Computing optimal transport distances such as the earth mover's distance is a fundamental
problem in machine learning, statistics, and computer vision. Despite the recent introduction …

We show that a constant number of self-attention layers can efficiently simulate, and be
simulated by, a constant number of communication rounds of Massively Parallel …

Any graph with maximum degree Δ admits a proper vertex coloring with Δ+ 1 colors that can
be found via a simple sequential greedy algorithm in linear time and space. But can one find …

Graph clustering is a fundamental task in many data-mining and machine-learning
pipelines. In particular, identifying a good hierarchical structure is at the same time a …

We present O (loglog n)-round algorithms in the Massively Parallel Computation (MPC)
model, with Õ (n) memory per machine, that compute a maximal independent set, a 1+ ε …

There is a rapidly growing need for scalable algorithms that solve classical graph problems,
such as maximum matching and minimum vertex cover, on massive graphs. For massive …

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 …

An effective technique for solving optimization problems over massive data sets is to
partition the data into smaller pieces, solve the problem on each piece and compute a …

We present a (1+ ε)-approximate parallel algorithm for computing shortest paths in
undirected graphs, achieving poly (log n) depth and m poly (log n) work for n-nodes m …