Results 1  10
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14
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 23 (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.
Proximity Drawings of Outerplanar Graphs
, 1996
"... A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of nonadjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a d ..."
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Cited by 11 (4 self)
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A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of nonadjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a definition of proximity, is it possible to construct a proximity drawing of G? We consider this question for outerplanar graphs with respect to an infinite family of proximity drawings called fidrawings. These drawings include as special cases the wellknown Gabriel drawings (when fi = 1), and relative neighborhood drawings (when fi = 2). We first show that all biconnected outerplanar graphs are fidrawable for all values of fi such that 1 fi 2. As a side effect, this result settles in the affirmative a conjecture by Lubiw and Sleumer [20, 22], that any biconnected outerplanar graph admits a Gabriel drawing. We then show that there exist biconnected outerplanar graphs that do not admit any...
Tutte’s barycenter method applied to isotopies
 Computational Geometry: Theory and Applications
, 2001
"... This paper is concerned with applications of Tutte’s barycentric embedding theorem (Proc. London Math. Soc. 13 (1963), 743–768). It presents a method for building isotopies of triangulations in the plane, based on Tutte’s theorem and the computation of equilibrium stresses of graphs by Maxwell–Cremo ..."
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Cited by 10 (0 self)
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This paper is concerned with applications of Tutte’s barycentric embedding theorem (Proc. London Math. Soc. 13 (1963), 743–768). It presents a method for building isotopies of triangulations in the plane, based on Tutte’s theorem and the computation of equilibrium stresses of graphs by Maxwell–Cremona’s theorem; it also provides a counterexample showing that the analogue of Tutte’s theorem in dimension 3 is false.
Convex Drawings of Graphs in Two and Three Dimensions (Preliminary Version)
"... We provide O(n)time algorithms for constructing the following types of drawings of nvertex 3connected planar graphs: ffl 2D convex grid drawings with (3n) \Theta (3n=2) area under the edge L1 resolution rule; ffl 2D strictly convex grid drawings with O(n 3 ) \Theta O(n 3 ) area under the e ..."
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Cited by 6 (0 self)
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We provide O(n)time algorithms for constructing the following types of drawings of nvertex 3connected planar graphs: ffl 2D convex grid drawings with (3n) \Theta (3n=2) area under the edge L1 resolution rule; ffl 2D strictly convex grid drawings with O(n 3 ) \Theta O(n 3 ) area under the edge resolution rule; ffl 2D strictly convex drawings with O(1) \Theta O(n) area under the vertexresolution rule, and with vertex coordinates represented by O(n log n)bit rational numbers; ffl 3D convex drawings with O(1) \Theta O(1) \Theta O(n) volume under the vertexresolution rule, and with vertex coordinates represented by O(n log n)bit rational numbers. We also show the following lower bounds: ffl For infinitely many nvertex graphs G, if G has a straightline 2D convex drawing in a w \Theta h grid satisfying the edge L1 resolution rule then w;h 5n=6 +\Omega\Gamma20 and w + h 8n=3 + \Omega\Gamma838 ffl For infinitely many boundeddegree triconnected planar graphs G with n ver...
personal communication
"... We study the problem how to obtain a small drawing of a 3polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a onedimensional problem, since it is sufficient to guarantee distinct integer xcoordinates. We develop an algorithm that yields an embedding ..."
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Cited by 5 (0 self)
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We study the problem how to obtain a small drawing of a 3polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a onedimensional problem, since it is sufficient to guarantee distinct integer xcoordinates. We develop an algorithm that yields an embedding with the desired property such that the polytope is contained inside a 2(n − 2) × 2 × 1 box. The constructed embedding can be scaled to a grid embedding whose xcoordinates are contained in [0, 2(n − 2)]. Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant. Submitted:
Advances in the Theory and Practice of Graph Drawing
 Theor. Comp. Sci
, 1996
"... The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph d ..."
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Cited by 4 (0 self)
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The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph drawing. Specific topics include bounds and tradeoffs for drawing properties, threedimensional representations, methods for constraint satisfaction, and experimental studies. 1 Introduction In this paper, we survey selected research trends in graph drawing, and overview some recent results of the author and his collaborators. Graph drawing addresses the problem of constructing geometric representations of graphs, a key component of support tools for complex applications in science and engineering. Graph drawing is a young research field that has growth very rapidly in the last decade. One of its distinctive characteristics is to have furthered collaborative efforts between computer scien...