Detecting Triangle Inequality Violations in Internet Coordinate Systems by Supervised Learning

(Work in Progress)
  • Yongjun Liao
  • Mohamed Ali Kaafar
  • Bamba Gueye
  • François Cantin
  • Pierre Geurts
  • Guy Leduc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5550)

Abstract

Internet Coordinates Systems (ICS) are used to predict Internet distances with limited measurements. However the precision of an ICS is degraded by the presence of Triangle Inequality Violations (TIVs). Simple methods have been proposed to detect TIVs, based e.g. on the empirical observation that a TIV is more likely when the distance is underestimated by the coordinates. In this paper, we apply supervised machine learning techniques to try and derive more powerful criteria to detect TIVs. We first show that (ensembles of) Decision Trees (DTs) learnt on our datasets are very good models for this problem. Moreover, our approach brings out a discriminative variable (called OREE), which combines the classical estimation error with the variance of the estimated distance. This variable alone is as good as an ensemble of DTs, and provides a much simpler criterion. If every node of the ICS sorts its neighbours according to OREE, we show that cutting these lists after a given number of neighbours, or when OREE crosses a given threshold value, achieves very good performance to detect TIVs.

Keywords

Internet Coordinate System Triangle Inequality Violation Supervised Learning Decision Trees 

References

  1. 1.
    Azureus Bittorrent, http://azureus.sourceforge.net
  2. 2.
    Ratnasamy, S., Handley, M., Karp, R., Shenker, S.: Topologically-aware overlay construction and server selection. In: Proc. IEEE INFOCOM, New York, NY, USA (June 2002)Google Scholar
  3. 3.
    Zhang, R., Tang, C., Hu, Y.C., Fahmy, S., Lin, X.: Impact of the inaccuracy of distance prediction algorithms on internet applications: an analytical and comparative study. In: Proc. IEEE INFOCOM, Barcelona, Spain (April 2006)Google Scholar
  4. 4.
    Ng, T.S.E., Zhang, H.: A network positioning system for the internet. In: Proc. of USENIX Annual Technical Conference (June 2004)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.
    Costa, M., Castro, M., Rowstron, R., Key, P.: Pic: practical internet coordinates for distance estimation. In: Proc. the ICDCS, pp. 178–187 (2004)Google Scholar
  7. 7.
    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
  8. 8.
    Lee, S., Zhang, Z., Sahu, S., Saha, D.: On suitability of euclidean embedding of internet hosts. SIGMETRICS 34(1), 157–168 (2006)CrossRefGoogle Scholar
  9. 9.
    Kaafar, M.A., Gueye, B., Cantin, F., Leduc, G., Mathy, L.: Towards a two-tier internet coordinate system to mitigate the impact of triangle inequality violations. In: Das, A., Pung, H.K., Lee, F.B.S., Wong, L.W.C. (eds.) NETWORKING 2008. LNCS, vol. 4982, pp. 397–408. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Kaafar, M.A., Cantin, F., Gueye, B., Leduc, G.: Detecting triangle inequality violations for internet coordinate systems. In: Proc. International Workshop on the Network of the Future, Dresden, Germany (June 2009)Google Scholar
  11. 11.
    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, pp. 175–188 (October 2007)Google Scholar
  12. 12.
    Littman, M.L., Ravi, N., Fenson, E., Howard, R.: Reinforcement learning for autonomic network repair. In: 1st International Conference on Autonomic Computing, ICAC (2004)Google Scholar
  13. 13.
    Khayat, I.E., Geurts, P., Leduc, G.: Machine-learnt versus analytical models of TCP throughput. Computer Networks 51(10), 2631–2644 (2007)CrossRefMATHGoogle 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.
    PEPITO: A data mining software, http://www.pepite.be
  17. 17.
    Fawcett, T.: Roc graphs: Notes and practical considerations for researchers. Technical report, HP Laboratories (March 2004)Google Scholar
  18. 18.
    Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Wadsworth International, California (1984)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Yongjun Liao
    • 1
  • Mohamed Ali Kaafar
    • 2
  • Bamba Gueye
    • 1
  • François Cantin
    • 1
  • Pierre Geurts
    • 3
  • Guy Leduc
    • 1
  1. 1.Research Unit in Networking (RUN)University of LiègeBelgium
  2. 2.INRIAFrance
  3. 3.Systems and ModelingUniversity of LiègeBelgium

Personalised recommendations