Hopsets and spanners are fundamental graph structures, playing a key role in shortest path
computation, distributed communication, and more. A (near-exact) hopset for a given graph …

This paper introduces stronger notions for approximate single-source shortest-path
distances and gives simple reductions to compute them from weaker standard notions of …

For an n-vertex digraph G=(V, E), a shortcut set is a (small) subset of edges H taken from the
transitive closure of G that, when added to G guarantees that the diameter of G∪ H is small …

The single-source shortest-path (SSSP) problem is a notoriously hard problem in the
parallel context. In practice, the Δ-stepping algorithm of Meyer and Sanders has been widely …

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 …

For a graph G, a D-diameter-reducing exact hopset is a small set of additional edges H that,
when added to G, maintains its graph metric but guarantees that all node pairs have a …

We study the well-known shortcut set problem: how much can one decrease the diameter of
a directed graph by adding a small set of shortcuts from the transitive closure of the graph …

This paper presents a randomized parallel single-source shortest paths (SSSP) algorithm for
directed graphs with non-negative integer edge weights that solves the problem exactly in O …

This brief announcement presents an algorithm for (1+ ε) approximate single-source shortest
paths for directed graphs with non-negative real edge weights in the CONGEST model that …

In this paper, we present an efficient parallel derandomization method for randomized
algorithms that rely on concentrations such as the Chernoff bound. This settles a classic …