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 …

The “short cycle removal” technique was recently introduced by Abboud, Bringmann, Khoury
and Zamir (STOC'22) to prove fine-grained hardness of approximation. Its main technical …

Among the most important graph parameters is the Diameter, the largest distance between
any two vertices. There are no known very efficient algorithms for computing the Diameter …

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 …

In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in
undirected graphs. For unweighted graphs, we provide an algorithm for 2-approximate …

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 …

Let G=(V, E) be an unweighted undirected graph on n vertices and m edges. For a fixed pair
of real values α≥ 1, β≥ 0, an (α, β) distance oracle of G is a space-efficient data structure …

A distance oracle (DO) for a graph G is a data structure that, when queried with vertices s,t,
returns an estimate d(s,t) of their distance in G. The oracle has stretch (α,β) if the estimate …