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Fault-Tolerant Approximate Shortest-Path Trees

  • Davide Bilò
  • Luciano Gualà
  • Stefano Leucci
  • Guido Proietti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)

Abstract

The resiliency of a network is its ability to remain effectively functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the requirement of being resilient. In this paper we address this trade-off for the prominent case of the broadcasting routing scheme, and we build efficient (i.e., sparse and fast) fault-tolerant approximate shortest-path trees, for both the edge and vertex single-failure case. In particular, for an n-vertex non-negatively weighted graph, and for any constant ε > 0, we design two structures of size \(O(\frac{n \log n}{\varepsilon^2})\) which guarantee (1 + ε)-stretched paths from the selected source also in the presence of an edge/vertex failure. This favorably compares with the currently best known solutions, which are for the edge-failure case of size O(n) and stretch factor 3, and for the vertex-failure case of size O(n logn) and stretch factor 3. Moreover, we also focus on the unweighted case, and we prove that an ordinary (α,β)-spanner can be slightly augmented in order to build efficient fault-tolerant approximate breadth-first-search trees.

Keywords

Short Path Path Decomposition Source Vertex Unweighted Graph Unweighted Case 
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 2014

Authors and Affiliations

  • Davide Bilò
    • 1
  • Luciano Gualà
    • 2
  • Stefano Leucci
    • 3
  • Guido Proietti
    • 3
    • 4
  1. 1.Dipartimento di Scienze Umanistiche e SocialiUniversità di SassariItaly
  2. 2.Dipartimento di Ingegneria dell’ImpresaUniversità di Roma “Tor Vergata”Italy
  3. 3.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaItaly
  4. 4.Istituto di Analisi dei Sistemi ed InformaticaCNRRomaItaly

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