Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Formal-Language-Constrained Path Problems
SIAM Journal on Computing
On the economics of Internet peering
Netnomics
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Characterizing and measuring path diversity of internet topologies
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Oriented paths in mixed graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Cuts and disjoint paths in the valley-free path model of internet BGP routing
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
An exact algorithm for IP column generation
Operations Research Letters
Internet routing resilience to failures: analysis and implications
CoNEXT '07 Proceedings of the 2007 ACM CoNEXT conference
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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.