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72
Multilevel graph layout on the GPU
 IEEE TRANS. VIS. COMPUT. GRAPH
, 2007
"... This paper presents a new algorithm for force directed graph layout on the GPU. The algorithm, whose goal is to compute layouts accurately and quickly, has two contributions. The first contribution is proposing a general multilevel scheme, which is based on spectral partitioning. The second contri ..."
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Cited by 33 (1 self)
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This paper presents a new algorithm for force directed graph layout on the GPU. The algorithm, whose goal is to compute layouts accurately and quickly, has two contributions. The first contribution is proposing a general multilevel scheme, which is based on spectral partitioning. The second contribution is computing the layout on the GPU. Since the GPU requires a data parallel programming model, the challenge is devising a mapping of a naturally unstructured graph into a wellpartitioned structured one. This is done by computing a balanced partitioning of a general graph. This algorithm provides a general multilevel scheme, which has the potential to be used not only for computation on the GPU, but also on emerging multicore architectures. The algorithm manages to compute high quality layouts of large graphs in a fraction of the time required by existing algorithms of similar quality. An application for visualization of the topologies of ISP (Internet Service Provider) networks is presented. Index Terms—Graph layout, GPU, graph partitioning.
Drawing Huge Graphs by Algebraic Multigrid Optimization. Multiscale Modeling and Simulation
, 2003
"... Abstract. We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of node ..."
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Cited by 31 (3 self)
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Abstract. We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is expressed as a generalized eigenvalue problem, which is solved rapidly using a novel algebraic multigrid technique. The same generalized eigenvalue problem seems to come up also in other fields, hence ACE appears to be applicable outside graph drawing too.
An Experimental Study on DistanceBased Graph Drawing (Extended Abstract)
, 2009
"... In numerous application areas, general undirected graphs need to be drawn, and forcedirected layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms base ..."
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Cited by 26 (7 self)
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In numerous application areas, general undirected graphs need to be drawn, and forcedirected layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity. We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand.
Drawing graphs by eigenvectors: Theory and practice
 Computers and Mathematics with Applications
, 2005
"... Abstract. The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this ..."
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Cited by 25 (1 self)
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Abstract. The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this paper we explore spectral visualization techniques and study their properties from different points of view. We also suggest a novel algorithm for calculating spectral layouts resulting in an extremely fast computation by optimizing the layout within a small vector space.
ZAME: Interactive Largescale Graph Visualization
"... We present the Zoomable Adjacency Matrix Explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and p ..."
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Cited by 25 (6 self)
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We present the Zoomable Adjacency Matrix Explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and panning with interactive performance from an overview to the most detailed views. Several components work together in the ZAME tool to make this possible. Efficient matrix ordering algorithms group related elements. Individual data cases are aggregated into higherorder metarepresentations. Aggregates are arranged into a pyramid hierarchy that allows for ondemand paging to GPU shader programs to support smooth multiscale browsing. Using ZAME, we are able to explore the entire French Wikipedia—over 500,000 articles and 6,000,000 links—with interactive performance on standard consumerlevel computer hardware.
Curvilinar graph drawing using the forcedirected method
 Proc. 12th Int. Symposium on Graph Drawing, 2004, Springer LNCS 3383
"... Abstract. We present a method for modifying a forcedirected graph drawing algorithm into an algorithm for drawing graphs with curved lines. Our method is based on embedding control points as dummy vertices so that edges can be drawn as splines. Our experiments show that our method yields aesthetica ..."
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Cited by 19 (0 self)
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Abstract. We present a method for modifying a forcedirected graph drawing algorithm into an algorithm for drawing graphs with curved lines. Our method is based on embedding control points as dummy vertices so that edges can be drawn as splines. Our experiments show that our method yields aesthetically pleasing curvilinear drawing with improved angular resolution. Applying our method to the GEM algorithm on the test suite of the “Rome Graphs ” resulted in an average improvement of 46 % in angular resolution and of almost 6 % in edge crossings. 1
Visual Analysis of Graphs with Multiple Conencted Components
"... In this paper, we present a system for the interactive visualization and exploration of graphs with many weakly connected components. The visualization of large graphs has recently received much research attention. However, specific systems for visual analysis of graph data sets consisting of many s ..."
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Cited by 15 (4 self)
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In this paper, we present a system for the interactive visualization and exploration of graphs with many weakly connected components. The visualization of large graphs has recently received much research attention. However, specific systems for visual analysis of graph data sets consisting of many such components are rare. In our approach, we rely on graph clustering using an extensive set of topology descriptors. Specifically, we use the SelfOrganizingMap algorithm in conjunction with a useradaptable combination of graph features for clustering of graphs. It offers insight into the overall structure of the data set. The clustering output is presented in a grid containing clusters of the connected components of the input graph. Interactive feature selection and tasktailored data views allow the exploration of the whole graph space. The system provides also tools for assessment and display of cluster quality. We demonstrate the usefulness of our system by application to a shareholder structure analysis problem based on a large realworld data set. While so far our approach is applied to weighted directed graphs only, it can be used for various graph types.
A TwoWay Visualization Method for Clustered Data
, 2003
"... We describe a novel approach to the visualization of hierarchical clustering that superimposes the classical dendrogram over a fully synchronized lowdimensional embedding, thereby gaining the benefits of both approaches. In a single image one can view all the clusters, examine the relations between ..."
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Cited by 13 (3 self)
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We describe a novel approach to the visualization of hierarchical clustering that superimposes the classical dendrogram over a fully synchronized lowdimensional embedding, thereby gaining the benefits of both approaches. In a single image one can view all the clusters, examine the relations between them and study many of their properties. The method is based on an algorithm for lowdimensional embedding of clustered data, with the property that separation between all clusters is guaranteed, regardless of their nature. In particular, the algorithm was designed to produce embeddings that strictly adhere to a given hierarchical clustering of the data, so that every two disjoint clusters in the hierarchy are drawn separately.
A MaxentStress Model for Graph Layout
"... In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an in ..."
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Cited by 11 (3 self)
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In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial allpairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because nodes overlap unnecessarily. We propose a solution, called the maxentstress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a forceaugmented stress majorization algorithm that solves the maxentstress model. Numerical results show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.
Rapid Graph Layout Using Space Filling Curves
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... Network data frequently arises in a wide variety of fields, and nodelink diagrams are a very natural and intuitive representation of such data. In order for a nodelink diagram to be effective, the nodes must be arranged well on the screen. While many graph layout algorithms exist for this purpose ..."
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Cited by 11 (2 self)
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Network data frequently arises in a wide variety of fields, and nodelink diagrams are a very natural and intuitive representation of such data. In order for a nodelink diagram to be effective, the nodes must be arranged well on the screen. While many graph layout algorithms exist for this purpose, they often have limitations such as high computational complexity or node colocation. This paper proposes a new approach to graph layout through the use of space filling curves which is very fast and guarantees that there will be no nodes that are colocated. The resulting layout is also aesthetic and satisfies several criteria for graph layout effectiveness.