2,307 research outputs found
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
Performance analysis of parallel branch and bound search with the hypercube architecture
With the availability of commercial parallel computers, researchers are examining new classes of problems which might benefit from parallel computing. This paper presents results of an investigation of the class of search intensive problems. The specific problem discussed is the Least-Cost Branch and Bound search method of deadline job scheduling. The object-oriented design methodology was used to map the problem into a parallel solution. While the initial design was good for a prototype, the best performance resulted from fine-tuning the algorithm for a specific computer. The experiments analyze the computation time, the speed up over a VAX 11/785, and the load balance of the problem when using loosely coupled multiprocessor system based on the hypercube architecture
Radial Stellar Pulsation and 3D Convection. I. Numerical Methods and Adiabatic Test Cases
We are developing a 3D radiation hydrodynamics code to simulate the
interaction of convection and pulsation in classical variable stars. One key
goal is the ability to carry these simulations to full amplitude in order to
compare them with observed light and velocity curves. Previous 2D calculations
were prevented from doing this because of drift in the radial coordinate
system, due to the algorithm defining radial movement of the coordinate system
during the pulsation cycle. We remove this difficulty by defining our
coordinate system flow algorithm to require that the mass in a spherical shell
remain constant throughout the pulsation cycle. We perform adiabatic test
calculations to show that large amplitude solutions repeat over more than 150
pulsation periods. We also verify that the computational method conserves the
peak kinetic energy per period, as must be true for adiabatic pulsation models
Robust and Optimal Methods for Geometric Sensor Data Alignment
Geometric sensor data alignment - the problem of finding the
rigid transformation that correctly aligns two sets of sensor
data without prior knowledge of how the data correspond - is a
fundamental task in computer vision and robotics. It is
inconvenient then that outliers and non-convexity are inherent to
the problem and present significant challenges for alignment
algorithms. Outliers are highly prevalent in sets of sensor data,
particularly when the sets overlap incompletely. Despite this,
many alignment objective functions are not robust to outliers,
leading to erroneous alignments. In addition, alignment problems
are highly non-convex, a property arising from the objective
function and the transformation. While finding a local optimum
may not be difficult, finding the global optimum is a hard
optimisation problem. These key challenges have not been fully
and jointly resolved in the existing literature, and so there is
a need for robust and optimal solutions to alignment problems.
Hence the objective of this thesis is to develop tractable
algorithms for geometric sensor data alignment that are robust to
outliers and not susceptible to spurious local optima.
This thesis makes several significant contributions to the
geometric alignment literature, founded on new insights into
robust alignment and the geometry of transformations. Firstly, a
novel discriminative sensor data representation is proposed that
has better viewpoint invariance than generative models and is
time and memory efficient without sacrificing model fidelity.
Secondly, a novel local optimisation algorithm is developed for
nD-nD geometric alignment under a robust distance measure. It
manifests a wider region of convergence and a greater robustness
to outliers and sampling artefacts than other local optimisation
algorithms. Thirdly, the first optimal solution for 3D-3D
geometric alignment with an inherently robust objective function
is proposed. It outperforms other geometric alignment algorithms
on challenging datasets due to its guaranteed optimality and
outlier robustness, and has an efficient parallel implementation.
Fourthly, the first optimal solution for 2D-3D geometric
alignment with an inherently robust objective function is
proposed. It outperforms existing approaches on challenging
datasets, reliably finding the global optimum, and has an
efficient parallel implementation. Finally, another optimal
solution is developed for 2D-3D geometric alignment, using a
robust surface alignment measure.
Ultimately, robust and optimal methods, such as those in this
thesis, are necessary to reliably find accurate solutions to
geometric sensor data alignment problems
Average resistance of toroidal graphs
The average effective resistance of a graph is a relevant performance index
in many applications, including distributed estimation and control of network
systems. In this paper, we study how the average resistance depends on the
graph topology and specifically on the dimension of the graph. We concentrate
on -dimensional toroidal grids and we exploit the connection between
resistance and Laplacian eigenvalues. Our analysis provides tight estimates of
the average resistance, which are key to study its asymptotic behavior when the
number of nodes grows to infinity. In dimension two, the average resistance
diverges: in this case, we are able to capture its rate of growth when the
sides of the grid grow at different rates. In higher dimensions, the average
resistance is bounded uniformly in the number of nodes: in this case, we
conjecture that its value is of order for large . We prove this fact
for hypercubes and when the side lengths go to infinity.Comment: 24 pages, 6 figures, to appear in SIAM Journal on Control and
Optimization (SICON
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