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 …

Connected networks are a fundamental structure of neurobiology. Understanding these
networks will help us elucidate the neural mechanisms of computation. Mathematically …

For a multi-robot team that collaboratively explores an unknown environment, it is of vital
importance that the collected information is efficiently shared among robots in order to …

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 …

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 …

We study the problem of releasing the weights of all-pairs shortest paths in a weighted
undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed …

For a multi-robot team that collaboratively explores an unknown environment, it is of vital
importance that collected information is efficiently shared among robots in order to support …

The hereditary discrepancy of a set system is a certain quantitative measure of the
pseudorandom properties of the system. Roughly, hereditary discrepancy measures how …