77 research outputs found
PT-Scotch: A tool for efficient parallel graph ordering
The parallel ordering of large graphs is a difficult problem, because on the
one hand minimum degree algorithms do not parallelize well, and on the other
hand the obtainment of high quality orderings with the nested dissection
algorithm requires efficient graph bipartitioning heuristics, the best
sequential implementations of which are also hard to parallelize. This paper
presents a set of algorithms, implemented in the PT-Scotch software package,
which allows one to order large graphs in parallel, yielding orderings the
quality of which is only slightly worse than the one of state-of-the-art
sequential algorithms. Our implementation uses the classical nested dissection
approach but relies on several novel features to solve the parallel graph
bipartitioning problem. Thanks to these improvements, PT-Scotch produces
consistently better orderings than ParMeTiS on large numbers of processors
Cholesky-factorized sparse Kernel in support vector machines
Support Vector Machine (SVM) is one of the most powerful machine learning algorithms due to its convex optimization formulation and handling non-linear classification. However, one of its main drawbacks is the long time it takes to train large data sets. This limitation is often aroused when applying non-linear kernels (e.g. RBF Kernel) which are usually required to obtain better separation for linearly inseparable data sets. In this thesis, we study an approach that aims to speed-up the training time by combining both the better performance of RBF kernels and fast training by a linear solver, LIBLINEAR. The approach uses an RBF kernel with a sparse matrix which is factorized using Cholesky decomposition. The method is tested on large artificial and real data sets and compared to the standard RBF and linear kernels where both the accuracy and training time are reported. For most data sets, the result shows a huge training time reduction, over 90\%, whilst maintaining the accuracy
Engineering Data Reduction for Nested Dissection
Many applications rely on time-intensive matrix operations, such as
factorization, which can be sped up significantly for large sparse matrices by
interpreting the matrix as a sparse graph and computing a node ordering that
minimizes the so-called fill-in. In this paper, we engineer new data reduction
rules for the minimum fill-in problem, which significantly reduce the size of
the graph while producing an equivalent (or near-equivalent) instance. By
applying both new and existing data reduction rules exhaustively before nested
dissection, we obtain improved quality and at the same time large improvements
in running time on a variety of instances. Our overall algorithm outperforms
the state-of-the-art significantly: it not only yields better elimination
orders, but it does so significantly faster than previously possible. For
example, on road networks, where nested dissection algorithms are typically
used as a preprocessing step for shortest path computations, our algorithms are
on average six times faster than Metis while computing orderings with less
fill-in
PowerGrid - A Computation Engine for Large-Scale Electric Networks
This Final Report discusses work on an approach for analog emulation of large scale power systems using Analog Behavioral Models (ABMs) and analog devices in PSpice design environment. ABMs are models based on sets of mathematical equations or transfer functions describing the behavior of a circuit element or an analog building block. The ABM concept provides an efficient strategy for feasibility analysis, quick insight of developing top-down design methodology of large systems and model verification prior to full structural design and implementation. Analog emulation in this report uses an electric circuit equivalent of mathematical equations and scaled relationships that describe the states and behavior of a real power system to create its solution trajectory. The speed of analog solutions is as quick as the responses of the circuit itself. Emulation therefore is the representation of desired physical characteristics of a real life object using an electric circuit equivalent. The circuit equivalent has within it, the model of a real system as well as the method of solution. This report presents a methodology of the core computation through development of ABMs for generators, transmission lines and loads. Results of ABMs used for the case of 3, 6, and 14 bus power systems are presented and compared with industrial grade numerical simulators for validation
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