Journal of Applied Mathematics

An Improved Approach to the PageRank Problems

Yue Xie, Ting-Zhu Huang, Chun Wen, and De-An Wu

Full-text: Open access

Abstract

We introduce a partition of the web pages particularly suited to the PageRank problems in which the web link graph has a nested block structure. Based on the partition of the web pages, dangling nodes, common nodes, and general nodes, the hyperlink matrix can be reordered to be a more simple block structure. Then based on the parallel computation method, we propose an algorithm for the PageRank problems. In this algorithm, the dimension of the linear system becomes smaller, and the vector for general nodes in each block can be calculated separately in every iteration. Numerical experiments show that this approach speeds up the computation of PageRank.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 438987, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808320

Digital Object Identifier
doi:10.1155/2013/438987

Mathematical Reviews number (MathSciNet)
MR3147877

Zentralblatt MATH identifier
06950680

Citation

Xie, Yue; Huang, Ting-Zhu; Wen, Chun; Wu, De-An. An Improved Approach to the PageRank Problems. J. Appl. Math. 2013 (2013), Article ID 438987, 8 pages. doi:10.1155/2013/438987. https://projecteuclid.org/euclid.jam/1394808320


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References

  • S. Brin, L. Page, R. Motwami, and T. Winograd, “The PageRank citation ranking: bringing order to the web,” Tech. Rep. 1999-0120, Computer Science Department, Stanford University, Stanford, Calif, USA, 1999.
  • J. M. Kleinberg, “Authoritative sources in a hyperlinked environment,” Journal of the ACM, vol. 46, no. 5, pp. 604–632, 1999.
  • R. Lempel and S. Moran, “The stochastic approach for link-structure analysis (SALSA) and the TKC effect,” in Proceedings of the 9th International Conference on the World Wide Web, pp. 387–401, ACM Press, New York, NY, USA, 2000.
  • S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, “Exploiting the block structure of the web for computing PageRank,” Tech. Rep. 2003-17, Stanford University, Stanford, Calif, USA, 2003.
  • E. Minkov, “Adaptive graph walk based similarity measures in entity-relation graphs,” type CMU-LTI-09-004, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pa, USA, 2008.
  • T. H. Haveliwala and S. D. Kamvar, “The second eigenvalue of the Google matrix,” Tech. Rep. 2003-20, Stanford University, Stanford, Calif, USA, 2003.
  • G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Md, USA, Third edition, 1996.
  • R. S. Wills and I. C. F. Ipsen, “Ordinal ranking for Google's PageRank,” SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 4, pp. 1677–1696, 2008/09.
  • A. Arasu, J. Novak, A. Tomkins, and J. Tomlin, “PageRank computation and the structure of the web: experiments and algorithms,” in Proceedings of the 11th International World Wide Web Conference, ACM Press, New York, NY, USA, 2002.
  • A. Broder, R. Kumar, and F. Maghoul, “Graph structure in the web: experiments and models,” in Proceedings of the 9th International World Wide Web Conference, 2000.
  • S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, “Extrapolation methods for accelerating the computation of PageRank,” in Proceedings of the 12th International World Wide Web Conference, pp. 261–270, ACM Press, New York, NY, USA, 2003.
  • K. Avrachenkov, N. Litvak, D. Nemirovsky, and N. Osipova, “Monte Carlo methods in pagerank computation: when one iteration is sufficient,” SIAM Journal on Numerical Analysis, vol. 45, no. 2, pp. 890–904, 2007.
  • D. F. Gleich, A. P. Gray, C. Greif, and T. Lau, “An inner-outer iteration for computing PageRank,” SIAM Journal on Scientific Computing, vol. 32, no. 1, pp. 349–371, 2010.
  • C. P. Lee, G. H. Golub, and S. A. Zenios, “Partial state spaceaggregation based on lumpability and its application to PageRank,” Tech. Rep., Stanford University, 2003.
  • S. D. Kamvar, T. H. Haveliwala, and G. H. Golub, “Adaptive methods for the computation of PageRank,” Tech. Rep. 2003-26, Stanford University, Stanford, Calif, USA, 2003.
  • A. Cevahir, C. Aykanat, A. Turk, and B. B. Cambazoglu, “Site-based partitioning and repartitioning techniques for parallel pagerank computation,” IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 5, pp. 786–802, 2011.
  • D. Gleich, L. Zhukov, and P. Berkhin, “Fast parallel PageRank: a linear system approach,” Tech. Rep. YRL-2004-038, 2004.
  • C. Kohlschtter, R. Chirita, and W. Nejdl, “Efficient parallel computation of PageRank,” in Proceedings of the 28th European Conference on IR Research (ECIR '06), pp. 241–252, 2006.
  • G. Kollias and E. Gallopoulos, “Asynchronous PageRank computation in an interactive multithreading environment,” in Proceedings of the Seminar Web Information Retrieval and Linear Algebra Algorithms, 2007.
  • G. Kollias, E. Gallopoulos, and D. B. Szyld, “Asynchronous iterative computations with web information retrieval structures: the PageRank case,” in Proceedings of the ParCo, 2006.
  • B. Manaskasemsak and A. Rungsawang, “An efficient partition-based parallel PageRank algorithm,” in Proceedings of the 11th International Conference on Parallel and Distributed Systems Workshops (ICPADS '05), pp. 257–263, July 2005.
  • A. N. Langville and C. D. Meyer, “A reordering for the PageRank problem,” SIAM Journal on Scientific Computing, vol. 27, no. 6, pp. 2112–2120, 2006.
  • A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, vol. 9, SIAM, Philadelphia, Pa, USA, 1994.
  • C. P. Lee, G. H. Golub, and S. A. Zenios, “A fast two-stage algorithm for computing PageRank and its extensions,” Tech. Rep. SCCM-03-15, Stanford University, Stanford, Calif, usa, 2003.
  • J. Hirai, S. Raghavan, H. Garcia-Molina, and A. Paepcke, “WebBase: a repository of Web pages,” Computer Networks, vol. 33, no. 1, pp. 277–293, 2000.
  • G. H. Golub and C. Greif, “Arnoldi-type algorithms for computing stationary distribution vectors, with application to PageRank,” Tech. Rep. SCCM-2004-15, Scientific Computation and Computational Mathematics, Stanford University, Stanford, Calif, USA, 2004. \endinput