, Volume 74, Issue 4, pp 1363–1385 | Cite as

On Resilient Graph Spanners

  • Giorgio Ausiello
  • Paolo G. Franciosa
  • Giuseppe F. Italiano
  • Andrea Ribichini


We introduce and investigate a new notion of resilience in graph spanners. Let \(S\) be a spanner of a weighted graph \(G\). Roughly speaking, we say that \(S\) is resilient if all its point-to-point distances are resilient to edge failures. Namely, whenever any edge in \(G\) fails, then as a consequence of this failure all distances do not degrade in \(S\) substantially more than in \(G\) (i.e., the relative distance increases in \(S\) are very close to those in the underlying graph \(G\)). In this paper we show that sparse resilient spanners exist, and that they can be computed efficiently.


Graph algorithms Graph spanners Fault tolerance   Algorithm complexity 



We thank the anonymous referees for their thoughtful reading of the paper and the valuable comments.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  • Paolo G. Franciosa
    • 2
  • Giuseppe F. Italiano
    • 3
  • Andrea Ribichini
    • 1
  1. 1.Dipartimento di Ingegneria Informatica, Automatica e GestionaleUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Dipartimento di Scienze StatisticheUniversità di Roma “La Sapienza”RomeItaly
  3. 3.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità di Roma “Tor Vergata”RomeItaly

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