1,215 research outputs found
CLEX: Yet Another Supercomputer Architecture?
We propose the CLEX supercomputer topology and routing scheme. We prove that
CLEX can utilize a constant fraction of the total bandwidth for point-to-point
communication, at delays proportional to the sum of the number of intermediate
hops and the maximum physical distance between any two nodes. Moreover, %
applying an asymmetric bandwidth assignment to the links, all-to-all
communication can be realized -optimally both with regard to
bandwidth and delays. This is achieved at node degrees of ,
for an arbitrary small constant . In contrast, these
results are impossible in any network featuring constant or polylogarithmic
node degrees. Through simulation, we assess the benefits of an implementation
of the proposed communication strategy. Our results indicate that, for a
million processors, CLEX can increase bandwidth utilization and reduce average
routing path length by at least factors respectively in comparison to
a torus network. Furthermore, the CLEX communication scheme features several
other properties, such as deadlock-freedom, inherent fault-tolerance, and
canonical partition into smaller subsystems
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
The coupling of fluids, dynamics, and controls on advanced architecture computers
This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown
On the Distributed Complexity of Large-Scale Graph Computations
Motivated by the increasing need to understand the distributed algorithmic
foundations of large-scale graph computations, we study some fundamental graph
problems in a message-passing model for distributed computing where
machines jointly perform computations on graphs with nodes (typically, ). The input graph is assumed to be initially randomly partitioned among
the machines, a common implementation in many real-world systems.
Communication is point-to-point, and the goal is to minimize the number of
communication {\em rounds} of the computation.
Our main contribution is the {\em General Lower Bound Theorem}, a theorem
that can be used to show non-trivial lower bounds on the round complexity of
distributed large-scale data computations. The General Lower Bound Theorem is
established via an information-theoretic approach that relates the round
complexity to the minimal amount of information required by machines to solve
the problem. Our approach is generic and this theorem can be used in a
"cookbook" fashion to show distributed lower bounds in the context of several
problems, including non-graph problems. We present two applications by showing
(almost) tight lower bounds for the round complexity of two fundamental graph
problems, namely {\em PageRank computation} and {\em triangle enumeration}. Our
approach, as demonstrated in the case of PageRank, can yield tight lower bounds
for problems (including, and especially, under a stochastic partition of the
input) where communication complexity techniques are not obvious.
Our approach, as demonstrated in the case of triangle enumeration, can yield
stronger round lower bounds as well as message-round tradeoffs compared to
approaches that use communication complexity techniques
PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks
In this paper, we present PolarStar, a novel family of diameter-3 network
topologies derived from the star product of two low-diameter factor graphs. The
proposed PolarStar construction gives the largest known diameter-3 network
topologies for almost all radixes. When compared to state-of-the-art diameter-3
networks, PolarStar achieves 31% geometric mean increase in scale over
Bundlefly, 91% over Dragonfly, and 690% over 3-D HyperX.
PolarStar has many other desirable properties including a modular layout,
large bisection, high resilience to link failures and a large number of
feasible sizes for every radix. Our evaluation shows that it exhibits
comparable or better performance than other diameter-3 networks under various
traffic patterns.Comment: 13 pages, 13 figures, 4 table
- …