This survey provides a guiding reference to researchers seeking an overview of the large
body of literature about graph spanners. It surveys the current literature covering various …

We study breadth-first search (BFS) spanning trees, and address the problem of designing a
sparse fault-tolerant BFS structure, or FT-BFS for short, resilient to the failure of up to two …

A k-spanner of a graph G is a sparse subgraph H whose shortest path distances match
those of G up to a multiplicative error k. In this paper we study spanners that are resistant to …

We introduce new data structures for answering connectivity queries in graphs subject to
batched vertex failures. A deterministic structure processes a batch of d≦d_⋆ failed vertices …

A Trivial Yet Optimal Solution to Vertex Fault Tolerant Spanners Page 1 A Trivial Yet Optimal
Solution to Vertex Fault Tolerant Spanners Greg Bodwin gbodwin6@cc.gatech.edu Georgia …

Given p node pairs in an n-node graph, a distance preserver is a sparse subgraph that
agrees with the original graph on all of the given pairwise distances. We prove the following …

The famous shortest path tree lemma states that, for any node s in a graph G=(V, E), there is
a subgraph on O (n) edges that preserves all distances between node pairs in the set {s}× V …

Let G be an unweighted n-node undirected graph. A β-additive spanner of G is a spanning
subgraph H of G such that distances in H are stretched at most by an additive term β wrt the …

A fault-tolerant structure for a network is required to continue functioning following the failure
of some of the network's edges or vertices. This article addresses the problem of designing a …

A (1+ ε)-spanner for a doubling metric (X, δ) is a subgraph H of the complete graph
corresponding to (X, δ), which preserves all pairwise distances to within a factor of 1+ ε. A …