3,585 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Tree-based Coarsening and Partitioning of Complex Networks
Many applications produce massive complex networks whose analysis would
benefit from parallel processing. Parallel algorithms, in turn, often require a
suitable network partition. For solving optimization tasks such as graph
partitioning on large networks, multilevel methods are preferred in practice.
Yet, complex networks pose challenges to established multilevel algorithms, in
particular to their coarsening phase.
One way to specify a (recursive) coarsening of a graph is to rate its edges
and then contract the edges as prioritized by the rating. In this paper we (i)
define weights for the edges of a network that express the edges' importance
for connectivity, (ii) compute a minimum weight spanning tree with
respect to these weights, and (iii) rate the network edges based on the
conductance values of 's fundamental cuts. To this end, we also (iv)
develop the first optimal linear-time algorithm to compute the conductance
values of \emph{all} fundamental cuts of a given spanning tree. We integrate
the new edge rating into a leading multilevel graph partitioner and equip the
latter with a new greedy postprocessing for optimizing the maximum
communication volume (MCV). Experiments on bipartitioning frequently used
benchmark networks show that the postprocessing already reduces MCV by 11.3%.
Our new edge rating further reduces MCV by 10.3% compared to the previously
best rating with the postprocessing in place for both ratings. In total, with a
modest increase in running time, our new approach reduces the MCV of complex
network partitions by 20.4%
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
Search Result Clustering via Randomized Partitioning of Query-Induced Subgraphs
In this paper, we present an approach to search result clustering, using
partitioning of underlying link graph. We define the notion of "query-induced
subgraph" and formulate the problem of search result clustering as a problem of
efficient partitioning of given subgraph into topic-related clusters. Also, we
propose a novel algorithm for approximative partitioning of such graph, which
results in cluster quality comparable to the one obtained by deterministic
algorithms, while operating in more efficient computation time, suitable for
practical implementations. Finally, we present a practical clustering search
engine developed as a part of this research and use it to get results about
real-world performance of proposed concepts.Comment: 16th Telecommunications Forum TELFOR 200
A Parallel Solver for Graph Laplacians
Problems from graph drawing, spectral clustering, network flow and graph
partitioning can all be expressed in terms of graph Laplacian matrices. There
are a variety of practical approaches to solving these problems in serial.
However, as problem sizes increase and single core speeds stagnate, parallelism
is essential to solve such problems quickly. We present an unsmoothed
aggregation multigrid method for solving graph Laplacians in a distributed
memory setting. We introduce new parallel aggregation and low degree
elimination algorithms targeted specifically at irregular degree graphs. These
algorithms are expressed in terms of sparse matrix-vector products using
generalized sum and product operations. This formulation is amenable to linear
algebra using arbitrary distributions and allows us to operate on a 2D sparse
matrix distribution, which is necessary for parallel scalability. Our solver
outperforms the natural parallel extension of the current state of the art in
an algorithmic comparison. We demonstrate scalability to 576 processes and
graphs with up to 1.7 billion edges.Comment: PASC '18, Code: https://github.com/ligmg/ligm
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