Many modern parallel systems, such as MapReduce, Hadoop and Spark, can be modeled
well by the MPC model. The MPC model captures well coarse-grained computation on large …

In this paper, we present new randomized algorithms that improve the complexity of the
classic (Δ+ 1)-coloring problem, and its generalization (Δ+ 1)-list-coloring, in three well …

We design a generic method to reduce the task of finding weighted matchings to that of
finding short augmenting paths in unweighted graphs. This method enables us to provide …

Identifying the connected components of a graph, apart from being a fundamental problem
with countless applications, is a key primitive for many other algorithms. In this paper, we …

We introduce a method for “sparsifying” distributed algorithms and exhibit how it leads to
improvements that go past known barriers in two algorithmic settings of large-scale graph …

We develop a framework for graph sparsification and sketching, based on a new tool, short
cycle decomposition, which is a decomposition of an unweighted graph into an edge-disjoint …

The study of approximate matching in the Massively Parallel Computations (MPC) model
has recently seen a burst of breakthroughs. Despite this progress, however, we still have a …

We present the first conditional hardness results for massively parallel algorithms for some
central graph problems including (approximating) maximum matching, vertex cover …

We provide a simple new randomized contraction approach to the global minimum cut
problem for simple undirected graphs. The contractions exploit 2-out edge sampling from …

We consider the problem of designing fundamental graph algorithms on the model of
Massive Parallel Computation (MPC). The input to the problem is an undirected graph G …