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Robustness of the Internet at the Topology and Routing Level

  • Thomas Erlebach
  • Alexander Hall
  • Linda Moonen
  • Alessandro Panconesi
  • Frits Spieksma
  • Danica Vukadinović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4028)

Abstract

Classical measures of network robustness are the number of disjoint paths between two nodes and the size of a smallest cut separating them. In the Internet, the paths that traffic can take are constrained by the routing policies of the individual autonomous systems (ASs). These policies mainly depend on the economic relationships between ASs, e.g., customer-provider or peer-to-peer. Paths that are consistent with these policies can be modeled as valley-free paths. We give an overview of existing approaches to the inference of AS relationships, and we survey recent results concerning the problem of computing a maximum number of disjoint valley-free paths between two given nodes, and the problem of computing a smallest set of nodes whose removal disconnects two given nodes with respect to all valley-free paths. For both problems, we discuss NP-hardness and inapproximability results, approximation algorithms, and exact algorithms based on branch-and-bound techniques. We also summarize experimental findings that have been obtained with these algorithms in a comparison of different graph models of the AS-level Internet with respect to robustness properties.

Keywords

Exact Algorithm Disjoint Path Sibling Relationship Border Gateway Protocol Mixed Graph 
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.

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References

  1. 1.
    Agarwal, S., Subramanian, L., Rexford, J., Katz, R.H.: Characterizing the Internet hierarchy from multiple vantage points, project web-page (2002-2003), http://www.cs.berkeley.edu/~sagarwal/research/BGP-hierarchy/
  2. 2.
    Ahuja, A., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  3. 3.
    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)MATHGoogle Scholar
  4. 4.
    Baake, P., Wichmann, T.: On the economics of Internet peering. Netnomics 1(1) (1999)Google Scholar
  5. 5.
    Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., Vance, P.: Branch-and-price: Column generation for solving huge integer programs. Operations Research 46(3), 316–329 (1998)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Barrett, C.L., Jacob, R., Marathe, M.: Formal language constrained path problems. SIAM J. Comput. 30(3), 809–837 (2000)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Di Battista, G., Patrignani, M., Pizzonia, M.: Computing the types of the relationships between Autonomous Systems, project web-page, http://www.dia.uniroma3.it/~compunet/relationships/
  8. 8.
    Di Battista, G., Patrignani, M., Pizzonia, M.: Computing the types of the relationships between autonomous systems. In: Proceedings of INFOCOM 2003 (2003)Google Scholar
  9. 9.
    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, pp. 538–545 (2002)Google Scholar
  10. 10.
    Erlebach, T., Hall, A., Panconesi, A., Vukadinović, D.: Cuts and disjoint paths in the valley-free path model. TIK-Report 180, Computer Engineering and Networks Laboratory (TIK), ETH Zürich (2003), available electronically at: ftp://ftp.tik.ee.ethz.ch/pub/publications/TIK-Report180.pdf
  11. 11.
    Erlebach, T., Hall, A., Panconesi, A., Vukadinović, D.: Cuts and Disjoint Paths in the Valley-Free Path Model of Internet BGP Routing. In: López-Ortiz, A., Hamel, A.M. (eds.) CAAN 2004. LNCS, vol. 3405, pp. 49–62. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Erlebach, T., Moonen, L.S., Spieksma, F.C.R., Vukadinović, D.: Connectivity measures for Internet topologies. DTEW Research Report 0550, Katholieke Universiteit Leuven, Leuven, Belgium (2005)Google Scholar
  13. 13.
    Figueiredo, D.R., Ge, Z., Jaiswal, S.: Logical relationship inference program (implementation of algorithms from [14]), http://www-net.cs.umass.edu/~ratton/AS/
  14. 14.
    Gao, L.: On inferring Autonomous System relationships in the Internet. IEEE/ ACM Transactions on Networking 9(6), 733–745 (2001)CrossRefGoogle Scholar
  15. 15.
    Gao, L., Wang, F.: The extent of AS path inflation by routing policies. In: Proceedings of IEEE Global Internet Symposium 2002 (2002)Google Scholar
  16. 16.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Springer, Berlin (1988)MATHGoogle Scholar
  17. 17.
    Huston, G.: Interconnection, peering and settlements—Part I. Internet Protocol Journal 2(1), 2–16 (1999)Google Scholar
  18. 18.
    Huston, G.: Interconnection, peering and settlements—Part II. Internet Protocol Journal 2(2), 2–23 (1999)MathSciNetGoogle Scholar
  19. 19.
    ILOG CPLEX Optimizer, version 9.0, http://www.ilog.com/products/cplex/
  20. 20.
    Labovitz, C., Ahuja, A., Wattenhofer, R., Venkatachary, S.: The impact of Internet policy and topology on delayed routing convergence. In: Proceedings of INFOCOM 2001 (2001)Google Scholar
  21. 21.
    Library of efficient data types and algorithms (LEDA), http://www.algorithmic-solutions.com/enleda.htm
  22. 22.
    Rimondini, M., Pizzonia, M., Di Battista, G., Patrignani, M.: Algorithms for the Inference of the Commercial Relationships between Autonomous Systems: Results Analysis and Model Validation. In: Proceedings of IPS 2004, International Workshop on Inter-domain Performance and Simulation (2004)Google Scholar
  23. 23.
    Route Views project web-site, University of Oregon, http://www.routeviews.org
  24. 24.
    Subramanian, L., Agarwal, S., Rexford, J., Katz, R.: Characterizing the Interenet hierarchy from multiple vantage points. In: Proceedings of INFOCOM 2002 (2002)Google Scholar
  25. 25.
    Tangmunarunkit, H., Govindan, R., Shenker, S.: Internet path inflation due to policy routing. In: Proceedings of SPIE ITCom 2001 (2001)Google Scholar
  26. 26.
    Tangmunarunkit, H., Govindan, R., Shenker, S., Estrin, D.: The impact of routing policy on Internet paths. In: Proceedings of INFOCOM 2001 (2001)Google Scholar
  27. 27.
    Teixeira, R., Marzullo, K., Savage, S., Voelker, G.: Characterizing and measuring path diversity of Internet topologies. In: Proceedings of ACM SIGMETRICS 2003 (2003)Google Scholar
  28. 28.
    Vanderbeck, F., Wolsey, L.A.: An exact algorithm for IP column generation. Operations Research Letters 19, 151–159 (1996)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Wanke, E., Kötter, R.: Oriented paths in mixed graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 629–643. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  30. 30.
    Xia, J., Gao, L.: On the Evaluation of AS Relationship Inferences. In: Proceedings of IEEE Global Communications Conference (GLOBECOM 2004) (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thomas Erlebach
    • 1
  • Alexander Hall
    • 2
  • Linda Moonen
    • 3
  • Alessandro Panconesi
    • 4
  • Frits Spieksma
    • 3
  • Danica Vukadinović
    • 5
  1. 1.Department of Computer ScienceUniversity of LeicesterEngland
  2. 2.Department of Computer ScienceETH ZürichSwitzerland
  3. 3.Department of Applied EconomicsKatholieke Universiteit LeuvenBelgium
  4. 4.DSIUniversità La SapienzaRomeItaly
  5. 5.Computer Engineering and Networks Laboratory (TIK), Department of Information Technology and Electrical EngineeringETH ZürichSwitzerland

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