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A MultiScale Algorithm for the Linear Arrangement Problem
 Proc. 28th Inter. Workshop on GraphTheoretic Concepts in Computer Science (WG’02), LNCS 2573
, 2002
"... Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running ti ..."
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Cited by 31 (4 self)
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Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running time is significantly better, enabling it to deal with much larger graphs. The paper contains a general multiscale construction, which may be used for a broader range of ordering problems.
Hierarchy Measure for Complex Networks
"... Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and d ..."
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Cited by 11 (1 self)
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Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of realworld networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the mreach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the
Visual Navigation Through Large Directed Graphs and Hypergraphs ∗ ABSTRACT
"... We describe Dynasty, a system for browsing large (possibly infinite) directed graphs and hypergraphs. Only a small subgraph is visible at any given time. We sketch how we lay out the visible subgraph, and how we update the layout smoothly and dynamically in an asynchronous environment. We also sketc ..."
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Cited by 2 (2 self)
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We describe Dynasty, a system for browsing large (possibly infinite) directed graphs and hypergraphs. Only a small subgraph is visible at any given time. We sketch how we lay out the visible subgraph, and how we update the layout smoothly and dynamically in an asynchronous environment. We also sketch our user interface for browsing and annotating such graphs—in particular, how we try to make keyboard navigation usable.
AxisbyAxis Stress Minimization
 Proceedings of Graph Drawing 2003
, 2003
"... Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensio ..."
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Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling.
Resource Toward Rigorous Comprehension of Biological Complexity: Modeling, Execution, and Visualization of Thymic TCell Maturation
"... One of the problems biologists face is a data set too large to comprehend in full. Experimenters generate data at an evergrowing pace, each from their own niche of interest. Current theories are each able, at best, to capture and model only a small part of the data. We aim to develop a general appr ..."
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One of the problems biologists face is a data set too large to comprehend in full. Experimenters generate data at an evergrowing pace, each from their own niche of interest. Current theories are each able, at best, to capture and model only a small part of the data. We aim to develop a general approach to modeling that will help broaden biological understanding. Tcell maturation in the thymus is a telling example of the accumulation of experimental data into a large disconnected data set. The thymus is responsible for the maturation of stem cells into mature T cells, and its complexity divides research into different fields, for example, cell migration, cell differentiation, histology, electron microscopy, biochemistry, molecular biology, and more. Each field forms its own viewpoint and its own set of data. In this study we present the results of a comprehensive integration of large parts of this data set. The integration is performed in a twotiered visual manner. First, we use the visual language of Statecharts, which makes specification precise, legible, and executable on computers. We then set up a moving graphical interface that dynamically animates the cells, their receptors, the different gradients, and the interactions that constitute thymic maturation. This interface also provides a means for interacting with the simulation. [Supplemental material is available online at www.genome.org and at www.wisdom.weizmann.ac.il/sol/ sysbio2002/.] What Do Biologists Try to Understand?
OneDimensional Graph Drawing: Part II — AxisbyAxis Stress Minimization
"... Abstract. Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. Such algorithms were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of dat ..."
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Abstract. Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. Such algorithms were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling. In this paper we suggest a novel algorithm for axisbyaxis minimization of the Stress energy. This algorithm is suitable for a onedimensional layout, where one axis of the drawing is already given and an additional axis needs to be computed. In general, the proposed algorithm produces aesthetically superior layouts compared to other 1D drawing algorithms. Moreover, our algorithm can be used for multidimensional graph drawing, where it has time and space complexity advantages compared with other stress minimization algorithms. 1
OneDimensional Graph Drawing: Part I — Drawing Graphs by Axis Separation
"... Abstract. In this paper we discuss a useful family of graph drawing algorithms, characterized by their ability to draw graphs in one dimension. The most important application of this family seems to be achieving graph drawing by axis separation, where each axis of the drawing addresses different asp ..."
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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. The most important application of this family seems to be achieving graph drawing by axis separation, where each axis of the drawing addresses different aspects of aesthetics. We define the special requirements from such algorithms and show how several graph drawing algorithms can be generalized to handle this task. 1