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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 13 (5 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.
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...
Approximation Algorithms for Finding Best Viewpoints
 Proc. 6th International Symp. on Graph Drawing (GD ’98
, 1997
"... . We address the problem of finding viewpoints that preserve the relational structure of a threedimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint "goodness" were proposed. Unfortunately, ..."
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Cited by 6 (0 self)
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. We address the problem of finding viewpoints that preserve the relational structure of a threedimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint "goodness" were proposed. Unfortunately, the inherent combinatorial complexity of the problem makes finding exact solutions is impractical. In this paper, we propose two approximation algorithms for the problem, commenting on their design, and presenting results on their performance. 1 Introduction Since it was first considered by the graph drawing community [6,10], there has been much research into threedimensional graph drawing. There is some experimental evidence that threedimensional graph drawings have advantages over their twodimensional counterparts. It is claimed [16] that three dimensions allow users to work with larger graphs  the natural threedimensional actions of rotation and translation allow a user to res...
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.
On threedimensional layout of pyramid networks
 Proc. 2002 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS ’02
"... The pyramid networks are wellknown as suitable structures for parallel computations such as image processing. This paper shows a practical 3D VLSI layout of the Nvertex pyramid network with volume O(N) and wirelength O ( 3 √ N). Since the known best lower bounds for the volume and wirelength of ..."
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Cited by 1 (0 self)
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The pyramid networks are wellknown as suitable structures for parallel computations such as image processing. This paper shows a practical 3D VLSI layout of the Nvertex pyramid network with volume O(N) and wirelength O ( 3 √ N). Since the known best lower bounds for the volume and wirelength of a 3D layout for an Nvertex pyramid network are Ω(N) and Ω ( 3 √ N / log N), respectively, the volume of our layout is optimal, and the wirelength of our layout is close to the optimal. 1.