22 research outputs found
Exponentially Faster Massively Parallel Maximal Matching
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 far more limited understanding of maximal matching
which is one of the central problems of parallel and distributed computing. All
known MPC algorithms for maximal matching either take polylogarithmic time
which is considered inefficient, or require a strictly super-linear space of
per machine.
In this work, we close this gap by providing a novel analysis of an extremely
simple algorithm a variant of which was conjectured to work by Czumaj et al.
[STOC'18]. The algorithm edge-samples the graph, randomly partitions the
vertices, and finds a random greedy maximal matching within each partition. We
show that this algorithm drastically reduces the vertex degrees. This, among
some other results, leads to an round algorithm for
maximal matching with space (or even mildly sublinear in using
standard techniques).
As an immediate corollary, we get a approximate minimum vertex cover in
essentially the same rounds and space. This is the best possible approximation
factor under standard assumptions, culminating a long line of research. It also
leads to an improved round algorithm for
approximate matching. All these results can also be implemented in the
congested clique model within the same number of rounds.Comment: A preliminary version of this paper is to appear in the proceedings
of The 60th Annual IEEE Symposium on Foundations of Computer Science (FOCS
2019
Dynamic Algorithms for the Massively Parallel Computation Model
The Massive Parallel Computing (MPC) model gained popularity during the last
decade and it is now seen as the standard model for processing large scale
data. One significant shortcoming of the model is that it assumes to work on
static datasets while, in practice, real-world datasets evolve continuously. To
overcome this issue, in this paper we initiate the study of dynamic algorithms
in the MPC model.
We first discuss the main requirements for a dynamic parallel model and we
show how to adapt the classic MPC model to capture them. Then we analyze the
connection between classic dynamic algorithms and dynamic algorithms in the MPC
model. Finally, we provide new efficient dynamic MPC algorithms for a variety
of fundamental graph problems, including connectivity, minimum spanning tree
and matching.Comment: Accepted to the 31st ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA 2019