There has been significant recent interest in parallel graph processing due to the need to
quickly analyze the large graphs available today. Many graph codes have been designed …

We present an algorithm that on input of an n-vertex m-edge weighted graph G and a value
k produces an incremental sparsifier ̂G with n-1+m/k edges, such that the relative condition …

In the single-source shortest paths problem, the goal is to compute the shortest path tree
from a designated source vertex in a weighted, directed graph. We present the first near …

This paper is centered on the complexity of graph problems in the well-studied LOCAL
model of distributed computing, introduced by Linial [FOCS'87]. It is widely known that for …

We present the first parallel algorithm for solving systems of linear equations in symmetric,
diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work …

We show an improved parallel algorithm for decomposing an undirected unweighted graph
into small diameter pieces with a small fraction of the edges in between. These …

In this work we revisit the fundamental Single-Source Shortest Paths (SSSP) problem with
possibly negative edge weights. A recent breakthrough result by Bernstein, Nanongkai and …

Miller et al.[48] devised a distributed1 algorithm in the CONGEST model that, given a
parameter k= 1, 2,…, constructs an O (k)-spanner of an input unweighted n-vertex graph with …

In this paper we provide an O (m loglog O (1) n log (1/ϵ))-expected time algorithm for solving
Laplacian systems on n-node m-edge graphs, improving upon the previous best expected …

We use exponential start time clustering to design faster parallel graph algorithms involving
distances. Previous algorithms usually rely on graph decomposition routines with strict …