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39
A system for graphbased visualization of the evolution of software
 In Proceedings of the 2003 ACM symposium on Software visualization
, 2003
"... We describe Gevol, a system that visualizes the evolution of software using a novel graph drawing technique for visualization of large graphs with a temporal component. Gevol extracts information about a Java program stored within a CVS version control system and displays it using a temporal graph v ..."
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Cited by 89 (13 self)
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We describe Gevol, a system that visualizes the evolution of software using a novel graph drawing technique for visualization of large graphs with a temporal component. Gevol extracts information about a Java program stored within a CVS version control system and displays it using a temporal graph visualizer. This information can be used by programmers to understand the evolution of a legacy program: Why is the program structured the way it is? Which programmers were responsible for which parts of the program during which time periods? Which parts of the program appear unstable over long periods of time and may need to be rewritten? This type of information will complement that produced by more static tools such as source code browsers, slicers, and static analyzers. 1
A Fast MultiScale Method for Drawing Large Graphs
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2002
"... We present a multiscale layout algorithm for the aesthetic drawing of undirected graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that are substantially larger than those we have encountered in prior work. For example, the paper contains a drawi ..."
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Cited by 83 (10 self)
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We present a multiscale layout algorithm for the aesthetic drawing of undirected graphs with straightline edges. The algorithm is extremely fast, and is capable of drawing graphs that are substantially larger than those we have encountered in prior work. For example, the paper contains a drawing of a graph with over 15,000 vertices. Also we achieve "nice" drawings of 1000 vertex graphs in about 1 second. The proposed algorithm embodies a new multiscale scheme for drawing graphs, which was motivated by the earlier multiscale algorithm of Hadany and Harel [HH99]. In principle, it could significantly improve the speed of essentially any forcedirected method (regardless of that method's ability of drawing weighted graphs or the continuity of its costfunction).
Graph drawing by stress majorization
 GRAPH DRAWING
, 2004
"... One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In th ..."
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Cited by 72 (11 self)
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One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS community for more than two decades. It appears that majorization has advantages over the technique of Kamada and Kawai in running time and stability. We also present a few extensions to the basic energy model which can improve layout quality and computation speed in practice. Majorizationbased optimization is essential to these extensions.
Graph Drawing by HighDimensional Embedding
 In GD02, LNCS
, 2002
"... We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seco ..."
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Cited by 64 (10 self)
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We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seconds. The new method appears to have several advantages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs.
ACE: A Fast Multiscale Eigenvector Computation for Drawing Huge Graphs
, 2002
"... We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits ..."
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Cited by 64 (13 self)
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We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of a million nodes in less than a minute. Moreover, the algorithm can deal with more general entities, such as graphs with masses and negative weights (to be defined in the text), and it appears to be applicable outside of graph drawing too.
An Energy Model for Visual Graph Clustering
 Proceedings of the 11th International Symposium on Graph Drawing (GD 2003), LNCS 2912
, 2003
"... We introduce an energy model whose minimum energy drawings reveal the clusters of the drawn graph. Here a cluster is a set of nodes with many internal edges and few edges to nodes outside the set. The drawings of the bestknown force and energy models do not clearly show clusters for graphs whose ..."
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Cited by 44 (4 self)
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We introduce an energy model whose minimum energy drawings reveal the clusters of the drawn graph. Here a cluster is a set of nodes with many internal edges and few edges to nodes outside the set. The drawings of the bestknown force and energy models do not clearly show clusters for graphs whose diameter is small relative to the number of nodes. We formally characterize the minimum energy drawings of our energy model. This characterization shows in what sense the drawings separate clusters, and how the distance of separated clusters to the other nodes can be interpreted.
Online Dynamic Graph Drawing
"... This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user’s mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution cu ..."
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Cited by 36 (1 self)
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This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user’s mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution culling methods in order to reduce the layout time and handle large dynamic graphs. Techniques for representing graphs on the GPU allow a speedup by a factor of up to 17 compared to the CPU implementation. The scalability of the algorithm across GPU generations is demonstrated. Applications of the algorithm to the visualization of discussion threads in Internet sites and to the visualization of social networks are provided.
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 30 (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.
Visual Clustering of Graphs with Nonuniform Degrees
 Proceedings of the 13th International Symposium on Graph Drawing (GD 2005
, 2004
"... We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the nodenormalized cut (also called cut ratio) and the edgenormalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to ..."
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Cited by 28 (2 self)
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We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the nodenormalized cut (also called cut ratio) and the edgenormalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria.
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 22 (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.