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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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Correspondence to Paolo G. Franciosa.

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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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