Abstract
In the valley-free path model, a path in a given directed graph is valid if it consists of a sequence of forward edges followed by a sequence of backward edges. This model is motivated by BGP routing policies of autonomous systems in the Internet. Robustness considerations lead to the problem of computing a maximum number of disjoint paths between two nodes, and the minimum size of a cut that separates them. We study these problems in the valley-free path model. For the problem of computing a maximum number of edge- or vertex-disjoint valid paths between two given vertices s and t, we give a 2-approximation algorithm and show that no better approximation ratio is possible unless P = NP. For the problem of computing a minimum vertex cut that separates s and t with respect to all valid paths, we give a 2-approximation algorithm and prove that the problem is APX-hard. The corresponding problem for edge cuts is shown to be polynomial-time solvable. We present additional results for acyclic graphs.
Keywords
- Disjoint Path
- Border Gateway Protocol
- Valid Path
- Forward Part
- Edge Version
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.
Research partially supported 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 for the Swiss participants provided by the Swiss Federal Office for Education and Science.
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Erlebach, T., Hall, A., Panconesi, A., Vukadinović, D. (2005). Cuts and Disjoint Paths in the Valley-Free Path Model of Internet BGP Routing. In: López-Ortiz, A., Hamel, A.M. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2004. Lecture Notes in Computer Science, vol 3405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527954_6
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DOI: https://doi.org/10.1007/11527954_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27873-3
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