4,250 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
A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes
We describe a finite-volume method for solving the Poisson equation on
oct-tree adaptive meshes using direct solvers for individual mesh blocks. The
method is a modified version of the method presented by Huang and Greengard
(2000), which works with finite-difference meshes and does not allow for shared
boundaries between refined patches. Our algorithm is implemented within the
FLASH code framework and makes use of the PARAMESH library, permitting
efficient use of parallel computers. We describe the algorithm and present test
results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor
revisions in response to referee's comments; added char
MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation
MADNESS (multiresolution adaptive numerical environment for scientific
simulation) is a high-level software environment for solving integral and
differential equations in many dimensions that uses adaptive and fast harmonic
analysis methods with guaranteed precision based on multiresolution analysis
and separated representations. Underpinning the numerical capabilities is a
powerful petascale parallel programming environment that aims to increase both
programmer productivity and code scalability. This paper describes the features
and capabilities of MADNESS and briefly discusses some current applications in
chemistry and several areas of physics
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
Partitioning Complex Networks via Size-constrained Clustering
The most commonly used method to tackle the graph partitioning problem in
practice is the multilevel approach. During a coarsening phase, a multilevel
graph partitioning algorithm reduces the graph size by iteratively contracting
nodes and edges until the graph is small enough to be partitioned by some other
algorithm. A partition of the input graph is then constructed by successively
transferring the solution to the next finer graph and applying a local search
algorithm to improve the current solution.
In this paper, we describe a novel approach to partition graphs effectively
especially if the networks have a highly irregular structure. More precisely,
our algorithm provides graph coarsening by iteratively contracting
size-constrained clusterings that are computed using a label propagation
algorithm. The same algorithm that provides the size-constrained clusterings
can also be used during uncoarsening as a fast and simple local search
algorithm.
Depending on the algorithm's configuration, we are able to compute partitions
of very high quality outperforming all competitors, or partitions that are
comparable to the best competitor in terms of quality, hMetis, while being
nearly an order of magnitude faster on average. The fastest configuration
partitions the largest graph available to us with 3.3 billion edges using a
single machine in about ten minutes while cutting less than half of the edges
than the fastest competitor, kMetis
Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values
This work is motivated by the needs of predictive analytics on healthcare
data as represented by Electronic Medical Records. Such data is invariably
problematic: noisy, with missing entries, with imbalance in classes of
interests, leading to serious bias in predictive modeling. Since standard data
mining methods often produce poor performance measures, we argue for
development of specialized techniques of data-preprocessing and classification.
In this paper, we propose a new method to simultaneously classify large
datasets and reduce the effects of missing values. It is based on a multilevel
framework of the cost-sensitive SVM and the expected maximization imputation
method for missing values, which relies on iterated regression analyses. We
compare classification results of multilevel SVM-based algorithms on public
benchmark datasets with imbalanced classes and missing values as well as real
data in health applications, and show that our multilevel SVM-based method
produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625
Parallel Graph Partitioning for Complex Networks
Processing large complex networks like social networks or web graphs has
recently attracted considerable interest. In order to do this in parallel, we
need to partition them into pieces of about equal size. Unfortunately, previous
parallel graph partitioners originally developed for more regular mesh-like
networks do not work well for these networks. This paper addresses this problem
by parallelizing and adapting the label propagation technique originally
developed for graph clustering. By introducing size constraints, label
propagation becomes applicable for both the coarsening and the refinement phase
of multilevel graph partitioning. We obtain very high quality by applying a
highly parallel evolutionary algorithm to the coarsened graph. The resulting
system is both more scalable and achieves higher quality than state-of-the-art
systems like ParMetis or PT-Scotch. For large complex networks the performance
differences are very big. For example, our algorithm can partition a web graph
with 3.3 billion edges in less than sixteen seconds using 512 cores of a high
performance cluster while producing a high quality partition -- none of the
competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach
arXiv:1402.328
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