Network Distance Prediction Based on Decentralized Matrix Factorization

  • Yongjun Liao
  • Pierre Geurts
  • Guy Leduc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6091)

Abstract

Network Coordinate Systems (NCS) are promising techniques to predict unknown network distances from a limited number of measurements. Most NCS algorithms are based on metric space embedding and suffer from the inability to represent distance asymmetries and Triangle Inequality Violations (TIVs). To overcome these drawbacks, we formulate the problem of network distance prediction as guessing the missing elements of a distance matrix and solve it by matrix factorization. A distinct feature of our approach, called Decentralized Matrix Factorization (DMF), is that it is fully decentralized. The factorization of the incomplete distance matrix is collaboratively and iteratively done at all nodes with each node retrieving only a small number of distance measurements. There are no special nodes such as landmarks nor a central node where the distance measurements are collected and stored. We compare DMF with two popular NCS algorithms: Vivaldi and IDES. The former is based on metric space embedding, while the latter is also based on matrix factorization but uses landmarks. Experimental results show that DMF achieves competitive accuracy with the double advantage of having no landmarks and of being able to represent distance asymmetries and TIVs.

Keywords

Network Coordinate System Matrix Factorization Decentralized Matrix Factorization Regularization 

References

  1. 1.
    Hari, D.A., Andersen, D., Balakrishnan, H., Kaashoek, F., Morris, R.: Resilient overlay networks, 131–145 (2001)Google Scholar
  2. 2.
    Azureus Bittorrent, http://azureus.sourceforge.net
  3. 3.
    Donnet, B., Gueye, B., Kaafar, M.A.: A survey on network coordinates systems, design, and security. To appear in IEEE Communication Surveys and Tutorial (December 2010)Google Scholar
  4. 4.
    Ng, T.S.E., Zhang, H.: Predicting Internet network distance with coordinates-based approaches. In: Proc. IEEE INFOCOM, New York, NY, USA (June 2002)Google Scholar
  5. 5.
    Dabek, F., Cox, R., Kaashoek, F., Morris, R.: Vivaldi: A decentralized network coordinate system. In: Proc. ACM SIGCOMM, Portland, OR, USA (August 2004)Google Scholar
  6. 6.
    Zheng, H., Lua, E.K., Pias, M., Griffin, T.: Internet Routing Policies and Round-Trip-Times. In: Proc. the PAM Conference, Boston, MA, USA (April 2005)Google Scholar
  7. 7.
    Lee, S., Zhang, Z., Sahu, S., Saha, D.: On suitability of euclidean embedding of internet hosts. SIGMETRICS 34(1), 157–168 (2006)CrossRefGoogle Scholar
  8. 8.
    Wang, G., Zhang, B., Ng, T.S.E.: Towards network triangle inequality violation aware distributed systems. In: Proc. the ACM/IMC Conference, San Diego, CA, USA, October 2007, pp. 175–188 (2007)Google Scholar
  9. 9.
    Banerjee, S., Griffin, T.G., Pias, M.: The interdomain connectivity of PlanetLab nodes. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 73–82. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Mao, Y., Saul, L., Smith, J.M.: Ides: An internet distance estimation service for large networks. IEEE Journal on Selected Areas in Communications (JSAC), Special Issue on Sampling the Internet, Techniques and Applications 24(12), 2273–2284 (2006)CrossRefGoogle Scholar
  11. 11.
    Chen, Y., Wang, X., Song, X., Lua, E.K., Shi, C., Zhao, X., Deng, B., Li., X.: Phoenix: Towards an accurate, practical and decentralized network coordinate system. In: Proc. IFIP Networking Conference, Aachen, Germany (May 2009)Google Scholar
  12. 12.
    Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)MATHGoogle Scholar
  13. 13.
    Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: NIPS, pp. 556–562. MIT Press, Cambridge (2001)Google Scholar
  14. 14.
    A simulator for peer-to-peer protocols, http://www.pdos.lcs.mit.edu/p2psim/index.html
  15. 15.
    Wong, B., Slivkins, A., Sirer, E.: Meridian: A lightweight network location service without virtual coordinates. In: Proc. the ACM SIGCOMM (August 2005)Google Scholar
  16. 16.
    Tang, L., Crovella, M.: Geometric exploration of the landmark selection problem. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 63–72. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yongjun Liao
    • 1
  • Pierre Geurts
    • 2
    • 3
  • Guy Leduc
    • 1
  1. 1.Research Unit in Networking (RUN)University of LiègeBelgium
  2. 2.Systems and ModelingUniversity of LiègeBelgium
  3. 3.Research associate, FRS-F.N.R.S.Belgium)

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