comprehensive review of all major issues which are associated with PageRank problem, covering the basic topics, the iterative methods, lumping of nodes, the modification of lumping the nodes, rank-one perturbation, rank-r perturbation, advanced numerical linear algebra methods, conditioning, a new method by power series, and outlines for future studies. Mathematics Subject Classification: 65-02, 65F15

[1]  Gene H. Golub,et al.  Exploiting the Block Structure of the Web for Computing , 2003 .

[2]  Sebastiano Vigna,et al.  Traps and Pitfalls of Topic-Biased PageRank , 2007, WAW.

[3]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[4]  Sebastiano Vigna TruRank: taking PageRank to the limit , 2005, WWW '05.

[5]  Lars Eldén The Eigenvalues of the Google Matrix , 2004 .

[6]  Amy Nicole Langville,et al.  Updating pagerank with iterative aggregation , 2004, WWW Alt. '04.

[7]  Amy Nicole Langville,et al.  A Reordering for the PageRank Problem , 2005, SIAM J. Sci. Comput..

[8]  Timothy Sauer,et al.  Numerical Analysis , 2005 .

[9]  Ricardo A. Baeza-Yates,et al.  Generalizing PageRank: damping functions for link-based ranking algorithms , 2006, SIGIR.

[10]  Konstantin Avrachenkov,et al.  The Effect of New Links on Google Pagerank , 2006 .

[11]  Gene H. Golub,et al.  Extrapolation methods for accelerating PageRank computations , 2003, WWW '03.

[12]  Gianna M. Del Corso,et al.  Fast PageRank Computation via a Sparse Linear System , 2005, Internet Math..

[13]  Taher H. Haveliwala,et al.  Adaptive methods for the computation of PageRank , 2004 .

[14]  Stefano Serra Capizzano,et al.  A General Setting for the Parametric Google Matrix , 2006, Internet Math..

[15]  Gang Wu Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem , 2008 .

[16]  Gang Wu,et al.  A Power–Arnoldi algorithm for computing PageRank , 2007, Numer. Linear Algebra Appl..

[17]  Konstantin Avrachenkov,et al.  A Singular Perturbation Approach for Choosing the PageRank Damping Factor , 2008, Internet Math..

[18]  Taher H. Haveliwala,et al.  The Second Eigenvalue of the Google Matrix , 2003 .

[19]  Sebastiano Vigna,et al.  Graph fibrations, graph isomorphism, and PageRank , 2006, RAIRO Theor. Informatics Appl..

[20]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .

[21]  Amy Nicole Langville,et al.  A Survey of Eigenvector Methods for Web Information Retrieval , 2005, SIAM Rev..

[22]  Ilse C. F. Ipsen,et al.  Convergence Analysis of a PageRank Updating Algorithm by Langville and Meyer , 2005, SIAM J. Matrix Anal. Appl..

[23]  Stefano Serra Capizzano,et al.  Google PageRanking problem: The model and the analysis , 2007, J. Comput. Appl. Math..

[24]  Pavel Berkhin,et al.  A Survey on PageRank Computing , 2005, Internet Math..

[25]  Gene H. Golub,et al.  Computing PageRank using Power Extrapolation , 2003 .

[26]  G. Stewart Matrix Algorithms, Volume II: Eigensystems , 2001 .

[27]  Claude Brezinski,et al.  Extrapolation methods for PageRank computations , 2005 .

[28]  Stefano Serra Capizzano Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation , 2005, SIAM J. Matrix Anal. Appl..

[29]  Ilse C. F. Ipsen,et al.  PageRank Computation, with Special Attention to Dangling Nodes , 2007, SIAM J. Matrix Anal. Appl..

[30]  Yimin Wei,et al.  Comments on "Jordan Canonical Form of the Google Matrix" , 2008, SIAM J. Matrix Anal. Appl..

[31]  Sergei Maslov,et al.  Finding scientific gems with Google's PageRank algorithm , 2006, J. Informetrics.

[32]  Michael Brinkmeier,et al.  PageRank revisited , 2006, TOIT.

[33]  Guangming Yao,et al.  The eigenvalue problem of a specially updated matrix , 2007, Appl. Math. Comput..

[34]  Carl D. Meyer,et al.  Deeper Inside PageRank , 2004, Internet Math..

[35]  Yimin Wei,et al.  On computing PageRank via lumping the Google matrix , 2009 .