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.
- Disjoint Path
- Border Gateway Protocol
- Valid Path
- Forward Part
- Edge Version
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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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Print ISBN: 978-3-540-27873-3
Online ISBN: 978-3-540-31860-6