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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 ..."
Abstract

Cited by 59 (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.
Topological fisheye views for visualizing large graphs
 IEEE Transactions on Visualization and Computer Graphics
"... Graph drawing is a basic visualization tool. For graphs of up to hundreds of nodes and edges, there are many effective techniques available. At greater scale, data density and occlusion problems often negate its effectiveness. Conventional panandzoom, and multiscale and geometric fisheye views are ..."
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Cited by 43 (2 self)
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Graph drawing is a basic visualization tool. For graphs of up to hundreds of nodes and edges, there are many effective techniques available. At greater scale, data density and occlusion problems often negate its effectiveness. Conventional panandzoom, and multiscale and geometric fisheye views are not fully satisfactory solutions to this problem. As an alternative, we describe a topological zooming method. It is based on the precomputation of a hierarchy of coarsened graphs, which are combined onthefly into renderings with the level of detail dependent on the distance from one or more foci. We also discuss a related distortion method that allows our technique to achieve constant information density displays.
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.
A MultiScale Algorithm for the Linear Arrangement Problem
 Proc. 28th Inter. Workshop on GraphTheoretic Concepts in Computer Science (WG’02), LNCS 2573
, 2002
"... Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running ti ..."
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Cited by 26 (4 self)
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Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running time is significantly better, enabling it to deal with much larger graphs. The paper contains a general multiscale construction, which may be used for a broader range of ordering problems.
Topological landscapes: A terrain metaphor for scientific data
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex informat ..."
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Cited by 20 (8 self)
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Abstract—Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called “Topological Landscapes, ” which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an ndimensional scalar function to a twodimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.