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On Linear Layouts of Graphs
, 2004
"... In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp... ..."
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Cited by 31 (19 self)
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In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp...
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
Pathwidth and ThreeDimensional StraightLine Grid Drawings of Graphs
"... We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for ..."
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Cited by 24 (12 self)
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We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for
GIOTTO3D: A System for Visualizing Hierarchical Structures in 3D
 Proceedings of Graph Drawing ’96), Lecture Notes in Computer Science 1190
, 1997
"... Hierarchical structures represented by directed acyclic graphs are widely used in visualization applications (e.g., class inheritance diagrams and scheduling diagrams). 3D information visualization has received increasing attention in the last few years, motivated by the advances in hardware and ..."
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Cited by 18 (1 self)
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Hierarchical structures represented by directed acyclic graphs are widely used in visualization applications (e.g., class inheritance diagrams and scheduling diagrams). 3D information visualization has received increasing attention in the last few years, motivated by the advances in hardware and software technology for 3D computer graphics.
A New Algorithm and Open Problems in ThreeDimensional Orthogonal Graph Drawing
 Curtin University of Technology
, 1999
"... . In this paper we present an algorithm for 3D orthogonal drawing of arbitrary degree nvertex medge multigraphs with O(m 2 = p n) bounding box volume and 6 bends per edge route. This is the smallest known bound on the bounding box volume of 3D orthogonal multigraph drawings. We continue ..."
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Cited by 7 (3 self)
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. In this paper we present an algorithm for 3D orthogonal drawing of arbitrary degree nvertex medge multigraphs with O(m 2 = p n) bounding box volume and 6 bends per edge route. This is the smallest known bound on the bounding box volume of 3D orthogonal multigraph drawings. We continue the study of the tradeoff between bounding box volume and the number of bends in orthogonal graph drawings through a refined algorithm with O(m 2 ) bounding box volume and 5 bends per edge route. Many open problems in 3D orthogonal graph drawing are presented and potential avenues for their solution are discussed. 1 Introduction With applications including VLSI circuit design [4, 18, 20] and software engineering [14, 19, 23], there has been recent interest in 3D graph visualization. Proposed models include straightline drawings [6, 13, 16] and of interest in this paper orthogonal drawings [1, 2, 5, 8, 9, 10, 11, 15, 17, 25, 26, 27, 28]. The 3D orthogonal grid consists of grid po...
New Results in Graph Layout
 School of Computer Science, Carleton Univ
, 2003
"... A track layout of a graph consists of a vertex colouring, an edge colouring, and a total order of each vertex colour class such that between each pair of vertex colour classes, there is no monochromatic pair of crossing edges. This paper studies track layouts and their applications to other models o ..."
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Cited by 1 (1 self)
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A track layout of a graph consists of a vertex colouring, an edge colouring, and a total order of each vertex colour class such that between each pair of vertex colour classes, there is no monochromatic pair of crossing edges. This paper studies track layouts and their applications to other models of graph layout. In particular, we improve on the results of Enomoto and Miyauchi [SIAM J. Discrete Math., 1999] regarding stack layouts of subdivisions, and give analogous results for queue layouts. We solve open problems due to Felsner, Wismath, and Liotta [Proc. Graph Drawing, 2001] and Pach, Thiele, and Toth [Proc. Graph Drawing, 1997] concerning threedimensional straightline grid drawings. We initiate the study of threedimensional polyline grid drawings and establish volume bounds within a logarithmic factor of optimal.