2009
DOI: 10.1287/opre.1080.0677
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Connectivity Measures for Internet Topologies on the Level of Autonomous Systems

Abstract: 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 … Show more

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Cited by 12 publications
(8 citation statements)
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“…Min-cuts with Policies: Sobrinho et al [28] describe a model for understanding the connectivity provided by routevector protocols in the face of routing policies. Erlebach et al [29], [30] study valid s-t-paths and s-t-cuts in the valleyfree model and prove the NP-hardness of the vertex-disjoint min-cut problem. On the other hand, they prove that the edgedisjoint version can be solved in polynomial time for valley-free policies; we have verified this statement in our framework.…”
Section: Related Workmentioning
confidence: 99%
“…Min-cuts with Policies: Sobrinho et al [28] describe a model for understanding the connectivity provided by routevector protocols in the face of routing policies. Erlebach et al [29], [30] study valid s-t-paths and s-t-cuts in the valleyfree model and prove the NP-hardness of the vertex-disjoint min-cut problem. On the other hand, they prove that the edgedisjoint version can be solved in polynomial time for valley-free policies; we have verified this statement in our framework.…”
Section: Related Workmentioning
confidence: 99%
“…In order to have a measure of the path diversity, we need to enumerate all the paths connecting two nodes over a graph that satisfy given routing properties. This problem is often referred to as policy-compliant path diversity computation in the literature [23,37]. The common approach [23] to this problem is to convert the original graph into a type-of-relationship (ToR) graph [21], i.e., a directed graph in which (i) the relationship between two adjacent vertexes is expressed via the direction of the edge connecting them, then (ii) maximizing the total number of vertex-disjoint paths between nodes in this graph.…”
Section: Path Diversity Computationmentioning
confidence: 99%
“…It is known that routing policies substantially restrict which paths are permissible and constrain the effective path diversity [12]. Erlebach et al [10,11] study valid s-t-paths and st-cuts in the valley-free model and prove the NP-hardness of the node-disjoint min-cut problem. Teixeira et al [31] study node-and edge-disjoint paths in undirected Internet topology models, but without taking routing policies into account.…”
Section: Related Workmentioning
confidence: 99%