Near-optimal massively parallel graph connectivity
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 …
with countless applications, is a key primitive for many other algorithms. In this paper, we …
Weighted matchings via unweighted augmentations
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 …
finding short augmenting paths in unweighted graphs. This method enables us to provide …
Transformers, parallel computation, and logarithmic depth
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 …
simulated by, a constant number of communication rounds of Massively Parallel …
Exponentially faster massively parallel maximal matching
S Behnezhad, MT Hajiaghayi… - 2019 IEEE 60th Annual …, 2019 - ieeexplore.ieee.org
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 …
has recently seen a burst of breakthroughs. Despite this progress, however, we still have a …
Conditional hardness results for massively parallel computation from distributed lower bounds
We present the first conditional hardness results for massively parallel algorithms for some
central graph problems including (approximating) maximum matching, vertex cover …
central graph problems including (approximating) maximum matching, vertex cover …
Faster algorithms for edge connectivity via random 2-out contractions
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 …
problem for simple undirected graphs. The contractions exploit 2-out edge sampling from …
Massively parallel algorithms for finding well-connected components in sparse graphs
Massively parallel computation (MPC) algorithms for graph problems have witnessed a
resurgence of interest in recent years. Despite major progress for numerous graph problems …
resurgence of interest in recent years. Despite major progress for numerous graph problems …
Deterministic massively parallel connectivity
S Coy, A Czumaj - Proceedings of the 54th Annual ACM SIGACT …, 2022 - dl.acm.org
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 …
Massive Parallel Computation (MPC). The input to the problem is an undirected graph G …
Improved deterministic (Δ+ 1) coloring in low-space MPC
We present a deterministic O (log log log n)-round low-space Massively Parallel
Computation (MPC) algorithm for the classical problem of (Δ+ 1)-coloring on n-vertex …
Computation (MPC) algorithm for the classical problem of (Δ+ 1)-coloring on n-vertex …
Graph sparsification for derandomizing massively parallel computation with low space
The Massively Parallel Computation (MPC) model is an emerging model that distills core
aspects of distributed and parallel computation, developed as a tool to solve combinatorial …
aspects of distributed and parallel computation, developed as a tool to solve combinatorial …