Asynchronous Distributed Power Iteration with Gossip-Based Normalization

  • Márk Jelasity
  • Geoffrey Canright
  • Kenth Engø-Monsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4641)

Abstract

The dominant eigenvector of matrices defined by weighted links in overlay networks plays an important role in many peer-to-peer applications. Examples include trust management, importance ranking to support search, and virtual coordinate systems to facilitate managing network proximity. Robust and efficient asynchronous distributed algorithms are known only for the case when the dominant eigenvalue is exactly one. We present a fully distributed algorithm for a more general case: non-negative square matrices that have an arbitrary dominant eigenvalue. The basic idea is that we apply a gossip-based aggregation protocol coupled with an asynchronous iteration algorithm, where the gossip component controls the iteration component. The norm of the resulting vector is an unknown finite constant by default; however, it can optionally be set to any desired constant using a third gossip control component. Through extensive simulation results on artificially generated overlay networks and real web traces we demonstrate the correctness, the performance and the fault tolerance of the protocol.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical report, Stanford Digital Library Technologies Project (1998)Google Scholar
  2. 2.
    Sankaralingam, K., Sethumadhavan, S., Browne, J.C.: Distributed pagerank for p2p systems. In: Proc. HPDC-12, pp. 58–69 (2003)Google Scholar
  3. 3.
    Shi, S., Yu, J., Yang, G., Wang, D.: Distributed page ranking in structured p2p networks. In: Proc. ICPP 2003, pp. 179–186 (October 2003)Google Scholar
  4. 4.
    Parreira, J.X., Donato, D., Michel, S., Weikum, G.: Efficient and decentralized PageRank approximation in a peer-to-peer web search network. In: Proc. VLDB, pp. 415–426 (2006)Google Scholar
  5. 5.
    Kamvar, S.D., Schlosser, M.T., Garcia-Molina, H.: The eigentrust algorithm for reputation management in p2p networks. In: Proc. WWW, ACM Press, New York (2003)Google Scholar
  6. 6.
    Koren, Y.: On spectral graph drawing. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 496–508. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Dabek, F., Cox, R., Kaashoek, F., Morris, R.: Vivaldi: A decentralized network coordinate system. In: Proc. SIGCOMM 2004, ACM Press, New York (2004)Google Scholar
  8. 8.
    Lubachevsky, B., Mitra, D.: A chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit radius. J. of the ACM 33(1), 130–150 (1986)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Burgess, M., Canright, G., Engø-Monsen, K.: Importance-ranking functions derived from the eigenvectors of directed graphs. Technical Report DELIS-TR-0325, DELIS Project (2006)Google Scholar
  10. 10.
    Jelasity, M., Montresor, A., Babaoglu, O.: Gossip-based aggregation in large dynamic networks. ACM Transactions on Computer Systems 23(3), 219–252 (2005)CrossRefGoogle Scholar
  11. 11.
    Jelasity, M., Guerraoui, R., Kermarrec, A.M., van Steen, M.: The peer sampling service: Experimental evaluation of unstructured gossip-based implementations. In: Jacobsen, H.A. (ed.) Middleware 2004. LNCS, vol. 3231, pp. 79–98. Springer, Heidelberg (2004)Google Scholar
  12. 12.
  13. 13.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: Proc. FOCS 2003, pp. 482–491. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar
  14. 14.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74(1), 47–97 (2002)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  16. 16.
    Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, SIAM, Philadelphia (2000)Google Scholar
  17. 17.
    Albert, R., Jeong, H., Barabási, A.L.: Diameter of the world wide web. Nature 401, 130–131 (1999)CrossRefGoogle Scholar
  18. 18.
    Frommer, A., Szyld, D.B.: On asynchronous iterations. Journal of Computational and Applied Mathematics 123(1-2), 201–216 (2000)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Márk Jelasity
    • 1
  • Geoffrey Canright
    • 2
  • Kenth Engø-Monsen
    • 2
  1. 1.University of Szeged, HAS Research Group on AIHungary
  2. 2.Telenor R&D, FornebuNorway

Personalised recommendations