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On Resilient Graph Spanners

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Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Università di Roma “La Sapienza”, via Ariosto 25, 00185, Rome, Italy

    Giorgio Ausiello & Andrea Ribichini

  2. Dipartimento di Scienze Statistiche, Università di Roma “La Sapienza”, piazzale Aldo Moro 5, 00185, Rome, Italy

    Paolo G. Franciosa

  3. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

Authors
  1. Giorgio Ausiello
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  2. Paolo G. Franciosa
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  3. Giuseppe F. Italiano
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  4. Andrea Ribichini
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Corresponding author

Correspondence to Paolo G. Franciosa.

Additional information

Work partially supported by the Italian Ministry of Education, University, and Research (MIUR) under PRIN 2012C4E3KT national research project “AMANDA—Algorithmics for MAssive and Networked DAta”. A preliminary version of this paper was presented at the 21st Annual European Symposium on Algorithms, LNCS 8125, pp. 85–96.

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Ausiello, G., Franciosa, P.G., Italiano, G.F. et al. On Resilient Graph Spanners. Algorithmica 74, 1363–1385 (2016). https://doi.org/10.1007/s00453-015-0006-x

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  • DOI: https://doi.org/10.1007/s00453-015-0006-x

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