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Cuts and Disjoint Paths in the Valley-Free Path Model of Internet BGP Routing

  • Thomas Erlebach
  • Alexander Hall
  • Alessandro Panconesi
  • Danica Vukadinović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3405)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thomas Erlebach
    • 1
  • Alexander Hall
    • 2
  • Alessandro Panconesi
    • 3
  • Danica Vukadinović
    • 2
  1. 1.Dept. of Computer ScienceUniversity of LeicesterLeicesterUK
  2. 2.Computer Engineering and Networks Laboratory (TIK), Department of Information Technology and Electrical EngineeringETH ZurichSwitzerland
  3. 3.DSIUniversitàLa SapienzaRomeItaly

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