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It’s in the bag: Plane decompositions as tools for approximation
, 2005
"... 2. Background............................... 7 ..."
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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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.
Nothreeinlinein3D
 In Proc. 12th Int. Symp. on Graph Drawing (GD’04) [GD004
, 2004
"... The nothreeinline problem, introduced by Dudeney in 1917, asks for the maximum number of points in the nn grid with no three points collinear. In 1951, Erdos proved that the answer is (n). We consider the analogous threedimensional problem, and prove that the maximum number of points in the ..."
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The nothreeinline problem, introduced by Dudeney in 1917, asks for the maximum number of points in the nn grid with no three points collinear. In 1951, Erdos proved that the answer is (n). We consider the analogous threedimensional problem, and prove that the maximum number of points in the n n n grid with no three collinear is (n ).
Linkless symmetric drawings of series parallel digraphs
, 2004
"... In this paper, we present a linear time algorithm for constructing linkless drawings of series parallel digraphs with maximum number of symmetries. Linkless drawing in three dimensions is a natural extension to planar drawing in two dimensions. Symmetry is one of the most important aesthetic criteri ..."
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In this paper, we present a linear time algorithm for constructing linkless drawings of series parallel digraphs with maximum number of symmetries. Linkless drawing in three dimensions is a natural extension to planar drawing in two dimensions. Symmetry is one of the most important aesthetic criteria in graph drawing. More specifically, we present two algorithms: a symmetry finding algorithm which finds maximum number of three dimensional symmetries, and a drawing algorithm which constructs linkless symmetric drawings of series parallel digraphs in three dimensions.
Visual Analysis of Hierarchical Data Using 2.5D Drawing with Minimum Occlusion
"... In this paper, we consider 2.5D drawing of a pair of trees which are connected by some edges, representing relationships between nodes, as an attempt to develop a tool for analyzing pairwise hierarchical data. We consider two ways of drawing such a graph, called parallel and perpendicular drawings, ..."
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In this paper, we consider 2.5D drawing of a pair of trees which are connected by some edges, representing relationships between nodes, as an attempt to develop a tool for analyzing pairwise hierarchical data. We consider two ways of drawing such a graph, called parallel and perpendicular drawings, where the graph appears as a bipartite graph viewed from two orthogonal angles X and Y. We define the occlusion of a drawing as the sum of the edge crossings that can be seen in the two angles, and propose algorithms to minimize the occlusion based on the fundamental onesided crossing minimization problem. We also give some visualization examples of our method using phylogenetic trees and a mushroom database. 1