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ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
Abstract

Cited by 33 (13 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
Algorithms for Drawing Clustered Graphs
, 1997
"... In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics ..."
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Cited by 29 (2 self)
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In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics workstation as graph drawings. The usefulness of the relational model depends on whether the graph drawings effectively convey the relational information to the users. This thesis is concerned with finding good drawings of graphs. As the amount of information that we want to visualize becomes larger and the relations become more complex, the classical graph model tends to be inadequate. Many extended models use a node hierarchy to help cope with the complexity. This thesis introduces a new graph model called the clustered graph. The central theme of the thesis is an investigation of efficient algorithms to produce good drawings for clustered graphs. Although the criteria for judging the qua...
MultiDimensional Orthogonal Graph Drawing with Small Boxes
 Proc. 7th International Symp. on Graph Drawing (GD '99
, 1999
"... In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane. ..."
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Cited by 14 (6 self)
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In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane.
Orthogonal Drawing of High Degree Graphs with Small Area and Few Bends
 Proc. Algorithms and Data Structures: 5th International Workshop (WADS'97), volume 1272 of Lecture Notes in Cornput. Sci
, 1996
"... Most of the work that appears in the orthogonal graph drawing literature deals with graphs whose maximum degree is four. In this paper we present an algorithm for orthogonal drawings of simple graphs with degree higher than four. Vertices are represented by rectangular boxes of perimeter less than t ..."
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Cited by 6 (0 self)
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Most of the work that appears in the orthogonal graph drawing literature deals with graphs whose maximum degree is four. In this paper we present an algorithm for orthogonal drawings of simple graphs with degree higher than four. Vertices are represented by rectangular boxes of perimeter less than twice the degree of the vertex. Our algorithm is based on creating groups/pairs of vertices of the graph both ahead of time and in real drawing time. The orthogonal drawings produced by our algorithm have area at most (m 1) * (m/2 +2). Two important properties of our algorithm are that the drawings exhibit small total number of bends (less than m), and that there is at most one bend per edge.
Drawing Clustered Graphs on . . .
 J. GRAPH ALGORITHMS APPL
, 1999
"... Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which pro ..."
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Cited by 3 (0 self)
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Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. If the input graph has n vertices, then the algorithm produces in O(n) time a drawing with O(n²) area and at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that our algorithm is optimal in terms of the number of bends per edge.
Drawing Clustered Graphs on an Orthogonal Grid (Extended Abstract)
 J. GRAPH ALGORITHMS APPL
, 1997
"... Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produc ..."
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Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. We present an algorithm which produces such drawings with O(n²) area and with at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that the bend performance of our algorithm is optimal.
Information Processing Letters 72 (1999) 137–141 An optimal layout of multigrid networks
, 1999
"... In this paper, we study the problem of laying out a multigrid network,MN, on a grid of minimum area. Precisely, we describe a layout having area. 52N 3/ .3N 4/, which is of the same order of magnitude as the lower bound. Ó 1999 Published by ..."
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In this paper, we study the problem of laying out a multigrid network,MN, on a grid of minimum area. Precisely, we describe a layout having area. 52N 3/ .3N 4/, which is of the same order of magnitude as the lower bound. Ó 1999 Published by