3,193 research outputs found
Spectral Thresholds in the Bipartite Stochastic Block Model
We consider a bipartite stochastic block model on vertex sets and
, with planted partitions in each, and ask at what densities efficient
algorithms can recover the partition of the smaller vertex set.
When , multiple thresholds emerge. We first locate a sharp
threshold for detection of the partition, in the sense of the results of
\cite{mossel2012stochastic,mossel2013proof} and \cite{massoulie2014community}
for the stochastic block model. We then show that at a higher edge density, the
singular vectors of the rectangular biadjacency matrix exhibit a localization /
delocalization phase transition, giving recovery above the threshold and no
recovery below. Nevertheless, we propose a simple spectral algorithm, Diagonal
Deletion SVD, which recovers the partition at a nearly optimal edge density.
The bipartite stochastic block model studied here was used by
\cite{feldman2014algorithm} to give a unified algorithm for recovering planted
partitions and assignments in random hypergraphs and random -SAT formulae
respectively. Our results give the best known bounds for the clause density at
which solutions can be found efficiently in these models as well as showing a
barrier to further improvement via this reduction to the bipartite block model.Comment: updated version, will appear in COLT 201
Pregelix: Big(ger) Graph Analytics on A Dataflow Engine
There is a growing need for distributed graph processing systems that are
capable of gracefully scaling to very large graph datasets. Unfortunately, this
challenge has not been easily met due to the intense memory pressure imposed by
process-centric, message passing designs that many graph processing systems
follow. Pregelix is a new open source distributed graph processing system that
is based on an iterative dataflow design that is better tuned to handle both
in-memory and out-of-core workloads. As such, Pregelix offers improved
performance characteristics and scaling properties over current open source
systems (e.g., we have seen up to 15x speedup compared to Apache Giraph and up
to 35x speedup compared to distributed GraphLab), and makes more effective use
of available machine resources to support Big(ger) Graph Analytics
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
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