10,822 research outputs found
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
Multiscale approach for the network compression-friendly ordering
We present a fast multiscale approach for the network minimum logarithmic
arrangement problem. This type of arrangement plays an important role in a
network compression and fast node/link access operations. The algorithm is of
linear complexity and exhibits good scalability which makes it practical and
attractive for using on large-scale instances. Its effectiveness is
demonstrated on a large set of real-life networks. These networks with
corresponding best-known minimization results are suggested as an open
benchmark for a research community to evaluate new methods for this problem
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
HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part I. Multilevel Analysis
The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge-Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space-time discontinuous Galerkin discretization of the advection-diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for low and high cell Reynolds numbers and on highly stretched meshes
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
Lossless and near-lossless source coding for multiple access networks
A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {X-i}(i=1)(infinity), and {Y-i}(i=1)(infinity) is drawn independent and identically distributed (i.i.d.) according to joint probability mass function (p.m.f.) p(x, y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf describes all rates achievable by MASCs of infinite coding dimension (n --> infinity) and asymptotically negligible error probabilities (P-e((n)) --> 0). In this paper, we consider the properties of optimal instantaneous MASCs with finite coding dimension (n 0) performance. The interest in near-lossless codes is inspired by the discontinuity in the limiting rate region at P-e((n)) = 0 and the resulting performance benefits achievable by using near-lossless MASCs as entropy codes within lossy MASCs. Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary p(x, y), n, and P-e((n)) and polynomial-time design algorithms that approximate these optimal solutions
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