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 …

Distributed computing concerns environments in which many processors, located at different
sites, must operate in a noninterfering and cooperative manner. Each of the processors …

Let G=(V, E) be an unweighted undirected graph on n vertices. A simple argument shows
that computing all distances in G with an additive one-sided error of at most 1 is as hard as …

A tree t-spanner T of a graph G is a spanning tree in which the distance between every pair
of vertices is at most t times their distance in G. This notion is motivated by applications in …

A spanner is a sparse subgraph that approximately preserves the pairwise distances of the
original graph. It is well known that there is a smooth tradeoff between the sparsity of a …

A k-spanner of a connected graph G=(V, E) is a subgraph G'consisting of all the vertices of V
and a subset of the edges, with the additional property that the distance between any two …

We make improvements to the upper bounds on several popular types of distance
preserving graph sketches. The first part of our paper concerns pairwise distance …

In this paper we show that, for each chordal graphG, there is a treeTsuch thatTis a spanning
tree of the squareG2ofGand, for every two vertices, the distance between them inTis not …

An\em (α,β)-spanner of a graph G is a subgraph H such that dist_H(u,w)≤α⋅distt_G(u,w)+β
for every pair of vertices u, w, where distG'(u, w) denotes the distance between two vertices u …

Graph condensation (GC) is an emerging technique designed to learn a significantly smaller
graph that retains the essential information of the original graph. This condensed graph has …