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 …

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 …

We study distance preservers, hopsets, and shortcut sets in n-node, m-edge directed
graphs, and show improved bounds and new reductions for various settings for these …

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 …

In this paper we prove new results about the extremal structure of paths in directed graphs.
Say we are given a directed graph G=(V, E) on n nodes, a set of sources S⊆ V of size| S|= n …

Let G be a directed multi-graph on n vertices and m edges with a designated source vertex s
and a designated sink vertex t. We study the (s, t)-cuts of capacity minimum+ 1 and as an …

This paper considers a natural fault-tolerant shortest paths problem: for some constant
integer f, given a directed weighted graph with no negative cycles and two fixed vertices s …

In this paper we present succinct labeling schemes for supporting connectivity queries under
vertex faults. For a given $ n $-vertex graph $ G $, an $ f $-VFT (resp., EFT) connectivity …

In this paper, we consider the question of computing sparse subgraphs for any input directed
graph $ G=(V, E) $ on $ n $ vertices and $ m $ edges, that preserves reachability and/or …

Let G=(V, E) be an n-vertices m-edges directed graph with edge weights in the range 1, W
for some parameter W, and sϵ V be a designated source. In this article, we address several …