9 research outputs found
Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid
We propose a load balancing heuristic for parallel adaptive finite element method (FEM) simulations. In contrast to most existing approaches, the heuristic fo-cuses on good partition shapes rather than on mini-mizing the classical edge-cut metric. By applying Alge-braic Multigrid (AMG), we are able to speed up the two most time consuming calculations of the approach while maintaining its large amount of natural parallelism
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
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
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Accelerating Shape Optimizing Load Balancing for Parallel FEM Simulations by Algebraic Multigrid
We propose a load balancing heuristic for parallel adaptive finite element method (FEM) simulations. In contrast to most existing approaches, the heuristic focuses on good partition shapes rather than on minimizing the classical edge-cut metric. By applying Algebraic Multigrid (AMG), we are able to speed up the two most time consuming calculations of the approach while maintaining its large amount of natural parallelism