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.
Research partially supported by Hasler Foundation in DICS-project 1838, and by the European Commission in the 5th Framework Programme under contract IST-2001-32007 (APPOL II) and in the 6th Framework Programme under contract 001907 (DELIS), with funding in Switzerland provided by SBF.
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Erlebach, T., Hall, A., Moonen, L., Panconesi, A., Spieksma, F., Vukadinović, D. (2006). Robustness of the Internet at the Topology and Routing Level. In: Kohlas, J., Meyer, B., Schiper, A. (eds) Dependable Systems: Software, Computing, Networks. Lecture Notes in Computer Science, vol 4028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11808107_12
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