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15
Graph Visualization and Navigation in Information Visualization: a Survey
 IEEE Transactions on Visualization and Computer Graphics
, 2000
"... This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as web browsing, statetransition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs ..."
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Cited by 321 (3 self)
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This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as web browsing, statetransition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective. Index TermsInformation visualization, graph visualization, graph drawing, navigation, focus+context, fisheye, clustering. 1
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 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.
An Invitation to Discuss Computer Depiction
, 2002
"... This paper draws from art history and perception to place computer depiction in the broader context of picture production. It highlights the often underestimated complexity of the interactions between features in the picture and features of the represented scene. Depiction is not always a unidirecti ..."
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Cited by 43 (4 self)
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This paper draws from art history and perception to place computer depiction in the broader context of picture production. It highlights the often underestimated complexity of the interactions between features in the picture and features of the represented scene. Depiction is not always a unidirectional projection from a 3D scene to a 2D picture, but involves much feedback and influence from the picture space to the object space. Depiction can be seen as a preexisting 3D reality projected onto 2D, but also as a 2D pictorial representation that is superficially compatible with an hypothetic 3D scene. We show that depiction is essentially an optimization problem, producing the best picture given goals and constraints. We introduce a classification of basic depiction techniques based on four kinds of issue. The spatial system deals with the mapping of spatial properties between 3D and 2D (including, but not restricted to, perspective projection). The primitive system deals with the dimensionality and mappings between picture primitives and scene primitives. Attributes deal with the assignment of visual properties such as colors, texture, or thickness. Finally, marks are the physical implementations of the picture (e.g. brush strokes, mosaic cells). A distinction is introduced between interaction and picturegeneration methods, and techniques are then organized depending on the dimensionality of the inputs and outputs.
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
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Cited by 27 (10 self)
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vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
Really straight graph drawings
 Proc. 12th International Symp. on Graph Drawing (GD ’04
, 2004
"... We study straightline drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2trees, and planar 3trees. We prove that every 3connected plane graph on n vertices has a plane drawing with at most 5n/2 segme ..."
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Cited by 8 (2 self)
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We study straightline drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2trees, and planar 3trees. We prove that every 3connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes. We prove that every cubic 3connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of nonplanar graphs with few slopes are also considered. For example, interval graphs, cocomparability graphs and ATfree graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have drawings with O(log n) slopes. Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the
Graph Drawing with few Slopes
, 2006
"... ... G is the minimum number of distinct edgeslopes in a straightline drawing of G in the plane. We prove that for \Delta> = 5and all large n, there is a \Deltaregular nvertex graph with slopenumber at least n18+"\Delta +4. This is the best known lower bound on the slopenumber of a graphwi ..."
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Cited by 5 (2 self)
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... G is the minimum number of distinct edgeslopes in a straightline drawing of G in the plane. We prove that for \Delta> = 5and all large n, there is a \Deltaregular nvertex graph with slopenumber at least n18+"\Delta +4. This is the best known lower bound on the slopenumber of a graphwith bounded degree. We prove upper and lower bounds on the slopenumberof complete bipartite graphs. We prove a general upper bound on the slopenumber of an arbitrary graph in terms of its bandwidth. It follows that theslopenumber of interval graphs, cocomparability graphs, and ATfree graphs isat most a function of the maximum degree. We prove that graphs of boundeddegree and bounded treewidth have slopenumber at most O(log n). Finallywe prove that every graph has a drawing with one bend per edge, in which thenumber of slopes is at most one more than the maximum degree. In a companionpaper, planar drawings of graphs with few slopes are also considered.
Graph drawing techniques for geographic visualization
, 2004
"... Geovisualizers often need to represent data that consists of items related together. Such data sets can be abstracted to a mathematical structure, the graph. A graph contains nodes and edges where the nodes represent the items or concepts of interest, and the edges connect two nodes together accordi ..."
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Cited by 4 (0 self)
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Geovisualizers often need to represent data that consists of items related together. Such data sets can be abstracted to a mathematical structure, the graph. A graph contains nodes and edges where the nodes represent the items or concepts of interest, and the edges connect two nodes together according to some associational scheme. Examples of graph data include: network topologies; maps, where nodes represent
Nice Perspective Projections
"... this paper we consider the problem of computing a variety of nice perspective projections of threedimensional objects such as simple polygonal chains, wireframe drawings of graphs and geometric rooted trees. These problems arise in areas such as Computer Vision, Computer Graphics, Graph Drawin ..."
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Cited by 3 (0 self)
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this paper we consider the problem of computing a variety of nice perspective projections of threedimensional objects such as simple polygonal chains, wireframe drawings of graphs and geometric rooted trees. These problems arise in areas such as Computer Vision, Computer Graphics, Graph Drawing, Knot Theory and Computational Geometry. 1. INTRODUCTION When we draw or plot an image of a threedimensional (3D) object on a sheet of paper, or when we use a displaying device, such as a computer graphics screen, we obtain a 2D representation that necessarily approximates the 3D object and will never capture all its properties. It is obviously desirable to make this single * The research of the rst author was supported by MECDGESSEUID PB980933. The second author was supported by MECDGESSEUID PB980933 and DURSI 1999SGR00356. Research of the third author was supported by MECDGESSEUID PB980933 and DURSI 1999SGR00162. The fou
Optimal threedimensional layout of interconnection networks
 THEORETICAL COMPUTER SCIENCE
, 2001
"... The main bene ts of a threedimensional layout of interconnection networks are the savings in material (measured as volume) and the shortening of wires. The result presented in this paper is a general formula for calculating a lower bound on the volume. Moreover, for butter y and Xtree networks we ..."
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Cited by 2 (0 self)
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The main bene ts of a threedimensional layout of interconnection networks are the savings in material (measured as volume) and the shortening of wires. The result presented in this paper is a general formula for calculating a lower bound on the volume. Moreover, for butter y and Xtree networks we show layouts optimizing the maximum wire length and whose upper bounds on the volume are close to the lower bounds.
Really straight drawings II: Nonplanar graphs
, 2005
"... We study straightline drawings of nonplanar graphs with few slopes. Interval graphs, cocomparability graphs and ATfree graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have drawings ..."
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Cited by 1 (1 self)
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We study straightline drawings of nonplanar graphs with few slopes. Interval graphs, cocomparability graphs and ATfree graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have drawings with O(log n) slopes. Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the maximum degree. In a companion paper, planar drawings of graphs with few slopes are also considered.