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)


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.


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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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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