ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

  • Xuefei Li
  • Weiren Yu
  • Bo Yang
  • Jiajin Le
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6897)


Pervasive web applications increasingly require a measure of similarity among objects. Penetrating-Rank (P-Rank) has been one of the promising link-based similarity metrics as it provides a comprehensive way of jointly encoding both incoming and outgoing links into computation for emerging applications. In this paper, we investigate P-Rank efficiency problem that encompasses its accuracy, stability and computational time. (1) We provide an accuracy estimate for iteratively computing P-Rank. A symmetric problem is to find the iteration number K needed for achieving a given accuracy ε. (2) We also analyze the stability of P-Rank, by showing that small choices of the damping factors would make P-Rank more stable and well-conditioned. (3) For undirected graphs, we also explicitly characterize the P-Rank solution in terms of matrices. This results in a novel non-iterative algorithm, termed ASAP , for efficiently computing P-Rank, which improves the CPU time from O(n 4) to O( n 3 ). Using real and synthetic data, we empirically verify the effectiveness and efficiency of our approaches.


Weighting Factor Synthetic Data Undirected Graph Undirected Network Conditional Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amsler, R.: Application of citation-based automatic classification. Technical Report, The University of Texas at Austin, Linguistics Research Center (December 1972)Google Scholar
  2. 2.
    Kleinberg, J.M.: Authoritative sources in a hyperlinked environment. J. ACM 46(5), 604–632 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Small, H.: Co-citation in the scientific literature: A new measure of the relationship between two documents. J. Am. Soc. Inf. Sci. 24(4), 265–269 (1973)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Xi, W., Fox, E.A., Fan, W., Zhang, B., Chen, Z., Yan, J., Zhuang, D.: Simfusion: measuring similarity using unified relationship matrix. In: SIGIR (2005)Google Scholar
  5. 5.
    Jeh, G., Widom, J.: Simrank: a measure of structural-context similarity. In: KDD, pp. 538–543 (2002)Google Scholar
  6. 6.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab (November 1999)Google Scholar
  7. 7.
    Zhao, P., Han, J., Sun, Y.: P-rank: a comprehensive structural similarity measure over information networks. In: CIKM 2009: Proceeding of the 18th ACM Conference on Information and Knowledge Management (2009)Google Scholar
  8. 8.
    Lizorkin, D., Velikhov, P., Grinev, M.N., Turdakov, D.: Accuracy estimate and optimization techniques for simrank computation. VLDB J. 19(1) (2010)Google Scholar
  9. 9.
    Zhou, Y., Cheng, H., Yu, J.X.: Graph clustering based on structural/attribute similarities. PVLDB 2(1) (2009)Google Scholar
  10. 10.
    Antonellis, I., Garcia-Molina, H., Chang, C.C.: Simrank++: query rewriting through link analysis of the click graph. PVLDB 1(1) (2008)Google Scholar
  11. 11.
    Yu, W.: Efficiently computing p-rank similiarty on large networks. Technical report, The University of New South Wales (2011),
  12. 12.
    Li, C., Han, J., He, G., Jin, X., Sun, Y., Yu, Y., Wu, T.: Fast computation of simrank for static and dynamic information networks. In: EDBT (2010)Google Scholar
  13. 13.
    Golub, G.H., Loan, C.F.V.: Matrix computations, 3rd edn. John Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  14. 14.
    Yu, W., Lin, X., Le, J.: Taming computational complexity: Efficient and parallel simrank optimizations on undirected graphs. In: Chen, L., Tang, C., Yang, J., Gao, Y. (eds.) WAIM 2010. LNCS, vol. 6184, pp. 280–296. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Cai, Y., Zhang, M., Ding, C.H.Q., Chakravarthy, S.: Closed form solution of similarity algorithms. In: SIGIR, pp. 709–710 (2010)Google Scholar
  16. 16.
    Yu, W., Lin, X., Le, J.: A space and time efficient algorithm for simrank computation. In: APWeb, pp. 164–170 (2010)Google Scholar
  17. 17.
    He, G., Feng, H., Li, C., Chen, H.: Parallel simrank computation on large graphs with iterative aggregation. In: KDD (2010)Google Scholar
  18. 18.
    Fogaras, D., Rácz, B.: Scaling link-based similarity search. In: WWW (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xuefei Li
    • 1
  • Weiren Yu
    • 2
    • 3
  • Bo Yang
    • 3
  • Jiajin Le
    • 3
  1. 1.Fudan UniversityChina
  2. 2.University of New South Wales & NICTAAustralia
  3. 3.Donghua UniversityChina

Personalised recommendations