151,686 research outputs found
A distributed spanning tree algorithm for topology-aware networks
Abstract. A topology-aware network is a dynamic network in which the nodes can detect whether locally topology changes occur. Many modern networks, like IEEE 1394.1, are topology-aware networks. We present a distributed algorithm for computing and maintaining an arbitrary spanning tree in such a topology-aware network. Although usually minimal spanning trees are studied, in practice arbitrary spanning trees are often sufficient. Since our algorithm is not involved in the detection of topology changes, it performs better than the spanning tree algorithms in standards like IEEE 802.1. Because reasoning about distributed algorithms is rather tricky, we use a systematic approach to prove our algorithm
Distributed Computability in Byzantine Asynchronous Systems
In this work, we extend the topology-based approach for characterizing
computability in asynchronous crash-failure distributed systems to asynchronous
Byzantine systems. We give the first theorem with necessary and sufficient
conditions to solve arbitrary tasks in asynchronous Byzantine systems where an
adversary chooses faulty processes. In our adversarial formulation, outputs of
non-faulty processes are constrained in terms of inputs of non-faulty processes
only. For colorless tasks, an important subclass of distributed problems, the
general result reduces to an elegant model that effectively captures the
relation between the number of processes, the number of failures, as well as
the topological structure of the task's simplicial complexes.Comment: Will appear at the Proceedings of the 46th Annual Symposium on the
Theory of Computing, STOC 201
Optimal Dynamic Distributed MIS
Finding a maximal independent set (MIS) in a graph is a cornerstone task in
distributed computing. The local nature of an MIS allows for fast solutions in
a static distributed setting, which are logarithmic in the number of nodes or
in their degrees. The result trivially applies for the dynamic distributed
model, in which edges or nodes may be inserted or deleted. In this paper, we
take a different approach which exploits locality to the extreme, and show how
to update an MIS in a dynamic distributed setting, either \emph{synchronous} or
\emph{asynchronous}, with only \emph{a single adjustment} and in a single
round, in expectation. These strong guarantees hold for the \emph{complete
fully dynamic} setting: Insertions and deletions, of edges as well as nodes,
gracefully and abruptly. This strongly separates the static and dynamic
distributed models, as super-constant lower bounds exist for computing an MIS
in the former.
Our results are obtained by a novel analysis of the surprisingly simple
solution of carefully simulating the greedy \emph{sequential} MIS algorithm
with a random ordering of the nodes. As such, our algorithm has a direct
application as a -approximation algorithm for correlation clustering. This
adds to the important toolbox of distributed graph decompositions, which are
widely used as crucial building blocks in distributed computing.
Finally, our algorithm enjoys a useful \emph{history-independence} property,
meaning the output is independent of the history of topology changes that
constructed that graph. This means the output cannot be chosen, or even biased,
by the adversary in case its goal is to prevent us from optimizing some
objective function.Comment: 19 pages including appendix and reference
An Elementary Quantum Network of Single Atoms in Optical Cavities
Quantum networks are distributed quantum many-body systems with tailored
topology and controlled information exchange. They are the backbone of
distributed quantum computing architectures and quantum communication. Here we
present a prototype of such a quantum network based on single atoms embedded in
optical cavities. We show that atom-cavity systems form universal nodes capable
of sending, receiving, storing and releasing photonic quantum information.
Quantum connectivity between nodes is achieved in the conceptually most
fundamental way: by the coherent exchange of a single photon. We demonstrate
the faithful transfer of an atomic quantum state and the creation of
entanglement between two identical nodes in independent laboratories. The
created nonlocal state is manipulated by local qubit rotation. This efficient
cavity-based approach to quantum networking is particularly promising as it
offers a clear perspective for scalability, thus paving the way towards
large-scale quantum networks and their applications.Comment: 8 pages, 5 figure
QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment
Previous studies have reported that common dense linear algebra operations do
not achieve speed up by using multiple geographical sites of a computational
grid. Because such operations are the building blocks of most scientific
applications, conventional supercomputers are still strongly predominant in
high-performance computing and the use of grids for speeding up large-scale
scientific problems is limited to applications exhibiting parallelism at a
higher level. We have identified two performance bottlenecks in the distributed
memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear
algebra library. First, because ScaLAPACK assumes a homogeneous communication
network, the implementations of ScaLAPACK algorithms lack locality in their
communication pattern. Second, the number of messages sent in the ScaLAPACK
algorithms is significantly greater than other algorithms that trade flops for
communication. In this paper, we present a new approach for computing a QR
factorization -- one of the main dense linear algebra kernels -- of tall and
skinny matrices in a grid computing environment that overcomes these two
bottlenecks. Our contribution is to articulate a recently proposed algorithm
(Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in
order to confine intensive communications (ScaLAPACK calls) within the
different geographical sites. An experimental study conducted on the Grid'5000
platform shows that the resulting performance increases linearly with the
number of geographical sites on large-scale problems (and is in particular
consistently higher than ScaLAPACK's).Comment: Accepted at IPDPS10. (IEEE International Parallel & Distributed
Processing Symposium 2010 in Atlanta, GA, USA.
Characterizing the Shape of Activation Space in Deep Neural Networks
The representations learned by deep neural networks are difficult to
interpret in part due to their large parameter space and the complexities
introduced by their multi-layer structure. We introduce a method for computing
persistent homology over the graphical activation structure of neural networks,
which provides access to the task-relevant substructures activated throughout
the network for a given input. This topological perspective provides unique
insights into the distributed representations encoded by neural networks in
terms of the shape of their activation structures. We demonstrate the value of
this approach by showing an alternative explanation for the existence of
adversarial examples. By studying the topology of network activations across
multiple architectures and datasets, we find that adversarial perturbations do
not add activations that target the semantic structure of the adversarial class
as previously hypothesized. Rather, adversarial examples are explainable as
alterations to the dominant activation structures induced by the original
image, suggesting the class representations learned by deep networks are
problematically sparse on the input space
Tribes Is Hard in the Message Passing Model
We consider the point-to-point message passing model of communication in
which there are processors with individual private inputs, each -bit
long. Each processor is located at the node of an underlying undirected graph
and has access to private random coins. An edge of the graph is a private
channel of communication between its endpoints. The processors have to compute
a given function of all their inputs by communicating along these channels.
While this model has been widely used in distributed computing, strong lower
bounds on the amount of communication needed to compute simple functions have
just begun to appear. In this work, we prove a tight lower bound of
on the communication needed for computing the Tribes function,
when the underlying graph is a star of nodes that has leaves with
inputs and a center with no input. Lower bound on this topology easily implies
comparable bounds for others. Our lower bounds are obtained by building upon
the recent information theoretic techniques of Braverman et.al (FOCS'13) and
combining it with the earlier work of Jayram, Kumar and Sivakumar (STOC'03).
This approach yields information complexity bounds that is of independent
interest
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