81,220 research outputs found
A Distributed Multilevel Force-directed Algorithm
The wide availability of powerful and inexpensive cloud computing services
naturally motivates the study of distributed graph layout algorithms, able to
scale to very large graphs. Nowadays, to process Big Data, companies are
increasingly relying on PaaS infrastructures rather than buying and maintaining
complex and expensive hardware. So far, only a few examples of basic
force-directed algorithms that work in a distributed environment have been
described. Instead, the design of a distributed multilevel force-directed
algorithm is a much more challenging task, not yet addressed. We present the
first multilevel force-directed algorithm based on a distributed vertex-centric
paradigm, and its implementation on Giraph, a popular platform for distributed
graph algorithms. Experiments show the effectiveness and the scalability of the
approach. Using an inexpensive cloud computing service of Amazon, we draw
graphs with ten million edges in about 60 minutes.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
A Tabu Search Based Approach for Graph Layout
This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing. We formulated the task as a multi-criteria optimization problem with a number of
metrics which are used in a weighted fitness function to measure the aesthetic
quality of the graph layout. The main goal of this work is to speed up the graph
layout process without sacrificing layout quality. To achieve this, we use a tabu
search based method that goes through a predefined number of iterations to minimize
the value of the fitness function. Tabu search always chooses the best solution in
the neighbourhood. This may lead to cycling, so a tabu list is used to store moves
that are not permitted, meaning that the algorithm does not choose previous
solutions for a set period of time. We evaluate the method according to the time
spent to draw a graph and the quality of the drawn graphs. We give experimental
results applied on random graphs and we provide statistical evidence that our
method outperforms a fast search-based drawing method (hill climbing) in execution
time while it produces comparably good graph layouts.We also demonstrate the method
on real world graph datasets to show that we can reproduce similar results in a
real world setting
A Sparse Stress Model
Force-directed layout methods constitute the most common approach to draw
general graphs. Among them, stress minimization produces layouts of
comparatively high quality but also imposes comparatively high computational
demands. We propose a speed-up method based on the aggregation of terms in the
objective function. It is akin to aggregate repulsion from far-away nodes
during spring embedding but transfers the idea from the layout space into a
preprocessing phase. An initial experimental study informs a method to select
representatives, and subsequent more extensive experiments indicate that our
method yields better approximations of minimum-stress layouts in less time than
related methods.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Considerations about multistep community detection
The problem and implications of community detection in networks have raised a
huge attention, for its important applications in both natural and social
sciences. A number of algorithms has been developed to solve this problem,
addressing either speed optimization or the quality of the partitions
calculated. In this paper we propose a multi-step procedure bridging the
fastest, but less accurate algorithms (coarse clustering), with the slowest,
most effective ones (refinement). By adopting heuristic ranking of the nodes,
and classifying a fraction of them as `critical', a refinement step can be
restricted to this subset of the network, thus saving computational time.
Preliminary numerical results are discussed, showing improvement of the final
partition.Comment: 12 page
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
Flow-based Influence Graph Visual Summarization
Visually mining a large influence graph is appealing yet challenging. People
are amazed by pictures of newscasting graph on Twitter, engaged by hidden
citation networks in academics, nevertheless often troubled by the unpleasant
readability of the underlying visualization. Existing summarization methods
enhance the graph visualization with blocked views, but have adverse effect on
the latent influence structure. How can we visually summarize a large graph to
maximize influence flows? In particular, how can we illustrate the impact of an
individual node through the summarization? Can we maintain the appealing graph
metaphor while preserving both the overall influence pattern and fine
readability?
To answer these questions, we first formally define the influence graph
summarization problem. Second, we propose an end-to-end framework to solve the
new problem. Our method can not only highlight the flow-based influence
patterns in the visual summarization, but also inherently support rich graph
attributes. Last, we present a theoretic analysis and report our experiment
results. Both evidences demonstrate that our framework can effectively
approximate the proposed influence graph summarization objective while
outperforming previous methods in a typical scenario of visually mining
academic citation networks.Comment: to appear in IEEE International Conference on Data Mining (ICDM),
Shen Zhen, China, December 201
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