Inferring AS Relationships: Dead End or Lively Beginning?

  • Xenofontas Dimitropoulos
  • Dmitri Krioukov
  • Bradley Huffaker
  • kc claffy
  • George Riley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


Recent techniques for inferring business relationships between ASs [1,2] have yielded maps that have extremely few invalid BGP paths in the terminology of Gao[3]. However, some relationships inferred by these newer algorithms are incorrect, leading to the deduction of unrealistic AS hierarchies. We investigate this problem and discover what causes it. Having obtained such insight, we generalize the problem of AS relationship inference as a multiobjective optimization problem with node-degree-based corrections to the original objective function of minimizing the number of invalid paths. We solve the generalized version of the problem using the semidefinite programming relaxation of the MAX2SAT problem. Keeping the number of invalid paths small, we obtain a more veracious solution than that yielded by recent heuristics.


Multiobjective Optimization Node Degree Multiobjective Optimization Problem Valid Path Original Objective Function 
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.
    Battista, G.D., Patrignani, M., Pizzonia, M.: Computing the types of the relationships between Autonomous Systems. In: IEEE INFOCOM (2003)Google Scholar
  2. 2.
    Erlebach, T., Hall, A., Schank, T.: Classifying customer-provider relationships in the Internet. In: Proceedings of the IASTED International Conference on Communications and Computer Networks (CCN) (2002)Google Scholar
  3. 3.
    Gao, L.: On inferring Autonomous System relationships in the Internet. In: IEEE/ACM Transactions on Networking (2001)Google Scholar
  4. 4.
    Subramanian, L., Agarwal, S., Rexford, J., Katz, R.H.: Characterizing the Internet hierarchy from multiple vantage points. In: IEEE INFOCOM (2002)Google Scholar
  5. 5.
    Xia, J., Gao, L.: On the evaluation of AS relationship inferences. In: IEEE GLOBECOM (2004)Google Scholar
  6. 6.
    Rimondini, M.: Statistics and comparisons about two solutions for computing the types of relationships between Autonomous Systems (2002),
  7. 7.
    Siganos, G., Faloutsos, M.: Analyzing BGP policies: Methodology and tool. In: IEEE INFOCOM (2004)Google Scholar
  8. 8.
    Huber, B., Leinen, S., O’Dell, R., Wattenhofer, R.: Inferring AS relationships beyond counting edges. Technical Report TR 446, ETH Zürich (2004)Google Scholar
  9. 9.
    Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear time algorithm for testing the truth of certain quantified boolean formulae. Information Processing Letters 8, 121–123 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Berlin (1999)zbMATHGoogle Scholar
  11. 11.
    Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM 42, 1115–1145 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Lewin, M., Livnat, D., Zwick, U.: Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems. In: Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization (2002)Google Scholar
  13. 13.
    Håstad, J.: Some optimal inapproximability results. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing (1997)Google Scholar
  14. 14.
    Chang, H., Govindan, R., Jamin, S., Shenker, S.J., Willinger, W.: Towards capturing representative AS-level Internet topologies. Computer Networks Journal 44, 737–755 (2004)CrossRefGoogle Scholar
  15. 15.
    Meyer, D.: University of Oregon Route Views Project (2004)Google Scholar
  16. 16.
    A traceroute server list (2004),
  17. 17.
    Benson, S., Ye, Y., Zhang, X.: A dual-scaling algorithm for semidefinite programming (2004),
  18. 18.
    GmbH, A.S.S.: L E D A library (2004),
  19. 19.
    Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies. Springer, Berlin (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Xenofontas Dimitropoulos
    • 1
    • 2
  • Dmitri Krioukov
    • 2
  • Bradley Huffaker
    • 2
  • kc claffy
    • 2
  • George Riley
    • 1
  1. 1.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Cooperative Association for Internet Data Analysis (CAIDA)La Jolla

Personalised recommendations