On Resilient Graph Spanners

TL;DR

This paper introduces the concept of resilient graph spanners, demonstrating that sparse resilient spanners can be efficiently constructed, ensuring minimal distance degradation after edge failures.

Contribution

It defines a new resilience notion for graph spanners and proves the existence and efficient computability of sparse resilient spanners.

Findings

Sparse resilient spanners exist.

Resilient spanners can be computed efficiently.

Distances in resilient spanners remain close to original graph after failures.

Abstract

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.