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)
A BGP-based mechanism for lowest-cost routing
Proceedings of the twenty-first annual symposium on Principles of distributed computing
On the Spectrum and Structure of Internet Topology Graphs
IICS '02 Proceedings of the Second International Workshop on Innovative Internet Computing Systems
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
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
A measurement-based analysis of multihoming
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Scaling properties of the Internet graph
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Internet connectivity at the AS-level: an optimization-driven modeling approach
MoMeTools '03 Proceedings of the ACM SIGCOMM workshop on Models, methods and tools for reproducible network research
Towards capturing representative AS-level Internet topologies
Computer Networks: The International Journal of Computer and Telecommunications Networking
An empirical approach to modeling inter-AS traffic matrices
IMC '05 Proceedings of the 5th ACM SIGCOMM conference on Internet Measurement
Reliability as an interdomain service
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Internet routing resilience to failures: analysis and implications
CoNEXT '07 Proceedings of the 2007 ACM CoNEXT conference
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
Interdomain traffic engineering with BGP
IEEE Communications Magazine
An exact algorithm for IP column generation
Operations Research Letters
BGP routing policies in ISP networks
IEEE Network: The Magazine of Global Internetworking
A theory for the connectivity discovered by routing protocols
IEEE/ACM Transactions on Networking (TON)
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Classical measures of network connectivity are the number of disjoint paths between a pair of nodes and the size of a minimum cut. For standard graphs, these measures can be computed efficiently using network flow techniques. However, in the Internet on the level of autonomous systems (ASs), referred to as AS-level Internet, routing policies impose restrictions on the paths that traffic can take in the network. These restrictions can be captured by the valley-free path model, which assumes a special directed graph model in which edge types represent relationships between ASs. We consider the adaptation of the classical connectivity measures to the valley-free path model, where it is NP-hard to compute them. Our first main contribution consists of presenting algorithms for the computation of disjoint paths, and minimum cuts, in the valley-free path model. These algorithms are useful for ASs that want to evaluate different options for selecting upstream providers to improve the robustness of their connection to the Internet. Our second main contribution is an experimental evaluation of our algorithms on four types of directed graph models of the AS-level Internet produced by different inference algorithms. Most importantly, the evaluation shows that our algorithms are able to compute optimal solutions to instances of realistic size of the connectivity problems in the valley-free path model in reasonable time. Furthermore, our experimental results provide information about the characteristics of the directed graph models of the AS-level Internet produced by different inference algorithms. It turns out that (i) we can quantify the difference between the undirected AS-level topology and the directed graph models with respect to fundamental connectivity measures, and (ii) the different inference algorithms yield topologies that are similar with respect to connectivity and are different with respect to the types of paths that exist between pairs of ASs.