We introduce and investigate a new notion of resilience in graph spanners. Let S be a spanner of a graph G. Roughly speaking, we say that a spanner 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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