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DigCoLa: Directed graph layout through constrained energy minimization
 IEEE Symposium on Information Visualization, Infovis’05, 2005
"... We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance forcedirected placement (FDP) algorithm so that the directed nature of the graph is highlighted while useful properties of FDP — such as emphasis of symmetrie ..."
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Cited by 12 (4 self)
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We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance forcedirected placement (FDP) algorithm so that the directed nature of the graph is highlighted while useful properties of FDP — such as emphasis of symmetries and preservation of proximity relations — are retained. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. An interesting application of our algorithm is directional multidimensional scaling (DMDS). DMDS deals with lowdimensional embedding of multivariate data where we want to emphasize the overall flow in the data (e.g. chronological progress) along one of the axes.
Stress majorization with orthogonal ordering constraints
 In Proceedings of the 13th International Symposium on Graph Drawing (GD’05), volume 3843 of LNCS
, 2005
"... Abstract. The adoption of the stressmajorization method from multidimensional scaling into graph layout has provided an improved mathematical basis and better convergence properties for socalled “forcedirected placement ” techniques. In this paper we give an algorithm for augmenting such stress ..."
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Cited by 8 (5 self)
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Abstract. The adoption of the stressmajorization method from multidimensional scaling into graph layout has provided an improved mathematical basis and better convergence properties for socalled “forcedirected placement ” techniques. In this paper we give an algorithm for augmenting such stressmajorization techniques with orthogonal ordering constraints and we demonstrate several graphdrawing applications where this class of constraints can be very useful.
Drawing directed graphs using quadratic programming
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance forcedirected placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as em ..."
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Cited by 5 (4 self)
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We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance forcedirected placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as emphasis of symmetries and preservation of proximity relations. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. Our experiments show that this new approach is better able to convey the structure of large digraphs than the most widely used hierarchical graphdrawing method. An interesting application of our algorithm is directional multidimensional scaling (DMDS). DMDS deals with lowdimensional embedding of multivariate data where we want to emphasize the overall flow in the data (e.g., chronological progress) along one of the axes.
Twolayer planarization: Improving on parameterized algorithmics
 SOFSEM, volume 3381 of LNCS
, 2005
"... A bipartite graph is biplanar if the vertices can be placed on two parallel lines in the plane such that there are no edge crossings when edges are drawn as straightline segments connecting vertices on one line to vertices on the other line. We study two problems: • 2Layer Planarization: can k edg ..."
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Cited by 5 (2 self)
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A bipartite graph is biplanar if the vertices can be placed on two parallel lines in the plane such that there are no edge crossings when edges are drawn as straightline segments connecting vertices on one line to vertices on the other line. We study two problems: • 2Layer Planarization: can k edges be deleted from a given graph G so that the remaining graph is biplanar? • 1Layer Planarization: same question, but the order of the vertices on one layer is fixed. Improving on earlier works of Dujmović et al. (Proc. Graph Drawing GD 2001, pp. 1–15, 2002), we solve the 2Layer Planarization problem in O(k 2 · 5.1926 k + G) time and the 1Layer Planarization problem in O(k 3 · 2.5616 k + G  2) time. Moreover, we derive a small problem kernel for 1Layer Planarization.
One Dimensional Layout Optimization, with Applications to Graph Drawing by Axis Separation,” Computational Geometry: Theory and Applications
"... Abstract. In this paper we discuss a useful family of graph drawing algorithms, characterized by their ability to draw graphs in one dimension. We define the special requirements from such algorithms and show how several graph drawing techniques can be extended to handle this task. In particular, ..."
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Cited by 1 (1 self)
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Abstract. In this paper we discuss a useful family of graph drawing algorithms, characterized by their ability to draw graphs in one dimension. We define the special requirements from such algorithms and show how several graph drawing techniques can be extended to handle this task. In particular, we suggest a novel optimization algorithm that facilitates using the Kamada and Kawai model [17] for producing onedimensional layouts. The most important application of the algorithms seems to be in achieving graph drawing by axis separation, where each axis of the drawing addresses different aspects of aesthetics.
Neuron Perspective
"... Many theories of neural networks assume rules of connection between pairs of neurons that are based on their cell types or functional properties. It is finally becoming feasible to test such pairwise models of connectivity, due to emerging advances in neuroanatomical techniques. One method will be t ..."
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Many theories of neural networks assume rules of connection between pairs of neurons that are based on their cell types or functional properties. It is finally becoming feasible to test such pairwise models of connectivity, due to emerging advances in neuroanatomical techniques. One method will be to measure the functional properties of connected pairs of neurons, sparsely sampling pairs from many specimens. Another method will be to find a ‘‘connectome,’ ’ a dense map of all connections in a single specimen, and infer functional properties of neurons through computational analysis. For the latter method, the most exciting prospect would be to decode the memories that are hypothesized to be stored in connectomes. In constructing a neural network model of brain function, it is standard to start from a mathematical description of spiking and synaptic transmission, make assumptions about how neurons are connected by synapses and then numerically simulate or analytically derive the activity patterns of the network. Success is declared if the model’s activity patterns reproduce those measured by neurophysiologists. Initially, the model neurons used in such networks were highly
Using a Significant Spanning Tree . . .
, 2008
"... A directed graph can model any ordered relationship between objects. However, visualizing such graphs can be a challenging task. If the graph is undirected, a popular strategy is to choose a significant spanning tree, nominate a vertex as the root, for example the vertex whose distance from all othe ..."
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A directed graph can model any ordered relationship between objects. However, visualizing such graphs can be a challenging task. If the graph is undirected, a popular strategy is to choose a significant spanning tree, nominate a vertex as the root, for example the vertex whose distance from all other vertices is minimal, hang the significant spanning subtrees from this root and add in the remaining edges in some unobtrusive manner [19, 26, 27, 33]. In the directed case the spanning tree is a tree DAG and not simply a directed tree with one appropriate root. It may have multiple sources that all warrant root status and so the undirected approach must be modified somewhat. In this paper, we present a method of drawing directed graphs that emphasizes a significant spanning tree. It combines two steps of the Sugiyama framework [31] (leveling and crossing minimization) by finding, in linear time, a leveling of the graph that is level planar with respect to some spanning tree and restricting the permutations of the vertices on each level to those that constitute a level planar embedding of this subgraph. The edges of the spanning tree will therefore not cross each other. Using a globally oriented Fiedler vector we choose permutations of the vertices on each level that reduce the number of edge crossings between the remaining edges.