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 …

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 …

Spanners, emulators, and approximate distance oracles can be viewed as lossy
compression schemes that represent an unweighted graph metric in small space, say …

We prove better lower bounds on additive spanners and emulators, which are lossy
compression schemes for undirected graphs, as well as lower bounds on shortcut sets …

This paper proposes a novel free-weighting matrix (FWM) approach for the event-triggered
(ET) consensus and formation control of multi-agent systems over a directed graph. A new …

Maintaining and updating shortest paths information in a graph is a fundamental problem
with many applications. As computations on dense graphs can be prohibitively expensive …

We obtain improved lower bounds for additive spanners, additive emulators, and diameter-
reducing shortcut sets. Spanners and emulators are sparse graphs that approximately …

Abstract A (β, ϵ)-hopset is, informally, a weighted edge set that, when added to a graph,
allows one to get from point a to point b using a path with at most β edges (“hops”) and …

A classic 1993 paper by Althöfer et al. proved a tight reduction from spanners, emulators,
and distance oracles to the extremal function γ of high-girth graphs. This paper initiated a …

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 …