We (nearly) settle the time complexity for computing vertex fault-tolerant (VFT) spanners with
optimal sparsity (up to polylogarithmic factors). VFT spanners are sparse subgraphs that …

Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO)
for Euclidean space. A $(\tau,\rho) $-LSO is a collection $\Sigma $ of orderings such that for …

Recent work has established that, for every positive integer k, every n-node graph has a (2 k–
1)-spanner with O (f 1–1/kn 1+ 1/k) edges that is resilient to f edge or vertex faults. For vertex …

An f-edge fault-tolerant distance sensitive oracle (f-DSO) with stretch σ≥ 1 is a data structure
that preprocesses a given undirected, unweighted graph G with n vertices and m edges, and …

A $ k $-spanner of a graph $ G $ is a sparse subgraph that preserves its shortest path
distances up to a multiplicative stretch factor of $ k $, and a $ k $-emulator is similar but not …

Chan, Har-Peled, and Jones [2020] recently developed locality-sensitive ordering (LSO), a
new tool that allows one to reduce problems in the Euclidean space ℝ d to the 1 …

We study a new and stronger notion of fault-tolerant graph structures whose size bounds
depend on the degree of the failing edge set, rather than the total number of faults. For a …

In this article, we provide a unified and simplified approach to derandomize central results in
the area of fault-tolerant graph algorithms. Given a graph G, a vertex pair (s, t)∊ V (G)× V (G) …

We consider the adversarial CONGEST model of distributed computing in which a fixed
number of edges (or nodes) in the graph are controlled by a computationally unbounded …

A $ t $-emulator of a graph $ G $ is a graph $ H $ that approximates its pairwise shortest
path distances up to multiplicative $ t $ error. We study fault tolerant $ t $-emulators, under …