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Algorithmica

, Volume 80, Issue 12, pp 3437–3460 | Cite as

Fault-Tolerant Approximate Shortest-Path Trees

  • Davide Bilò
  • Luciano Gualà
  • Stefano LeucciEmail author
  • Guido Proietti
Article
  • 204 Downloads

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 \(\varepsilon >0\), we design two structures of size \(O\left( \frac{n \log n}{\varepsilon ^2}\right) \) which guarantee \((1+\varepsilon )\)-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 \(O(n \log n)\) and stretch factor 3. Moreover, we also focus on the unweighted case, and we prove that an ordinary spanner can be slightly augmented in order to build efficient fault-tolerant approximate breadth-first-search trees.

Keywords

Shortest-path trees Fault-tolerant structures Approximate distances 

Notes

Acknowledgements

We wish to thank the anonymous reviewers for their insightful comments and for their helpful suggestions for improving the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Davide Bilò
    • 1
  • Luciano Gualà
    • 2
  • Stefano Leucci
    • 3
    Email author
  • Guido Proietti
    • 4
    • 5
  1. 1.Dipartimento di Scienze Umanistiche e SocialiUniversità di SassariSassariItaly
  2. 2.Dipartimento di Ingegneria dell’ImpresaUniversità di Roma “Tor Vergata”RomeItaly
  3. 3.Department of Computer ScienceETH ZürichZürichSwitzerland
  4. 4.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaL’AquilaItaly
  5. 5.Istituto di Analisi dei Sistemi ed Informatica, CNRRomeItaly

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